Performance-Oriented Conceptual Design of Fastener Joint Configurations for Aerospace Equipment

Abstract

The joint configuration design of aerospace equipment requires a comprehensive balance of multiple factors, yet the process is often complex and time-consuming. Moreover, the Function–Behavior–Structure (FBS) conceptual design model lacks specificity for aerospace joint design. To address these issues, a Function–Performance–Structure (FPS)-based design method for joint configuration is proposed. Service performance is introduced as a bridge to map functional requirements to structural characteristics, thereby establishing a complete FPS conceptual design framework. Based on this, a conceptual design methodology for aerospace joint configurations is developed using typical aircraft structures as the research object. To verify the effectiveness and reliability of the method, a typical joint configuration is selected for instance validation. By integrating conceptual modeling with structural joint design, the proposed method offers a novel approach for aerospace joint configuration design, providing a theoretical foundation to enhance both the innovation capability and engineering value of aerospace equipment design.

1. Introduction

Aerospace equipment primarily includes aircraft, aero engines, and aviation equipment and systems. Currently, the industry is undergoing profound transformation, driven by trends such as intelligence, greenness, autonomy, innovation in new materials, and adjustments in global supply chains. These developments place new demands on structural joints: lightweight and ecofriendly designs require novel joint solutions compatible with advanced materials; autonomous operation and intelligent maintenance call for more reliable and easily inspectable connections; and globalized supply chains highlight the need for standardized and adaptable joint designs. As a critical part of aerospace equipment, joint structures play a key role in ensuring structural stability and functional integrity. However, studies have shown that approximately 75–80% of fatigue failures [1] occur in these joint areas, making joint quality crucial to the reliability and safety of the equipment.

Common joint methods include bolting, welding, riveting, and bonding. Among these methods, bolting and riveting are the most widely used. In this paper, the term “fastener joint configuration” is defined as the combination of these two types of fasteners and various connected components, under specific assembly conditions. To meet the demands of complex service conditions, such configurations must not only ensure sufficient mechanical performance, but also withstand extreme conditions such as high temperatures and corrosion [2]. In some cases, components at special positions must transfer forces or torque while accommodating relative motion with adjacent parts, thereby requiring higher physical performance. Currently, typical fastener joint configurations are generally classified into fixed joints (e.g., surface joints, cylindrical joints, I-beam joints) and movable joints (e.g., pin joints, hinge joints). The design process for aerospace equipment joints is complex, multidisciplinary, and held to extremely high standards. However, the lack of universal design specifications for these joints significantly affects the overall design cycle. Additionally, constraints such as the geometry of connected parts, surrounding structures, and application scenarios often lead to limited internal space, suboptimal aerodynamic layouts, increased structural weight, and difficulties in assembly and manufacturing [3].

Existing design methods, such as Design for Assembly (DFA) and Design for Manufacturing and Assembly (DFMA) [4], can assist decision-making to some extent. However, they primarily focus on mechanical performance evaluation and lack targeted guidance for system-level fastener joint configuration design. As a result, design processes often rely heavily on manual work and iterative verification, which leads to high design intensity, prolonged cycles [5], high redundancy, and low optimization efficiency. A universal, systematic, and reusable conceptual design method is urgently needed.

Facing this challenge, there is an urgent need to establish a more systematic and adaptable conceptual design framework for this field. The conceptual design [6,7,8] has a decisive impact on product quality and life cycle cost. According to studies, decisions made during this stage can affect up to 85% of the total lifecycle cost and over 70% of product quality [9]. The Function–Behavior–Structure (FBS) model, a classical framework for conceptual design, was proposed by Gero in 1990 [10]. It decomposes design problems into three layers and builds hierarchical mappings to guide the design evolution from abstract to concrete. It provides a mechanism for mapping between design intentions and product structures [11]. Over time, the FBS model has been extended in various ways to adapt to specific domains [12]. For instance, Umeda [13] introduced the Function–Behavior–State (FBS2) model with a “state” variable, which incorporated physical features and supported both the analysis and synthesis stages of functional design through computer-based tools. Wang et al. [14] proposed the Constraint-based Function–Behavior–Structure (CFBS) model using constraint aggregation to support reverse design, which established a human–computer interaction approach for product appearance design. Qin et al. [15] introduced the Reuse-oriented Function–Behavior–Structure–Evolution (RFBSE) model to enhance knowledge representation and evolution, enabling the capture and reuse of design knowledge and experience. Deng [16] developed the Function–Environment–Behavior–Structure (FEBS) model by adding environmental parameters for green design, and further defined a reasoning process, in which design schemes can be generated through reverse-path inference. These variants have achieved practical results across different fields, demonstrating the model’s extensibility and generality.

Although the FBS model has been widely applied in conceptual product design [17,18,19,20,21,22], and its extended forms (such as the CFBS, RFBSE, and FEBS models) have achieved certain successes in constraint handling, knowledge reuse, and green design, these studies have primarily focused on their respective specific application fields and have not yet provided effective solutions to the performance-driven issues in aerospace fastener joint configuration design. The core of this research challenge lies in the unique definition dilemma of the “behavior” layer in aerospace connection configuration design. In traditional product design paradigms, the behavior layer typically serves as a mediating bridge between function and structure. However, in the design of fastening joints, greater emphasis is placed on performance-oriented factors such as material property matching, adaptability to service environments, and feasibility of assembly processes. These factors are difficult to accurately represent using the traditional “behavior” concept. To address this, this study innovatively proposes replacing the “behavior” layer with a “performance” layer, thereby establishing a Function–Performance–Structure (FPS) design model. This model overcomes the limitations of traditional frameworks and more precisely reflects the essential needs of joint configuration design. Based on this, we have developed a comprehensive FPS-guided joint configuration conceptual design method, and its efficiency and feasibility are systematically validated through typical aircraft joint case studies.

The structure of the paper is organized as follows: Section 2 establishes the FPS conceptual design model and outlines the corresponding FPS-based design process. In Section 3, the FPS model is applied to aircraft structures, where an FPS-based mapping model for aircraft fastener joint configuration design is developed. Additionally, a configuration library that guides the output of the functional layer results and selection rule tables that provides the basis for FP mapping are introduced to provide a detailed description of the design process. Section 4 validates the proposed method’s feasibility and effectiveness through a typical aircraft fastener joint case study. Finally, Section 5 presents the conclusion.

2. Development of the FPS Model and Conceptual Design Process

2.1. FPS Model

The FBS conceptual design model is renowned for its broad generality and has been widely applied across various product design domains. However, due to this very generality, the FBS model often lacks operational specificity in practical design tasks, making its direct application challenging. Therefore, a practical approach to enhancing the effectiveness of conceptual design is to adapt the FBS framework and develop more concrete design models that are tailored to the specific needs of individual product designs.

