Ultimate Strength Analysis of Aluminium Honeycomb Sandwich Panels Subjected to Uniaxial Compressive Loads and Lateral Pressure

Abstract

Ultimate strength is critical for hull structures because it determines the maximum load the structure can withstand before catastrophic failure. Aluminium honeycomb sandwich panels provide excellent energy absorption and a high strength-to-weight ratio. However, further investigation of honeycomb sandwich panel structural performance is needed in typical marine conditions. This study focuses on the numerical analysis of honeycomb sandwich panels employing the nonlinear finite element method through the commercial software ANSYS. It investigates their performance under uniaxial compression and varying lateral pressure conditions while considering different cell edge lengths and core height configurations. Several structural configurations are compared to the experimental work published in the literature. Enhanced by experimental accuracy, the present study is a further step in expanding the application of honeycomb sandwich panels for ship hull applications that may lead to light and energy-efficient structures.

1. Introduction

Lightweight sandwich structures have been adopted in various industries, including aerospace, automotive, offshore, and shipbuilding [1,2,3,4]. These panels typically have thin face sheets bonded to a lightweight core, with the core’s design chosen based on the intended use to ensure optimal performance in each application [5,6,7]. Sandwich structures are classified into all-metal, hybrid metal, and composite categories; all-metal panels consist of metal skins and cores; hybrid panels combine metallic and non-metallic materials; and composite panels feature facings made from composite materials. Additionally, all-metal panels are further subdivided by core geometry [8,9,10,11]. Sandwich constructions offer several advantages over conventional steel structures, including a more streamlined design, reduced weight [12], and superior fatigue resistance [13]. Furthermore, applications provide enhanced performance characteristics such as effective thermal insulation [14], increased impact strength [15], and more excellent resistance to blasts and ballistic impacts [16].

Many studies have explored the mechanical properties of sandwich panels with honeycomb cores. However, less attention has been directed towards their buckling behaviour, including the additive-manufactured honeycomb sandwiches subjected to flexural loading [17]. Paik et al. [18] investigated the strength of aluminium honeycomb-cored sandwich panels through theoretical and experimental testing analyses under various loading conditions, such as three-point bending, axial compression, and lateral crushing. Furthermore, Hong et al. [19] conducted an experimental investigation into the behaviour of aluminium 5052-H38 honeycomb structures under inclined loading, emphasising both compression and impact responses. Through dynamic crushing experiments, they observed that as impact velocity increased, normal stress rose significantly, while shear stress showed minor change. The findings demonstrated that the honeycomb structures remained stable under compressive and inclined loads.

Kaman et al. [20] investigated the failure behaviour of honeycomb cores in panel structures, assessing the critical buckling load through numerical analysis and experimental testing. Their research also explored the influence of honeycomb core dimensions on the buckling behaviour of the structure, providing insights into how size variations impact structural stability.

In the research focused on the load capacity of honeycomb sandwich structures, JeyaKrishnan et al. [21] conducted an extensive analysis of the buckling behaviour of honeycomb sandwich panels with hexagonal cells, concentrating on supported boundary conditions under static loading. This research sought to evaluate the stability of the panels during edgewise compression tests and to optimise the theoretical coefficients used for determining the critical buckling load for various panel aspect ratios.

In the study by Zhao et al. [22], lateral compression tests and finite element analyses were used to investigate the lateral compressive buckling performance of a newly designed honeycomb panel, considering different length-to-thickness ratios.

Al-Shammari and Al-Waily [23] studied the impact of honeycomb core size on the critical buckling behaviour of sandwich plate structures. They proposed an analytical solution for the general buckling equation. Then, they compared the analytical buckling load results with numerical evaluations using finite element analysis to verify their accuracy. Their findings evaluated the mechanical properties of the honeycomb core and examined the influence of various parameters on the buckling load.

Cheng et al. [24] conducted a study to optimise the design of a honeycomb core structure utilising three testing standards. Their research involved simulation experiments conducted with a uniform design, and von Mises stresses were determined through finite element analysis. A genetic algorithm was employed to address the multi-objective optimisation problem and find the best solutions.

Finally, Corigliano et al. [25] conducted experimental and numerical analyses on honeycomb sandwich panels subjected to uniaxial compressive loads. Their results offer valuable insights for developing predictive models to estimate the uniaxial compressive load-carrying capacity of hybrid honeycomb sandwiches designed with aluminium alloys.