In general design contexts, the “Behavior” in the FBS model is generally defined as the responses or manifestations of a design object under specific conditions, including motion patterns, structural deformation, and so on. However, for aerospace joint configurations, these mechanistic responses are relatively predictable and provide limited abstraction or guidance for conceptual design. In contrast, “Performance” [23,24] refers to measurable service-oriented indicators, such as fatigue life, durability, and long-term reliability. Although these indicators depend on mechanical responses, they reflect higher-level engineering objectives that directly determine design feasibility. At the same time, Performance-Based Structural Design (PBSD) [25] has been widely adopted in both aerospace and civil engineering, providing quantifiable performance criteria and guiding engineering decision-making. Therefore, introducing “Performance” as a bridge between function and structure enhances the relevance of the conceptual model to aerospace joint design and helps ensure long-term reliability while satisfying functional requirements, thus addressing the limitations of the FBS model in joint configuration design.

In the design process of aerospace fastener joint configurations, user requirements generally fall into two categories: functional requirements and specific parameter requirements. The former describes the functional characteristics the joint configuration must achieve and serves as the input to the FPS model during the conceptual design phase. The latter includes explicit geometric, mechanical, or boundary parameters that support parametric design and the establishment of structural parameter sets in the structural layer. As the conceptual design progresses, a workpiece module representing the output of structural layer is ultimately obtained. Thus, in the new conceptual design model, functional requirements, as input, are denoted as “R”, while the workpiece module, as output, is denoted as “W”.

Based on this reasoning and drawing from the three-layer logic of the FBS model, an FPS conceptual design process model is developed, as illustrated in Figure 1. In this model, functional requirements represents the starting point of design activities; function (F) is defined the design objectives, describing the functional characteristics the joint configuration must fulfill; performance (P) specifies the design constraints, detailing the boundary conditions necessary for the structure; structure (S) refers to the configuration form that satisfies both the functional and the boundary conditions derived from performance; and the workpiece module (W) is the representation of the structure, serving as the final design outcome.

The FPS model defines a structured mapping mechanism encompassing three key relationships: function–performance (FP), performance–structure (PS), and function–structure (FS). In the FP mapping, the function, derived from user requirements, is constrained and guided by relevant performance parameters. These performance elements act as intermediaries, bridging the gap between functional intent and structural realization. The PS mapping is bidirectional: structural forms are derived in response to boundary constraints, and the resulting structures are then assessed against the same performance criteria. Discrepancies identified during evaluation feed back into the design process, enabling refinement of the structural forms to satisfy the performance objectives. When a structural solution fails to satisfy the intended functional requirements, the FS mapping mechanism enables an iterative feedback process. This process may involve modifying the structural elements in relation to their associated functions, and if necessary, adjusting the functional requirements themselves. The updated requirements then guide a new selection or refinement of structural solutions to ensure that the final design meets both functional and performance objectives.

2.2. Construction of the FPS-Based Design Process

In the field of aerospace equipment fastener joint structure design, it is necessary to systematically analyze the design prerequisites and key influencing factors based on existing typical joint solutions. By introducing the mapping logic of the FPS model, hierarchical analysis can be carried out from three dimensions: function (F), performance (P), and structure (S). Each dimension can be further subdivided into sublayers: subfunctions (F_m), subperformances (P_m), and substructures (S_m). Among these, the subitems of the function and performance layers can be further decomposed into elemental contents (F_mn, P_mn). This multi-level classification approach enables systematic organization of design elements, thereby constructing a complete FPS model framework suitable for aerospace equipment joint configuration. Based on this framework, by collecting and organizing existing joint configuration cases, a structured design knowledge base can be established, providing comprehensive information support for the subsequent conceptual design phase.

Accordingly, an FPS based conceptual design process is illustrated in Figure 2, specifically aimed at the design of fastener joint configurations for aerospace equipment. The process begins with analyzing user requirements to identify relevant functional elements. These elements, combined with the case knowledge library, form an initial element composition of the workpiece module. These functional elements are then translated into performance constraints, which define the product constraint conditions required to meet functional intent. Guided by these constraint conditions, appropriate substructures are selected and configured to form a structural description, which is then combined with the specific parameter requirements to generate a structure parameter set. Finally, by integrating the outputs across all three layers, a feasible conceptual design scheme is generated, which is further refined through computational analysis and verification. Once the design passes all performance checks, the final structural model is established.

In practical applications, the case knowledge library may contain multiple types of schematic diagrams that satisfy the same functional requirement. This leads to various possible combinations in the output of function layer, ultimately resulting in multiple candidate product design schemes. In such cases, a comparative evaluation considering adaptability, feasibility, and other relevant metrics is required to identify the optimal solution.

Given the complexity and multiplicity of factors in fastener joint configuration design, particularly in the FP mapping, parameter mapping equations [26,27,28] are adopted to formally represent the causal relationships among design layers. Taking the FP mapping as an example, let the input set be $\mathit{I}=\left\{F_{1n},F_{2n},F_{3n},\dots ,F_{mn}\right\}(n\ge 1)$ and the output set $\mathit{O}=\left\{P_{1n},P_{2n},P_{3n},\dots ,P_{mn}\right\}(n\ge 1)$. Each performance element $P_{in}(1\le i\le m)$ corresponds to a mapping equation $f_i(1\le i\le m)$, forming an equation set φ:

$$\mathit{\phi }=\left\{f_1,f_2,f_3,\dots ,f_m\right\},$$

(1)

where f_i is a mapping equation, capturing the relationship between selected functional elements in input set I and the corresponding performance elements in the i-th subperfomance. These mapping equations are typically defined using structured rule tables or expert knowledge bases, which are primarily derived from domain-specific design textbooks and the relevant literature. The rule tables and knowledge bases can be periodically updated or supplemented to incorporate new design practices or insights.

Ultimately, the complete equation set φ yields a comprehensive set of performance layer outputs, enabling a traceable mapping pathway from the function layer to structure layer. The output set O obtained through the equation set φ is as follows:

$$\mathit{O}=\left\{\begin{array}{l}{P}_{1n}=f_1\left(F_{2n},F_{3n},F_{4n}\right)\hfill \\ P_{2n}=f_2\left(F_{2n},F_{3n}\right)\hfill \\ P_{3n}=f_3\left(F_{2n}\right)\hfill \\ \dots \hfill \\ P_{mn}=f_m\left(F_{in}\right)\left(1\le i\le m\right)\hfill \end{array}\right..$$

(2)

When necessary, this descriptive approach can also be applied to the PS mapping process. Moreover, when multiple solutions satisfy the same functional requirements, two resolution strategies are proposed. Specifically, characteristics of alternative solutions are recorded in the structured rule tables, enabling designers to perform screening according to project-specific constraints or design objectives. Alternatively, several candidate solutions can be preserved and further developed into distinct design schemes, followed by comparative analysis and verification to determine the optimal configuration scheme. This dual-strategy mechanism ensures that the mapping process not only provides traceable relationships but also remains flexible in handling uncertainties in design choices.

3. FPS-Based Design Method for Aircraft Fastener Joint Configurations

In the design of fastener joint configurations for aerospace equipment, the connected parts and their structural forms are diverse. In cases involving complex spatial relationships or high strength requirements, it is often necessary to introduce intermediate components or ribs within it. Therefore, the conceptual design phase primarily focuses on structural model design of both fasteners and intermediate components. To better align the FPS model framework with the practical requirements of fastener joint configuration design, this section applies it to aircraft structures, and a corresponding FPS configuration mapping model is constructed.

3.1. FPS Mapping Model for Aircraft Fastener Joint Configurations

Using aircraft structures as the research object, a detailed classification and summary of fastener joint configurations was made, through extensive offline investigations, design books, and a literature review. The similarities and differences among various joint configurations, along with their underlying causes, were analyzed, and the logical steps required for joint configuration design were derived. The design of fastener joint configurations must first consider key factors, such as the relative positions of the connected components, application scenarios, loading modes, and disassembly requirements. These design-driving factors are categorized as subfunctions under the function layer.

From these subfunctions, a series of constraints can be derived, such as fastener type, anti-loosening method, lubrication approach, constraint design, and fit conditions, which are categorized as subperformances within the performance layer. Notably, both the function and performance layers directly or indirectly determine the elements of the structure layer. Accordingly, the structure layer is further divided into two substructures: intermediate component and fastener. Figure 3 presents the FPS-based mapping model for aircraft fastener joint configurations, in which elements of the three layers were denoted by codes, with clearly defined mapping relationships.

The function layer is defined as the source of connection requirements, encompassing structural relations, working environments, and operational demands that the joint must satisfy. The performance layer is located between the functional layer and the structural layer, providing executable design constraints for functions. With reference to relevant connection design manuals and aerospace engineering cases [29,30,31,32,33], the function and performance layers are further refined. The corresponding function elements and performance elements within each subfunction and subperformance are clearly specified, as summarized in

Table 1. Function elements content.

F1 Relative Positions		F2 Application Scenarios		F3 Load Types		F4 Disassembly Requirements
No.	Functional element	No.	Functional element	No.	Functional element	No.	Functional element
F11	Perpendicular face	F21	High-load area	F31	Tension	F41	Detachable
F12	Parallel face	F22	Aerodynamically sensitive area	F32	Shear	F42	Non-detachable
F13	Annular face	F23	Main load-bearing area	F33	Bending moment
F14	Intersecting pipes	F24	Lightweight design area	F34	Torque
F15	Parallel pipes	F25	High-vibration area	F35	Combined loads
F16	Vertical pipes	F26	Aerodynamic contour region
F17	Pipe butt joint	F27	High-temperature zone
F18	Two-bar motion	F28	Sealed area
F19	Multi-bar motion

and

Table 2. Performance elements content.

P1 Fastener Type		P2 Anti-Loosening Method		P3 Lubrication Method		P4 Constraint Design		P5 Fit Conditions
No.	Performance element	No.	Performance element	No.	Performance element	No.	Performance element	No.	Performance element
P11	Standard bolt	P21	Mechanical locking	P31	Molybdenum disulfide (MoS2)	P41	Force analysis	P51	Transition fit
P12	High-lock bolt	P22	Chemical locking	P32	PTFE coating	P42	Bolt design	P52	Clearance fit
P13	Heat-resistant bolt	P23	Preload control	P33	Graphite-based lubricant	P43	Rivet design	P53	Interference fit
P14	Composite-special bolt	P24	Structural self-locking	P34	Mineral grease	P44	Fastener layout design	P54	Press fit
P15	Solid rivet	P25	Deformation locking	P35	Dry film lubricant	P45	Intermediate component design
P16	Special rivet
P17	Blind rivet

, respectively, to ensure broad coverage of typical engineering design scenarios.

The structure layer provides the final physical design output. Guided by the defined performance parameters, it configures the substructures and describes them using parametric form. The substructures include the intermediate component S₁ and the fastener S₂, and their conceptual descriptions are provided from a feature perspective, as shown in

Table 3. Fastener joint configuration structure parameter set.

Substructure	Conceptual Description
S1	Contact surface dimensions (length, L × width, W); thickness, T; rib plate dimensions (length, l × width, b; thickness, t)
S2	Diameter, D; quantity, z; rows, r; columns, c; spacing, S; pitch, r; edge distance, e

.

3.2. FPS Design Process for Aircraft Fastener Joint Configurations

To introduce the FPS model into the design process of fastener joint configurations in aircraft structures, a practical design process is proposed, as illustrated in Figure 4. A configuration library is introduced to support decision-making, particularly under the default design scenario, in which the user must define a joint for a specific location within the aircraft structure. This methodology can also be adapted for other aerospace equipment through appropriate model and database extensions.

3.2.1. Requirement Analysis

The process begins with requirement analysis, where the functional elements in the function layer are identified. Specifically, during the analysis of application scenarios, users often provide the specific joint location. A reference mapping between the joint location and scenario type, as shown in Figure 5, helps in selecting the appropriate subfunctions F₂. Next, guided by the configuration library and informed by subfunctions F₁ and the provided joint location, an initial set of configuration combinations is screened. Each combination includes a connection form diagram and a fastener layout diagram. Simultaneously, the functional elements F_1n, F_2n, F_3n, and F_4n identified in the function layer are used as input conditions for the performance layer.

Based on studies of journals and books [29,30,31,32,33,34,35,36], as well as onsite investigations at numerous aircraft maintenance facilities and exhibitions, we decomposed and categorized publicly available existing aerospace equipment joint structures to establish the configuration library. The compilation process of the library is presented in detail in the Supplementary Material, where the structural schematics of each joint configuration were abstracted through analyses of existing engineering cases in combination with the construction of structural simulation models. To ensure engineering applicability and reliability, each connection type and layout pattern was cross-validated against engineering cases, technical manuals, and expert knowledge. Furthermore, the configuration library can be updated by periodically incorporating newly published design data or validated engineering cases.

The classification and summary of joint configurations are integrated to establish a comprehensive configuration library, which includes two key aspects: connection types and fastener layout patterns. Under the connection type category, fastener joint configurations are classified into three main groups: surface joints, tube joints, and motion joints, as shown in

Table 4. (a) Surface joints in the configuration selection library: indirect joint. (b) Surface joints in the configuration selection library: direct joint.

(a)
With Stiffener	Positional Relationship		Schematic		Name		Structure Description
Ribbed joint	F11				“▲” shape		Wing–fuselage joint; frame–skin
					“Π” shape		Wing–fuselage joint
	F12				“q” shape		Wing–fuselage joint; hatch–frame in open area
Non-ribbed joint	F11				“U” shape		Longeron, stringer; inside tail; wing–fuselage joint
					“L” shape		Beam flange–web; longeron, stringer; web stiffener–rib; rib flange–web; rib support–web; frame–skin; inside tail
					“T” shape		Beam flange
					“H” shape		Beam, rib, web
	F12				“Ω” shape		Longeron, stringer
	F12				“Z” shape		Longeron, stringer; wing–fuselage joint
					“-” shape		Between skin panels; wheel rim
	F13				End-face connection		Inside engine
					Side-face connection		Inside engine
(b)
Positional Relationship		Schematic		Name		Structure Description
F12				“=” shape		Beam flange–support; between skin panels; Wing–fuselage central joint; frame–skin
				“2” shape		Between skin panels
				“Ψ” shape		Beam flange–support; between skin panels; Wing–fuselage central joint; inside propeller
F13				End-face connection		Inside engine
				Side-face connection		Inside engine; inside propeller

,

Table 5. Tube joints in the configuration selection library.