This study embarks on a systematic investigation to enhance ship structure design by transitioning from conventional steel stiffened panels to lightweight aluminium honeycomb panel solutions without compromising strength. Initially, a traditional steel stiffened panel was analysed as a benchmark to establish a baseline for its ultimate strength. From there, an equivalent aluminium panel was developed and designed to meet the same strength criteria while reducing weight. An advanced design was introduced by incorporating aluminium honeycomb sandwich panels, applied to the vessel’s bottom structure to further push the boundaries of structural efficiency. Through nonlinear finite element analysis (NLFEA) using ANSYS software (Release 22.2), this study evaluated the performance of these honeycomb aluminium sandwich panels under both uniaxial compressive loading and lateral pressure, reflecting realistic maritime conditions. Our findings offer new insights into the viability of aluminium honeycomb structures for marine structural applications, highlighting their potential to enhance structural resilience and lightweight efficiency in modern ship design.

This manuscript explores the performance of stiffened panels and honeycomb sandwich panels in marine structures, with Section 2 reviewing relevant case studies on these panel types. Section 3 focuses on numerical simulations, detailing the material properties, boundary conditions, loading scenarios, and the validation of numerical results with experimental data. Section 4 discusses the findings, focusing on the panels’ performance under different conditions. Finally, Section 5 concludes this study, highlighting the key implications for marine applications.

2. Case Study

2.1. Stiffened Panel

A stiffened panel located at the bottom of a coastal craft is used in the present study. The principal characteristics of the selected coastal craft are summarised in

Table 1. Principal particulars of the selected coastal craft.

Parameter	Value
Length Overall	28.00 m
Length between Perpendiculars	25.89 m
Breadth Moulded	05.69 m
Depth Moulded	3.04 m
Frame Spacing	0.915 m

. As depicted in Figure 1, the panel is longitudinally bounded between two transverse frames and transversely supported by two longitudinal girders. The accompanying notation scheme in the figure provides a comprehensive layout of the panel’s dimensions and stiffener arrangement.

The original panel is fabricated from high-tensile steel and was designed to meet the structural demands of the bottom hull section in a coastal vessel. A second panel is designed using aluminium to facilitate comparative analysis, with adjustments to the panel plate and stiffener thickness to match the steel panel’s ultimate strength. The aluminium panel is designed to perform identically to the steel panel under “equivalent loading conditions”, which means both panels were subjected to the same applied loads and pressure distribution, which includes a combination of in-plane loads and lateral pressure, to ensure a fair comparison of their structural performance. The dimensions of the aluminium panel were determined using a trial and error method, where adjustments to the thicknesses of the panel plate and stiffeners were made iteratively to match the steel panel’s ultimate strength.

Table 2. Geometric properties of the stiffened panels.

	Length a (mm)	Width b (mm)	Plate Thickness tp (mm)	Web Height hs (mm)	Web Thickness ts (mm)	Stiffener Spacing s (mm)
Steel	915	1143	5	89	5	381
Aluminium	915	1143	6	89	6	381

summarises the primary dimensions of both panels, detailing attributes such as length, width, thickness, and stiffener spacing. These standardised dimensions provide a controlled basis for accurately assessing each panel’s structural performance in marine applications.

2.2. Honeycomb Sandwich Panel

A honeycomb core sandwich panel is engineered by adhesively bonding two thin, rigid face sheets to a lightweight honeycomb core. This composite structure synergistically combines the mechanical properties of the face sheets, which provide both strength and rigidity, with the low density of the honeycomb core, resulting in a material that exhibits an exceptional strength-to-weight ratio and enhanced structural performance [26]. The honeycomb core is a fundamental component for classifying cores with multi-directional stiffening, facilitating a comprehensive assessment of different structural configurations and their associated mechanical properties [27,28]. Figure 2 presents the honeycomb-cored sandwich panel examined in this study. To simplify the analysis, the facings are assumed to have equal thickness, denoted by t_f, while the core height is indicated as h_c. The figure also highlights an individual honeycomb core unit with a thickness t_c and a side length l_c.