Fixation Mode	Schematic	Positional Relationship	Structure Description
Tube fixed to surface		F14	Internal pipelines in fuselage and wings
		F15
		F16
Tube fixed to shaft		F15	Internal pipelines in fuselage and wings
Tube fixed to tube		F15	Internal pipelines in fuselage and wings
		F17	Propeller–engine; internal pipelines in fuselage and wings

and

Table 6. Kinematic joints in the configuration selection library.

With Intermediate Component	Schematic	Joint Status	Positional Relationship	Structure Description
Indirect joint		Front joint	F18	Wing–flap joint; hatch cover–frame in opening area; tailplane–elevator joint; landing gear; engine–fuselage or engine–wing joint
		Inner side joint
		Outer side joint
Direct joint			F18	Landing gear
			F19

. For surface joints (Table 4), they are further categorized based on the relative positioning of components into vertical (F₁₁), parallel (F₁₂), and annular types (F₁₃). Additionally, configurations are differentiated by the requirement for intermediate components: either indirect (with intermediate parts) (Table 4a) or direct (without intermediate parts) (Table 4b). In the case of indirect configurations, the joint is further classified into ribbed or non-ribbed designs, depending on the structural load requirements. For tube joints (Table 5), configurations are divided into three types based on the connection state of the tube: fixed-to-surface, fixed-to-axis, and fixed-to-tube. These are further differentiated by the spatial relationship between the fixed components, including crossed (F₁₄), parallel (F₁₅), vertical (F₁₆), and butt-jointed (F₁₇) forms. Motion joints (Table 6) are classified into two categories: with intermediate components and without. According to the number of moving elements, they are further divided into two-bar (F₁₈) and multi-bar (F₁₉) configurations. For joints with intermediate components, three structural forms are identified based on how the intermediate component connects to the joined parts: front-side connection, inner-side connection, and outer-side connection. Each joint configuration type is accompanied by schematic illustrations and is named using letters or symbols based on its geometric shape, or descriptive terms are used for one-to-one correspondence according to the joint status. This ensures intuitive mapping and facilitates efficient retrieval and application when matched against the joint location provided by the user.

The fastener layout section includes both arrangement patterns and typical joint configuration layouts, as shown in

Table 7. Fastener arrangement patterns in the configuration selection library.

Schematic
Name	Full coverage	Linear	Wavy	Hybrid
Schematic
Name	Cross-shaped	Irregular	Inner circumference	Outer circumference

and

Table 8. Typical joint layouts in the configuration selection library.

Joint Location	Joint Layout
Wing skin lap joint (shear-dominated)	Double-row symmetric, rivets
Fuselage main beam (bending moment-dominated)	Double-row symmetric, bolts
Engine mount (vibration load)	Triple-row staggered, bolts
Composite fuselage (delamination resistance)	Four-row staggered, rivets
Cabin interior panel (lightweight design)	Single-row, bolts

. Each layout pattern can be flexibly combined with any of the defined connection types, allowing for adaptation to various structural requirements. In the schematic diagrams provided in these tables, solid lines represent the geometry of intermediate components, dashed lines indicate the profiles of connected components, and chain lines (alternating long and short dashes) represent the positions of fasteners (such as bolts or rivets).

3.2.2. FP Mapping

Guided by the selected functional elements, corresponding subperformance parameters are identified. Drawing on references [29,30,31,32,33,34,35,36], selection rule tables for fastener joint configurations are established, as shown in

Table 9. Selection rules for fastener types.

Fastener Types	Subtype	Function Element Basis	Fastener Characteristics	Lubrication Approach
P11	P111 High-strength steel bolt	F21	High tensile/shear strength; cadmium-plated for corrosion resistance	P31
	P112 Titanium bolt	F21	High specific strength, low galvanic corrosion; suitable for composites	P32/P33
	P113 Countersunk bolt	F22	Flush head reduces aerodynamic drag; requires precision countersinking	P31
P12	P121 Hi-Lok (shear type)	F23, F32	One-side installation; high shear capacity; controlled preload	P35/P32
	P122 Hi-Lite (tensile type)	F24, F31	Break-off tail design; lightweight; post-installation tail removal
P13	P131 Heat-resistant steel bolt	F27	Stable high-temp strength (A286: 900 MPa/650 °C); oxidation/creep resistant	P33
	P132 Heat-resistant titanium bolt	F27	Durable at 600 °C/400 MPa >12 h; crack-resistant with hot forging + thread rolling
P14		F23	Low galvanic corrosion for composite structures; delamination prevented via preload control	P32
P15	P151 General rivet (round/flat head)	F25	Double-side operation; high shear strength; suitable for thick sheets (>3 mm)
	P152 Countersunk rivet	F26	Flush surface; requires precise countersinking
P16	P161Titanium rivet	F23	Low galvanic corrosion; high specific strength; used in composite joints
	P162 High-temp rivet	F27	Nickel-based alloy; temperature resistance >300 °C	P35
P17	P171 Pull-type blind rivet	F28	Tail expands for self-locking; suitable for thin sheets (≤6 mm)	P34
	P172 Threaded blind rivet	F24, F41	Reusable; threaded for improved tensile performance

,

Table 10. Selection rules for anti-loosening methods.

Anti-Loosening Method	Subtype	Function Element Basis	Characteristics	Applicable Fasteners
P21	P211 Self-locking nut	F21	Built-in nylon ring or metal locking washer; reusable and easy to maintain	P111, P112
	P212 Cotter pin/safety pin	F21, F23	Physical limitations; absolute anti-loosening reliability; requires slotted bolt/nut	P11, P13
	P213 Serrated washer	F25, F35	Serrated surfaces mesh; self-tightening during vibration; no extra components needed	P113, P112
P22	Thread locker (sealant)	F24, F42	Fills thread gaps and cures; can be selected based on strength requirements (low/medium/high)	P11 P111, P132
P23	Torque method/hydraulic stretching method	F2	Preload needs to reach 60–80% of bolt yield strength; reduces loosening risk under cyclic loads	All
P24	Neck-breaking design + interference thread	F23	Requires specialized tools for installation; high preload control accuracy	P12, P14
P25	Riveting/swaged bolt tail	F24, F42	Plastic deformation locks the tail after installation; requires specialized tools	P15, P16

,

Table 11. Selection rules for lubrication methods.

Lubrication Approach	Function Element Basis	Characteristics	Applicable Fasteners
P3	F21, F27	Temperature resistant up to 400 °C; reduces friction coefficient (0.08–0.12)	P111, P113 P162, P12
P32	F24	Non-conductive; suitable for composite-metal connections; friction coefficient of 0.05–0.1	P112, P12 P14
P33	F27	Temperature resistant >500 °C; prevents seizing	P131
P34	F25, F32	Low cost, but prone to dust adhesion; high temperature loss	P111
P35	F23, F24, F27	Residue-free; does not interfere with thread sealant usage; precise threading	P11, P12

,

Table 12. Fastener constraint design selection rules-force analysis.

No.	Formula	Symbol Description	Function Element Basis
P411	$F={\displaystyle \frac{F_Q}{z}}$	F: Single bolt working tension z: Number of bolts	Axial load FQ
P412	$F^{\prime }\ge {\displaystyle \frac{K_f{F}_R}{z{\mu }_{s}m}}$	F′: Single bolt preload Kf: Reliability coefficient μs: Friction factor m: Number of contact surfaces	Tension bolt under lateral load FR
P413	$F_S={\displaystyle \frac{F_R}{z}}$	FS: Single bolt shear force	Shear bolt under lateral load FR
P414	$F^{\prime }\ge {\displaystyle \frac{K_{f}T}{{\mu }_S{\displaystyle \sum _{i=1}^z{r}_i}}}$	ri: Distance from each bolt center to the rotation center	Tension bolt under torque T
P415	$F_{S\max }={\displaystyle \frac{T{r}_{\max }}{{\displaystyle \sum _{i=1}^z{r_i}^2}}}$	rmax: Maximum distance from bolt center to rotation center	Shear bolt under torque T
P416	$F_{\max }={\displaystyle \frac{M{l}_{\max }}{{\displaystyle \sum _{i=1}^z{l_i}^2}}}$	li: Distance from each bolt center to the flip centerline lmax: Maximum distance from bolt center to flip centerline	Under overturning moment M

,

Table 13. Fastener constraint design selection rules for bolt and rivet design.

Calculation Type	Calculation Item	No.	Formula	Symbol Description	Function Element Basis
P42	Size Design	P421	$d_{\min }=\sqrt{{\displaystyle \frac{1.3F^{\prime }}{\frac{\pi }{4}[\sigma ]}}}$	dmin: Minimum diameter [σ]: Allowable stress	Only subject to preload
P42	Size Design	P422	$d_{\min }=\sqrt{{\displaystyle \frac{1.3F_0}{\frac{\pi }{4}[\sigma ]}}}$	$\mathrm{Static}\mathrm{load}:F_0=F^{″}+F=F^{\prime }+{\displaystyle \frac{c_1}{c_1+c_2}}F$ $\mathrm{Variable}\mathrm{load}:F_0=F^{\prime }+{\displaystyle \frac{c_1}{c_1+c_2}}F$ $F^{″}$$:\mathrm{Residual}\mathrm{preload};{\displaystyle \frac{c_1}{c_1+c_2}}$: Relative stiffness	Subject to both preload and working tension
		P423	$d_{\min }=\sqrt{{\displaystyle \frac{1.3F_S}{\frac{\pi }{4}m[\tau ]}}}$	m: Number of shear planes [τ]: Allowable shear stress	Subject to shear force
	Tensile Strength Check	P424	${\displaystyle \frac{1.3F^{\prime }}{\frac{\pi }{4}{d}^2}}\le [\sigma ]$	d: Selected diameter [σ]: Allowable stress	Only subject to preload
		P425	${\displaystyle \frac{1.3F_0}{\frac{\pi }{4}{d}^2}}\le [\sigma ]$	$\mathrm{Static}\mathrm{load}:F_0=F^{″}+F=F^{\prime }+{\displaystyle \frac{c_1}{c_1+c_2}}F$ $\mathrm{Variable}\mathrm{load}\mathrm{condition}:F_0=F^{\prime }+{\displaystyle \frac{c_1}{c_1+c_2}}F$	Subject to both preload and working tension
	Shear Strength Check	P426	${\displaystyle \frac{F_S}{dh}}\le [{\sigma }_P]$	h: Bolt compression height d: Shear plane diameter	Compression strength
		P427	${\displaystyle \frac{F_S}{\frac{\pi }{4}{d}^{2}m}}\le [\tau ]$	m: Number of shear planes [τ]: Allowable shear stress	Shear strength
	Joint Surface Strength Check	P428	${\sigma }_P={\displaystyle \frac{N}{A}}\le [{\sigma }_P]$	N: Total pressure on joint surface A: Joint surface area	Compressive strength
		P429	${\sigma }_P={\displaystyle \frac{M}{I}}\le [{\sigma }_P]$	M: Joint surface bending moment I: Moment of inertia of the joint surface	Bending strength
P43	Size Design	P431	$d\ge \sqrt{{\displaystyle \frac{4F}{\pi n[\tau ]}}}$	n: Number of shear planes (single shear = 1, double shear = 2)	F32
		P432	$L=1.1(t_{1 }+t_2 )$	t1, t2: Total thickness of connected components
	Strength Check	P433	${\displaystyle \frac{F_S}{\frac{\pi }{4}{d}^{2}m}}\le [\tau ]$	m: Number of shear planes [τ]: Allowable shear stress	Shear strength
		P434	${\displaystyle \frac{F^{\prime }}{\frac{\pi }{4}{d}^2}}\le [\sigma ]$	d: Selected diameter [σ]: Allowable stress	Tensile strength
		P435	${\displaystyle \frac{F}{dt}}\le [{\sigma }_P]$	d: Rivet diameter t: Thickness of connection plate

,

Table 14. Fastener constraint design selection rules for fastener layout and intermediate component design.

Calculation Type	Calculation Item	No.	Formula	Symbol Description	Function Element Basis
P44		P441	$r\ge 2.5d$(Bolting)	r: Pitch
		P442	$r\ge 3d$(Riveting)
		P443	$s\ge 3d$(Bolting)	s: Spacing
		P444	$s\ge 4d$(Riveting)
P44		P445	$e\ge 1.5d$(Bolting)	e: Edge distance
		P446	$e\ge 2d$(Riveting)
P45	Size design	P451	$w=2e+(n-1)s$	w: Width; n: Number of bolts per row
		P452	$T\ge {{\displaystyle \frac{F}{[\sigma ]\cdot w}}}_n$	T: Thickness F: Axial force wn = w − n·d: Net width (hole deduction) [σ]: Allowable tensile stress
	Rib plate design	P453	$t\ge \sqrt{{\displaystyle \frac{6M}{[\sigma ]b}}}$$\mathrm{or}t\ge {\displaystyle \frac{V}{[\tau ]b}}$	t: Thickness M: Bending moment V: Shear force b: Rib plate width	Thickness design
		P454	${\displaystyle \frac{k{\pi }^{2}E}{12(1-{\nu }^2)}} ({\displaystyle \frac{t}{b}}{)}^2\le [{\sigma }_c]$	k: Buckling coefficient E: Material modulus of elasticity ν: Poisson’s ratio	Buckling stress check
	Strength check	P455	${\displaystyle \frac{F}{(w-nd)\cdot T}} \le [\sigma ]$	n: Number of holes per row d: Hole diameter	Tensile strength
		P456	${\displaystyle \frac{F}{dT}} \le 0.8[{\sigma }_P]$	F: Single hole load	Compressive strength
		P457	${\displaystyle \frac{F}{LT}}\le [\tau ]$	L: Shear area length	Shear strength
		P458	$\lambda ={\displaystyle \frac{L}{r}}\le [\lambda ]$	L: Plate free length [λ]: Critical slenderness ratio $r=\sqrt{{\displaystyle \frac{I}{A}}}$: Radius of rotation	Buckling stability

and

Table 15. Selection rules for fit conditions.