This study investigates the structural performance of honeycomb sandwich panels under varying geometric configurations and lateral pressure conditions. The honeycomb panels are designed to provide a lightweight alternative with comparable structural performance in terms of maximum displacement and maximum von Mises stress under the same loading conditions as the stiffened steel and aluminium panels. The dimensions of the honeycomb panels, such as skin thickness, cell wall thickness, cell size, and core height, are chosen to optimise their mechanical properties. The panels consist of a 2 mm-thick face sheet and a honeycomb core with a nominal height of 45 mm. The cellular structure of the core was analysed by systematically varying the cell edge lengths to include configurations of 20 mm, 25 mm, and 30 mm while maintaining a uniform cell wall thickness of 1 mm across all cases. To evaluate the influence of core height on resistance to lateral pressure, the optimal configuration was selected for further analysis, with the core height adjusted by ±15 mm from the nominal 45 mm. The details of these configurations are summarised in

Table 3. Honeycomb sandwich panel configurations.

	Face Sheets Thickness tf (mm)	Cell Wall Thickness tc (mm)	Cell Edge Length lc (mm)	Core Height hc (mm)
Case 1	2	1	20	45
Case 2	2	1	25	45
Case 3	2	1	30	30–45–60

. This adjustment allowed a deeper understanding of how core height impacts the honeycomb sandwich structures’ lateral pressure resistance and mechanical behaviour. This study provides insights into the interplay between geometric configurations and structural performance by systematically varying these parameters.

3. Ultimate Compressive Strength

Zenkert [29] identified several failure modes for sandwich panels, each of which limits the structure’s load-bearing capacity. The significance of these failure modes varies based on the configuration of the sandwich panel and the type of loading, defining the limits of the structural performance. Among these modes, buckling is a critical consideration. However, it may not cause immediate damage to the structure. It should still be avoided, as a buckled panel can lose its functional integrity. Moreover, the actual buckling load may represent the ultimate load-carrying capacity since the sandwich panel cannot sustain additional loads once it has been buckled. In this context, sandwich panels are particularly susceptible to buckling failure under compressive loading.

Evaluating the ultimate strength of structural elements and systems is fundamentally important, as it represents their maximum load-bearing capacity. This analysis is essential for ensuring designs’ structural integrity and safety, enabling them to withstand anticipated loads throughout their operational lifespan [30,31,32].

This study employs NLFEA to evaluate honeycomb sandwich panels’ uniaxial compressive capacity and lateral pressure response, with results compared to those of conventionally stiffened panels. A linear eigenvalue analysis is performed to identify the initial imperfections necessary for subsequent nonlinear buckling analysis, using the resulting eigenmodes to construct an initially deformed model as input for the nonlinear assessment [33]. This setup of the linear buckling solution involves applying an initial out-of-plane deflection aligned with the first eigenmode under compressive loading, ensuring a more accurate representation of the panel’s structural behaviour during analysis [34,35]. Additionally, the Load Shortening Curve (LSC) illustrates the unidirectional shortening of the panel when subjected to a compressive load in the specified direction. The peak of the LSC marks the onset of panel failure, immediately followed by a sharp reduction in the panel’s ability to resist compressive stress, representing the ultimate buckling capacity of the panel.

3.1. Numerical Model Characteristics

The numerical modelling in this study is performed using SpaceClaim software within the ANSYS (2022 R2) package, which provides advanced capabilities for creating complex geometries [36]. SHELL181 elements are used to model the stiffened panels and the faces of the sandwich panels. Each SHELL181 element is defined by four nodes, each having six degrees of freedom, allowing for translation and rotation in the x, y, and z directions. This element is designed to analyse thin to moderately thick shell structures and can manage linear and nonlinear analyses. In contrast, the honeycomb core is modelled using SOLID186 elements. These 3D solid elements are defined by 20 nodes, each with three degrees of freedom corresponding to translations in the x, y, and z directions. SOLID186 elements support plasticity and stress stiffening and can account for large deflections and strains [37].

Due to the intricacies associated with accurately modelling adhesive behaviour, a bonded contact interaction has been established between the core, top, and bottom layers.

3.2. Material Characteristics

In this study, the conventional stiffened panel is typically constructed from steel. However, this study broadens its scope to encompass steel and aluminium materials [38], as detailed in

Table 4. Main characteristics of the materials.