Fit Conditions	Function Element Basis	Tolerance Grade	Characteristics
P51	F23	IT7 (Hole)/IT6 (Shaft)	Installation temperature control required (thermal expansion effect); composite structure requires hole processing after prepreg curing
P52	F42	IT8 (Hole)/IT6 (Shaft)	Anti-loosening washers or thread adhesive needed to compensate for gaps
P53	F21	IT7 (Hole)/IT6 (Shaft)	Interference fit prohibited for composites (risk of delamination); finite element analysis for stress distribution required
P54	P15, P16, P17	IT7 (Hole)/IT6 (Shaft)	Special rivets required (CherryMAX interference rivets); composite hole requires titanium alloy liner

. These tables clearly define the constraint equations associated with each subperformance and consider the interdependencies among them to ensure consistency and engineering feasibility across the overall performance parameter set.

In accordance with aerospace design and fastening technology standards, the fastener type selection table (Table 9) further refines each performance element into subtypes. For each subtype, the key fastener characteristics and commonly used lubrication methods are specified to support rational fastener selection. In the tables for anti-loosening (Table 10) and lubrication methods (Table 11), in addition to describing the applicability of each performance element, the corresponding fastener types are also listed to provide clear guidance for the selection of both anti-loosening and lubrication methods. In the tables for fit conditions (Table 15), the application characteristics of the performance elements are clarified, and recommended tolerance grades are given for direct reference in subsequent engineering drawings. In the constraint design tables (Table 12, Table 13 and Table 14), based on established design guidelines, the calculation types associated with each performance element are summarized. Detailed design formulas and symbol definitions are provided, and each formula is numbered according to subtype hierarchy. The subtypes defined in these selection tables represent the final categorization of performance elements, forming the output of the performance layer and serving as input to the structure layer. For consistency, a unified numbering scheme of the form $P_{mnz}(z\ge 1)$ is adopted to identify subtypes and their hierarchical contents.

During the mapping process, functional elements from the function layer are sequentially substituted into the mapping functions of the performance sublayers $P_n\left(n=1,2,3,4,5\right)$. The selection is carried out in ascending order of n, yielding both the fastener performance outputs (fastener type, anti-loosening method, lubrication method, and fit condition) and the parameter design workflow, which consists of the specific design equations identified in the constraint design subperformance.

3.2.3. PS Mapping

The fastener properties and parameter design procedure, outputted from the performance layer, is further translated into a detailed characteristic description of substructure. Specifically, the fastener properties directly correspond to the fasteners (S₁) in the structure layer. The design equations involved in the parameter design procedure are applied to the specific parameter requirements by the designer to calculate detailed structural dimensions, and the resulting values provide parameter descriptions for both the fasteners (S₁) and the intermediate components (S₂). Finally, these results, together with the parameters of the connected components contained in the specific requirements, are integrated to form a complete structural parameter set of the joint configuration, as shown in

Table 16. Structure parameter set of the designed fastener joint configuration.

Configuration Structure	Parameter Description
Connected component a	Overlap dimensions (length, Hn × width, Dn); thickness, en; loaded (shear force, FR; tension force, FQ; and torque, T)
S1	Contact surface dimensions (length, L × width, W); thickness, T; rib plate dimensions (length, l × width, b; thickness, t)
S2	Fastener type; diameter, D1; anti-loosening method; lubrication method; fit conditions and tolerance grade.	Diameter, D; quantity z; rows, r; columns, c; spacing, S; pitch, r; edge distance, e

, which serves as the output of the structure layer. Here, since the structure layer contains only a limited number of substructures, it is not necessary to employ mapping functions to explicitly express the mapping process.

The structural parameter set includes the basic geometric dimensions of the three key components in the joint configuration (connected components, intermediate components S₁, and fasteners S₂), as well as their specific parameter features (such as the loading conditions of the connected components, the rib dimensions of the intermediate components, and the layout parameters of the fasteners, etc.). This dataset supports downstream tasks including modeling, simulation, engineering drawing generation, and process implementation.

3.2.4. Design Scheme Generation

The outputs from all layers (including product elements, design constraints, and the structure parameter set) are integrated to generate one or more complete conceptual design schemes, as shown in

Table 17. Conceptual design schemes of the designed fastener joint configuration: (a) connected components, (b)substructures.

(a)
Connected Components		Parameter Description
Connected component 1		Overlap dimensions (length, H1 × width, D1); thickness, e1; loaded (shear force, FR1; tension force, FQ1; torque, T1)
Connected component 2		Overlap dimensions (length, H2 × width, D2); thickness, e2 (mm); loaded (shear force, FR2; tension force, FQ2; torque, T2)
(b)
Connection form diagram	Substructure	Parameter description
Connection form diagram 1	S1	Contact surface dimensions (length, L1 × width, W1); thickness, T1; rib plate dimensions (length, l1 × width, b1; thickness, t1)
	S2	Fastener type; diameter, D1; anti-loosening method; lubrication method; fit conditions; and tolerance grade	Connected component 1 side: quantity, z1: rows, r1; columns, c1; spacing, S1; pitch, r1; edge distance, e1
			Connected component 2 side: quantity, z2: rows, r2; columns, c2; spacing, S2; pitch, r2; edge distance, e2
Connection form diagram 2	S1	Contact surface dimensions (length, L1 × width, W1); thickness, T1; rib plate dimensions (length, l1 × width, b1; thickness, t1)
	S2	Fastener type; diameter, D2; anti-loosening method; lubrication method; fit conditions; and tolerance grade	Connected component 1 side: quantity, z1: rows, r1; columns, c1; spacing, S1; pitch, r1; edge distance, e1
			Connected component 2 side: quantity, z2: rows, r2; columns, c2; spacing, S2; pitch, r2; edge distance, e2

. Considering that users typically specify two connected components, the key parameters of both components, as well as those of the joint interfaces between the connected components and the intermediate component, are listed in detail. In cases involving multiple feasible configurations, the structural composition and dimensional features of each joint configuration can be listed sequentially in the table to facilitate comparison and selection.

In the final stage, the generated conceptual design schemes of the designed fastener joint configuration are subjected to evaluation based on performance. This involves general validation of fatigue life and reliability, as well as performance checks tailored to special application regions such as high-vibration, sealing, and aerodynamically sensitive areas. The specific verification formulas for performance criteria are provided in

Table 18. The performance indicator of the designed fastener joint configuration.