	Steel NV-27 (Baglietto, La Spezia SP, Italy)	Aluminium 5052-H38 (ASM Aerospace Specification Metals Inc., Pompano Beach, FL 33069, USA)	Units
Density	7800	2680	kg/m3
Young’s Modulus	200	70.3	GPa
Poisson’s Ratio	0.29	0.33
Yield Stress	265	255	Mpa

, along with examining honeycomb sandwich panels. The stress-strain curve is an idealised elastic, perfectly plastic model, neglecting any effects of material hardening.

3.3. Boundary and Loading Conditions

The degrees of freedom for all nodes along the model’s fore, aft, and lateral edges are defined to simulate longitudinal bending. The displacements in the X, Y, and Z directions are represented by Dx, Dy, and Dz, respectively, as shown in Figure 3. The boundary conditions are configured to act as simple supports. One end of the model is constrained in all directions, while the opposite end can move freely in the X direction. Furthermore, movement in the X direction is allowed at the lateral edges, and these boundary conditions are consistently applied across all models. This configuration ensures a reliable representation of the structural response under longitudinal loading conditions.

In conjunction with these boundary conditions, a forced displacement is applied at one edge of the model—either the fore or the aft—to derive load-end shortening curves and estimate the ultimate buckling capacity, with the corresponding reaction force calculated at the opposite edge. To evaluate the panel’s response under varying lateral pressure conditions, 0, 50, and 100 kPa are applied in different cases. For accurate results, the applied displacement magnitude is set large enough to produce deformations that exceed the ultimate buckling capacity of the panel.

In this study, the finite element model incorporates material nonlinearity and significant displacement effects to accurately capture the nonlinear behaviour of the panels accurately. The analysis uses adaptive time steps to ensure numerical stability, with a minimum time step of 50 and a maximum time step of 500. Additionally, the mesh used in the simulations has been refined to improve the precision of the results, with a mesh size of 10 mm. Mesh details are provided in Figure 4, offering a detailed view of the mesh configuration.

3.4. Numerical Validation

To verify the accuracy of the numerical simulations conducted in this study, a validation process was conducted through a comparison with the results reported in Corigliano et al. [25]. In this study, the honeycomb structure had a cell diameter of 3 mm and a core height of 9 mm, with face plates measuring 1.0 mm in thickness and honeycomb cell walls 0.07 mm thick. The sandwich specimen used had a width of 45 mm and a span length of 170 mm. Solid elements were used in the numerical model to simulate the sandwich plates. The geometric properties of this panel are identical to the configuration described in Section 2, ensuring consistency between the description and the experimental validation presented here.

Two experimental tests, T1 and T2, were conducted in [25] to ensure repeatability and consistency. The stress-strain curves from both the numerical simulations and the experimental tests were examined and compared. In Figure 5, the stresses represent the applied load divided by the cross-sectional area of the aluminium panel. At the same time, the strains are calculated based on the deformation relative to the original length. The yield stress (σy) used in the study is 155 MPa for the aluminium panel, and the corresponding yield strain (εy) is 0.002.

Additionally, the deformed shapes of the specimens during the experimental tests and their corresponding deformation patterns in the numerical simulations were compared, as shown in Figure 6. This analysis aimed to correlate the stress-strain response and failure modes of honeycomb sandwich panels subjected to uniaxial compressive loading. By comparing the numerical results with the experimental data from the study presented in [25], we evaluated the model’s ability to accurately capture the mechanical behaviour of the panels. The close match between the numerical and experimental data confirms the validity of the numerical approach. It demonstrates its reliability in predicting the structural performance of honeycomb sandwich panels under similar loading conditions.

4. Results and Discussion

This study comprehensively examines the structural performance of steel and aluminium stiffened panels under combined axial and lateral loading, honeycomb sandwich panels with varying cell edge lengths under uniaxial compression, and the influence of lateral pressure on the optimal honeycomb panel design with different core heights. This investigation aims to identify the most effective design configurations and material behaviours under diverse loading conditions.