Performance Indicator	Formula	Symbol Description	Substructures
Fatigue life	$L_{f,i} ={\displaystyle \frac{1 }{\Delta {ϵ}_i}}({\displaystyle \frac{{\sigma }_{f,i }}{{\sigma }_i }}{)}^m$	Lf,i: fatigue life of fastener i; Δϵi: strain range in fatigue cycle; σf,i: fatigue strength; σi: actual stress; m: material fatigue exponent	S2
Reliability	$R={\prod }_{i=1}^z{R}_i$	R: reliability of joint configuration; Ri: reliability of fastener i	S1, S2
Maximum stress in high-load area (F21)	${\sigma }_{max} ={\displaystyle \frac{F_{load}}{L\cdot W}} \le {\sigma }_{allowable}$	σmax: maximum stress; Fload: applied load; L, W: contact surface dimensions; σallowable: allowable stress	S1
Out-of-plane deformation in aerodynamically areas (F22, F26)	$f_n ={\displaystyle \frac{1}{2\pi }} \sqrt{{\displaystyle \frac{k_j}{m_j}}}$	fn: natural frequency; kj: joint configuration stiffness; mj: mass of joint configuration assembly	S1, S2
Natural frequency in high-vibration area (F25)	${\sigma }_{th} =E\cdot \alpha \cdot \Delta T$	σth: thermal stress; E: Young’s modulus; α: coefficient of thermal expansion; ΔT: temperature change	S1
Thermal stress in high-temperature zones (F27)	$p_c ={\displaystyle \frac{F_{c }}{L\cdot W}} \ge p_{min}$	pc: contact pressure; Fc: contact load; L, W: contact surface dimensions; pmin: minimum required contact pressure	S1
Contact pressure in sealed areas (F28)	${\delta }_{oop} ={\displaystyle \frac{ML }{EI}}\le {\delta }_{allowable}$	δoop: out-of-plane displacement; M: bending moment; L: span of joint configuration; E: Young’s modulus; I: moment of inertia of the cross-section; δallowable: maximum allowable displacement	S1

. If multiple candidate configurations pass the screening, the optimal scheme is determined by combining performance comparison with designer expertise. If none succeed, the process iterates: either by adjusting fastener layouts and reselecting the configuration diagram from the F layer, or modifying performance selections from the P layer, until a feasible design is achieved.

4. Case Study

4.1. Conceptual Design of the Joint Configuration Between the Mid-Fuselage Skin and the Annular Frame

To verify the applicability and effectiveness of the proposed FPS-based design method for aircraft fastener joint configurations, a typical connection scenario from the aircraft fuselage structure is selected.

The user requirement is defined as designing a detachable joint between the mid-fuselage skin and the annular frame to transfer aerodynamic loads and bending moments, while allowing for component replacement and maintenance. The detailed specifications of the connected components are as follows: The skin is made of 2024-T3 aluminum alloy, with a thickness of 3.5 mm. It is laid along the longitudinal direction of the fuselage and intersects perpendicularly with the annular frame. The overlap area is 300 mm in length and 40 mm in width. The main loading is the shearing force, $Q=80\mathrm{k}\mathrm{N}$. The frame is made of 7075-T6 aluminum alloy, with a thickness of 4 mm and an overlap width of 60 mm. It primarily carries bending moments.

Analyzing the user requirement reveals that the connection location and critical parameters are explicitly provided. According to the functional requirements, the following function elements from the F layer are extracted: F₁₁, F₂₃, F₃₂, F₃, and F₄₁.

According to the joint location specified, initial combinations of configuration can be referenced from the configuration library. Substituting F₁₁ and the skin–frame joint into Table 4 of the configuration library yields two preliminary applicable connection forms: the “L” shape and the “▲” shape. For fastener layout, according to Table 7 and Table 8, a dual-row linear pattern is selected to satisfy load transmission and compactness. Then, the set of function elements $\mathit{I}=\left\{F_{11},F_{23},F_{32},F_{33},F_{41}\right\}$ is mapped to the performance layer to derive the associated output set O:

$$\mathit{O}=\left\{\begin{array}{l}{P}_{14}=f_1\left(F_{23},F_{32},F_{33},F_{41}\right)\hfill \\ P_{26}=f_2\left(F_{23},F_{32},P_{14}\right)\hfill \\ P_{31}=f_3\left(F_{23},P_{14}\right)\hfill \\ {\mathit{P}}_4=f_4\left(F_{11},F_{32},P_{14}\right)\hfill \\ P_{51}=f_5\left(F_{23},F_{41}\right)\hfill \end{array}\right.,$$

(3)

where the output set for P₄ is the following:

$${\mathit{P}}_4=\left\{P_{412},P_{415},P_{423},P_{426},P_{427},P_{441},\right.\left.P_{443},P_{445},P_{451},P_{452},P_{453},P_{454},P_{458}\right\}.$$

(4)

The output of the performance layer further constrains the parametric design of substructures S₁ and S₂ in the structure layer, resulting in a structure parameter set of the skin–frame joint configuration. At this point, the conceptual design flow for the skin–frame joint configuration is completed, as shown in Figure 6. By integrating the outputs from all three layers, two complete design schemes are ultimately generated, as illustrated in

Table 19. Conceptual design schemes of the skin–frame fastener joint configuration: (a) connected components, (b)substructures.

(a)
Connected Components		Parameter Description
Connected component 1		Overlap dimensions (length, 300 mm × width, 40 mm); thickness, 3.5 mm; shear force, FR = 80 kN
Connected component 2		Overlap dimensions (length, 300 mm × width, 60 mm); thickness, 4 mm; torque, T)
(b)
Connection form diagram	Substructure	Parameter description
“▲” shape	S1	Contact surface dimensions (length, 300 mm × width, 40–60 mm); thickness, 3.5–4 mm; rib plate dimensions (length, 30 mm × width, 30 mm; thickness, 2 mm)
	S2	High-lock bolt M4.8; structural self-locking; dry film lubrication; transition fit	Connected component 1 side: quantity, 6; rows, 1; columns, 6; spacing, 50 mm; edge distance, 15 mm
			Connected component 2 side: quantity, 12; rows, 2; columns, 6; spacing, 50 mm; pitch, 15 mm; edge distance, 15 mm
“L” shape	S1	Contact surface dimensions (length, 300 mm × width, 40–60 mm); thickness, 3.5–4 mm; rib plate dimensions (length, 30 mm × width, 30 mm; thickness, 4 mm)
	S2	High-lock bolt M4.8; structural self-locking; dry film lubrication; transition fit	Connected component 1 side: quantity, 8; rows, 1; columns, 8; spacing, 37.5 mm; edge distance, 15 mm
			Connected component 2 side: quantity, 16; rows, 2; columns, 8; spacing, 37.5 mm; pitch, 15 mm; edge distance, 15 mm

.

According to Table 18, the two generated configurations were evaluated based on performance indicators. Numerical evaluation indicated that the “▲” shape joint configuration achieved a fatigue life of over 1.2 × 10⁵ load cycles and a reliability index of 0.995, thereby meeting the service life requirements. In contrast, the “L” shape joint configuration, although seemingly favorable under pure shear load sharing, showed a reduced fatigue life of only 6 × 10⁴ cycles and a reliability index of 0.96 due to secondary bending effects, failing to satisfy the design criteria. Based on both quantitative results and established design experience in fuselage joint structures, the “▲” shape joint configuration was finally adopted as the optimal joint design.

To further verify the robustness of the “▲” shape joint configuration under uncertainties, a Monte Carlo simulation was conducted considering variations in key parameters, including shear load, material strength, plate thickness, and fastener friction coefficient. Based on aerospace design experience, these parameters were assumed to follow normal or triangular distributions, as summarized in

Table 20. Uncertainty parameters and their distributions.