The first phase of the investigation focuses on evaluating the ultimate strength of stiffened panels subjected to axial loads combined with varying lateral pressure levels of 0, 50, and 100 kPa. This research involves an analysis of an as-built steel-stiffened panel and a designed aluminium-stiffened panel to evaluate their respective load-bearing characteristics. Moreover, insights derived from the performance and weight of the aluminium panel inform the design of aluminium honeycomb panels, which are subsequently assessed under identical loading conditions. This comprehensive approach aims to elucidate the mechanical behaviour of different panel configurations to optimise the strength-to-weight efficiency of aluminium-based structures for engineering applications.

The eigenvalue buckling analysis was performed, with Figure 7 displaying the first eigenmode for steel and aluminium stiffened panels. These results highlight the initial buckling patterns critical for assessing panel stability. To account for initial imperfections, a scale factor of 0.005 of the first buckling mode was applied to the numerical model in the nonlinear analysis. This value was chosen to reflect realistic imperfection magnitudes while ensuring numerical stability.

Figure 8 and Figure 9 present the representative deformed shapes from the nonlinear simulations of the steel and aluminium stiffened panels. For each panel, both 0 kPa and 100 kPa lateral pressures are applied with axial loading. Figure 8 shows the deformation of the steel stiffened panel under (a) combined axial load and 0 kPa lateral pressure and (b) combined axial load and 100 kPa lateral pressure. Figure 9 illustrates the deformation of the aluminium stiffened panel under (a) combined axial load and 0 kPa lateral pressure and (b) combined axial load and 100 kPa lateral pressure. As lateral pressure increases, both panels exhibit noticeable deformation, with the steel panel demonstrating higher overall stiffness than the aluminium panel due to material properties and structural design differences. Figure 10 illustrates the applied force-displacement curves of each panel type under the three lateral pressures.

Evaluating applied force capacity under combined axial and lateral loading provides critical insights into the structural integrity of stiffened panels. For the steel panel, the ultimate applied force was recorded as 877 kN at 0 kPa lateral pressure, decreasing slightly to 862 kN at 50 kPa and 845 kN at 100 kPa. The aluminium panel demonstrated an ultimate applied force of 883 kN at 0 kPa, dropping sharply to 841 kN at 50 kPa and 811 kN at 100 kPa.

These results underline the consistent reduction in load-bearing capacity with increasing lateral pressure for both materials. However, the aluminium panel exhibits greater sensitivity to lateral loading. For instance, the steel panel’s applied force capacity reduces by 1.71% when lateral pressure increases from 0 to 50 kPa and by 3.64% when lateral pressure reaches 100 kPa. In contrast, the aluminium panel experiences 4.75% and 8.16% reductions over the same pressure increments, highlighting its heightened vulnerability to combined loading conditions.

This difference can be attributed to material properties such as elasticity and yield strength, which influence the structural response under lateral pressure. Aluminium’s higher strength-to-weight ratio of 45.43 kN/kg compared to steel’s 18.60 kN/kg at 0 kPa demonstrates its efficiency in weight-sensitive applications like aerospace or automotive structures. However, the more pronounced reductions in aluminium’s force capacity under lateral loading suggest it may require additional reinforcement or design considerations in high-pressure environments.

In the second phase, honeycomb sandwich panels with varying cell edge lengths of 20 mm, 25 mm, and 30 mm are assessed under pure uniaxial compression. The force-displacement curves for the different configurations, as shown in Figure 11, highlight the maximum load capacities achieved for each design. The panels with a 20 mm cell edge length exhibited the highest load capacity of 1156.3 kN, followed by the 25 mm configuration with 943.66 kN and the 30 mm configuration with the lowest capacity of 898.02 kN. Significantly, all configurations exceeded the design limit of 883 kN set by the aluminium stiffened panel, highlighting the enhanced load-bearing capabilities of the honeycomb panels under uniaxial compression.

The weight of the panels was also assessed to determine their efficiency. As the cell edge length increased, the panel weight decreased due to reduced material usage. Specifically, the weights of the panels were 18.261 kg for the 20 mm configuration, 16.838 kg for 25 mm, and 15.928 kg for 30 mm. This represents a weight reduction of approximately 16% from the smallest to the most significant cell edge length. Comparing the results, the 30 mm configuration emerges as a balanced design, offering a competitive load capacity while being the lightest weight.

The final phase focused on analysing the impact of lateral pressure on honeycomb panels with core heights of 30 mm, 45 mm, and 60 mm, building on the 30 mm cell edge length configuration identified as the baseline for evaluation. The eigenvalue buckling results for the honeycomb sandwich panel selected from a range of configurations, with a 30 mm wall cell length and 30 mm core height, are shown in Figure 12.

Figure 13, Figure 14 and Figure 15 present the representative deformed shapes from the nonlinear simulations of honeycomb sandwich panels with a cell length of 30 mm and core heights of 30 mm, 45 mm, and 60 mm, considering both 0 kPa and 100 kPa lateral pressures for each panel. As the lateral pressure increases, panels with higher core heights (hc45 and hc60) experience more significant deformation, demonstrating the effect of core height on panel behaviour under different loading conditions. Specifically, at a maximum lateral pressure of 100 kPa, the deflection for the core height of 30 mm is 10.44 mm; for 45 mm, the core height is 6.58 mm; and for 60 mm, the core height is 5.45 mm.

The deformed shapes shown in Figure 13b, Figure 14b and Figure 15b are not perfectly symmetric concerning the centre of the panel due to the inclusion of material nonlinearity, geometric nonlinearity, initial imperfections, and the combined effects of uniaxial load and lateral pressure in the analysis.

The results summarised in

Table 5. Peak force (N) and percentage reduction under varying lateral pressures.

Core Height (hc)	Lateral Pressure (kPa)	Peak Force (KN)	Reduction from 0 kPa (%)
	0 kPa	905.34	-
30 mm	50 kPa	902.29	0.34%
	100 kPa	890.93	1.59%
	0 kPa	897.55	-
45 mm	50 kPa	896.50	0.12%
	100 kPa	894.64	0.32%
	0 kPa	902.19	-
60 mm	50 kPa	901.51	0.08%
	100 kPa	899.78	0.27%

indicate a consistent reduction in peak force with increasing lateral pressure for all panels, with the extent of reduction varying across core heights. Figure 16 presents the force-displacement curves for each model, offering a detailed visualisation of the structural response under different lateral pressure levels.

Our results revealed noticeable differences in sensitivity to lateral loading. Panels with the most diminutive core height (30 mm) exhibited the most significant reduction in peak force (1.59%) as lateral pressure increased from 0 to 100 kPa. This reduction can be attributed to the limited structural depth, which compromises stability under compressive stress.

Panels with medium (45 mm) and large (60 mm) core heights demonstrated superior resistance to lateral pressure, with reductions in the peak force of 0.32% and 0.27%, respectively. The increased core height provided enhanced stiffness and improved stress distribution, significantly mitigating the effects of lateral pressure. Notably, the 60 mm core height panel offered the most robust performance, maintaining structural integrity even under combined loading conditions.

5. Conclusions

This comprehensive study highlights the critical interplay between material properties, geometric configurations, and loading conditions in optimising structural panel performance. Steel and aluminium stiffened panels reduced load-bearing capacity as lateral pressure increased, with aluminium panels initially exhibiting higher capacity but showing greater sensitivity to combined axial and lateral loading. This suggests that while aluminium may offer superior strength in initial conditions, its use in environments subjected to significant lateral pressure requires careful consideration.

Honeycomb sandwich panels performed exceptionally well under uniaxial compression, with all configurations surpassing the load capacity of the aluminium-stiffened panels. The 20 mm cell edge length design achieved the highest capacity but at the expense of increased weight. The 30 mm configuration emerged as the most balanced design, offering competitive strength while minimising material usage and weight, making it particularly well-suited for applications where weight efficiency is critical.

The impact of lateral pressure on panel performance was further investigated through variations in core height. Panels with more considerable core heights, especially the 60 mm configuration, demonstrated remarkable resistance to lateral pressure, with minimal reductions in peak force. This highlights the importance of core height in enhancing structural stability under combined axial and lateral loading.

These findings significantly affect the designing of lightweight, resilient marine structures subjected to coupled uniaxial and lateral loads. Steel and aluminium stiffened panels can be tailored for specific loading conditions. In contrast, honeycomb panels provide a versatile solution for applications requiring a balance between strength, weight efficiency, and resistance to lateral loads. Future research could explore additional geometric configurations, materials, and multiaxial loading conditions to optimise these design strategies further and support advancements in complex ship hull applications.