Uncertainty Parameters	Distribution Type	Value
Shear force, Q	Normal distribution, N (μ, σ)	μ = 80 kN, σ = 8 kN
Material yield strength, σy	Normal distribution, N (μ, σ)	μ = 324 MPa, σ = 10 MPa
Friction coefficient, μ	Triangular distribution	min = 0.12, mode = 0.15, max = 0.18
Thickness, t	Normal distribution, N (μ, σ)	μ = 3.5 mm, σ = 0.1 mm

. Random samples were generated for each iteration, and the corresponding fatigue life and reliability index were calculated. The resulting distributions are presented in Figure 7.

As shown in Figure 7a, over 10,000 iterations, the fatigue life exhibited a mean of 1.43 × 10⁵ cycles, a standard deviation of 1.62 × 10⁴ cycles, and a 95% confidence interval of [1.16 × 10⁵,1.79 × 10⁵]. Figure 7b illustrates that the reliability index had a mean value of 3.236, a standard deviation of 0.100, and a 95% confidence interval of [3.040, 3.431]. These results indicate that the selected joint configuration maintains sufficient applicability and reliability under realistic variations in loading and material properties, providing a robust basis for the final design.

This configuration was selected as the final joint design scheme, and its corresponding 3D structural model was generated, as shown in Figure 8, illustrating the spatial arrangement and assembly scheme of the design.

4.2. Conceptual Design of the Joint Configuration Between the Engine Nacelle Pylon and Wing Box

To verify the robustness of the aircraft Fastener Joint Configuration design method based on the FPS model, a relatively complex connection scenario in the wing structure is selected as a case study, namely the connection between the engine nacelle pylon and the wing box.

The user requirements are defined as follows: to design a connection between the engine nacelle pylon and the wing box that provides high load transfer capacity while meeting the requirements for engine suspension and maintenance disassembly. The specified parameters of the connected components are the following: the wing box end beam, made of 7075-T6 aluminum alloy with a thickness of 4 mm, subjected to a vertical shear force from the pylon beam (box-type structure) of F_Q = 80 kN and a bending moment, with a connection length of 500 mm; the pylon box, made of 2024-T3 aluminum alloy with a thickness of 3.5 mm, which is subjected to the engine’s vertical shear force, bending moment, and torque.

Based on the requirement analysis, the connection location and key load data are explicitly defined, allowing the design of fasteners to be guided by the corresponding cases in the configuration library. According to the functional requirements, since this case simultaneously involves both the wing leading-edge region and the engine nacelle, it corresponds to the sub-functional application scenarios (F₂) of aerodynamically sensitive region, high-vibration region, and high-temperature region. Consequently, the functional elements extracted from the F layer are the following: parallel connection (F₁₂), aerodynamically sensitive region (F₂₂), high-vibration region (F₂₅), high-temperature region (F₂₇), subjected to shear force (F₃₂) and bending moment (F₃₃), and detachable connection (F₄₁).

According to the joint location specified, initial combinations of configuration can be referenced from the configuration library. By mapping the functional element F₁₂ and the nacelle pylon–wing box connection into the configuration library (Table 4, Table 5, Table 6, Table 7 and Table 8), the “Ψ” shape joint form is preliminarily selected. For fastener layout, a linear arrangement is chosen to balance load transfer efficiency and spatial compactness. Then, the set of function elements I = {F₁₂, F₂₂, F₂₅, F₂₇, F₃₂, F₃₃, F₄₁} is mapped to the performance layer to derive the associated output set O:

$$\mathit{O}=\left\{\begin{array}{l}{P}_{132}=f_1\left(F_{22},F_{25},F_{27},F_{32},F_{33},F_{41}\right)\hfill \\ P_{211}=f_2\left(F_{22},F_{25},F_{27},F_{32},P_{132}\right)\hfill \\ P_{35}=f_3\left(F_{22},F_{25},F_{27},P_{132}\right)\hfill \\ {\mathit{P}}_4=f_4\left(F_{12},F_{32},F_{33},P_{132}\right)\hfill \\ P_{51}=f_5\left(F_{23},F_{41}\right)\hfill \end{array}\right.,$$

(5)

where the output set for P₄ is the following:

$${\mathit{P}}_4=\left\{P_{413},P_{416},P_{423},P_{425},P_{429},P_{441},P_{445}\right\}$$

(6)

The output of the performance layer further constrains the parametric design of substructures S₂ in the structure layer, resulting in a structure parameter set of the engine nacelle pylon–wing box joint configuration. At this point, the conceptual design flow for the proposed joint configuration is completed, as shown in Figure 9. By integrating the outputs from all three layers, two complete design schemes are ultimately generated, as illustrated in

Table 21. Conceptual design schemes of the engine nacelle pylon–-wing box fastener joint configuration.

Substructure	Conceptual Description
Connected component 1	Lug dimensions (length, 50 mm × width, 30 mm; thickness, 10 mm; quantity, 4); thickness, 4 mm; subjected to bending moment, M, and shear force, FQ = 80 kN
Connected component 2	Lug dimensions (length, 50 mm × width, 30 mm; thickness, 10 mm; quantity, 4); thickness, 3.5 mm; subjected to bending moment, M, and shear force, FQ = 80 kN
S2	Heat-resistant titanium bolt M8; self-locking nut; dry film lubrication; transition fit	Quantity, 8; spacing, 24 mm; edge distance, 20 mm

.

According to the performance indices in Table 18, the design scheme is evaluated. Numerical results show that the fatigue life of the “Ψ” shape structure is far beyond the limiting requirement, the reliability index reaches 3.68, the natural frequency is 22.5 Hz (different from the operating frequencies of the wing and engine), the thermal stress is 289 MPa, and the aerodynamic out-of-plane deformation is 0.5 mm. All indices meet the design requirements. Therefore, the “Ψ” shape structure is determined as the final design solution, and a corresponding 3D structural diagram (Figure 10) is generated to illustrate its spatial configuration and assembly scheme.

5. Conclusions

To address the lack of systematic methods and clearly defined performance constraints in the design of aircraft fastener joint structures, an FPS based conceptual design methodology for joint structures is proposed. First, service performance requirements are introduced as an intermediary to establish the FPS model. Then, the model and design process are detailed with respect to aircraft structures. Finally, the feasibility and effectiveness of the proposed method are validated through a typical joint configuration design example. This approach integrates conceptual design with structural design and enables a complete reasoning path from user requirements to structural realization.

However, due to the limited availability of data and the rapid development of aerospace equipment design, the configuration library and mapping rules cannot achieve complete coverage and require continuous expansion and refinement. Currently, the current method still relies heavily on manual selection and rule-based mapping. While this approach is effective for conventional joint designs, it may face limitations when dealing with unconventional or novel configurations, where the existing rules may not fully capture unique structural or functional requirements. Future work will focus on expanding the configuration library and mapping rules while incorporating intelligent algorithms and automated modeling tools. In particular, the integration of AI and machine learning techniques (such as knowledge-based reasoning, physics-informed neural networks, or optimization algorithms) will be explored to evolve the methodology into a smart design system with enhanced engineering applicability and decision-making support.

Although the proposed FPS-based conceptual design methodology is developed for aerospace fastener joint structures, its underlying principles are general. With appropriately constructed configuration libraries and carefully selected rule tables, the approach can be adapted to other domains. This underscores the potential broader applicability of the methodology beyond aerospace engineering.