Search Results (14)

The structural design of aeronautical composite components requires numerical models which capture multilayer behaviour while keeping computational costs manageable. High-fidelity three-dimensional (3D) finite element models are often too expensive for systematic optimisation, whereas classical 1D and 2D formulations rely on simplifying assumptions. This work investigates the Carrera Unified Formulation (CUF) as a cost-effective composite simulation tool, using Equivalent Single-Layer (ESL) and Layer-Wise (LW) beam models whose hierarchical cross-sectional expansions approximate 2D/3D behaviour within a one-dimensional framework. A representative composite stiffened panel is analysed to compare 3D solid, 2D shell, CUF-ESL, and CUF-LW models in terms of static response and computational cost. High-order CUF-ESL models reproduce 3D strain fields with 2–7% error while reducing analysis time by over 89%. The CUF–FEM framework is then integrated into a gradient-based optimisation scheme with Automatic Differentiation, adjoint sensitivities, and Kreisselmeier–Steinhauser constraint aggregation. Panel optimisation achieves a 64% mass reduction in six iterations with CUF-ESL, compared with 56% in 18 iterations for the 2D shell model. The results prove that CUF-ESL beam models are a computationally cost-effective tool for preliminary sizing of composite structures. Full article

The combination of variable-angle tow composites with shell geometries presents significant potential in various engineering and technical applications, particularly with regard to structural performance. Nevertheless, the numerical modeling of these structures can be challenging, as the larger number of unknowns significantly increases computational effort. The Carrera’s unified formulation has demonstrated promising results in the analysis of plates and shells reinforced with curvilinear fibers, offering an effective balance between numerical accuracy and the number of variables. This paper extends the unified formulation to more complex variable-angle tow shell structures characterized by variable curvature radii within their physical domain. The governing equations of the dynamic problem are derived using a displacement-based variational method, and the results are validated through comparisons with reference solutions from Abaqus 3D models. The First-Order Shear Deformation Theory (FSDT) is presented for a broader comparison of the proposed models. The maximum percentage error in terms of frequency shift observed for the FSDT model is $3.44\%$, whereas the corresponding error for the most refined model is only $0.19\%$. Across all examined cases, the computed fundamental frequencies and mode shapes closely match the reference results, demonstrating the reliability and effectiveness of the proposed method. Full article

This work develops and validates a high-order, three-dimensional Carrera Unified Formulation (CUF) framework for coupled structural–acoustic eigenanalysis, aiming at accurate low-frequency modal characterization of interior cavity-structure systems with significantly reduced degrees of freedom. The proposed approach employs high-order polynomial expansions to discretize both the structural and fluid domains. The methodology integrates fully coupled fluid-structure analyses into a unified variational formulation, enabling the systematic assembly of global stiffness and mass matrices via sophisticated numerical integration techniques. Validation against a Comsol Multiphysics benchmark model confirms that the CUF-based high-order frameworks converge with significantly fewer degrees of freedom and reliably capture the intricate interactions at the fluid–structure interface. In addition, the approach is versatile, accommodating a range of boundary conditions and material models, underscoring its broad applicability in modern engineering design. Overall, this work advances the state of the art in vibroacoustic analysis by offering a robust tool for predicting natural frequencies and mode shapes, and it lays the groundwork for future extensions to nonlinear, transient, and data-driven applications. Full article

This paper investigates the dynamic behavior of shell structures presenting variable-angle tow laminations. The choice of placing fibers along curvilinear patterns allows for a broader structural design space, which is advantageous in several engineering contexts, provided that more complex numerical analyses are managed. In this regard, Carrera’s unified formulation has been widely used for studying variable-angle tow plates and shells. This article aims to expand this formulation through the derivation of the complete formulation for a generic shell reference surface. The principle of virtual displacements is used as a variational statement for obtaining, in a weak sense, the stiffness and mass matrices within the finite element solution method. The free vibration problem of singly and doubly curved variable-angle tow shells is then addressed. The proposed approach is compared to Abaqus three-dimensional reference solutions and classical theories to investigate the effectiveness of the developed models in predicting the vibrational frequencies and modes. The results demonstrate a good agreement between the proposed approach and reference solutions. Full article

Variable-Angle Tow (VAT) laminates can improve straight fiber composites’ mechanical properties thanks to the application of curvilinear fibers. This characteristic allows one to achieve ambitious objectives for design and performance purposes. Nevertheless, the wider design space and the higher number of parameters result in a more complex structural problem. Among the various approaches that have been used for VAT study, Carrera’s Unified Formulation (CUF) allows one to obtain multiple theories within the same framework, guaranteeing a good compromise between the results’ accuracy and the computational cost. In this article, the linear buckling behavior of VAT laminates is analyzed through the extension of CUF 2D plate models within Reissner’s Mixed Variational Theorem (RMVT). The results show that RMVT can better approximate the prebuckling nonuniform stress field of the plate when compared to standard approaches, thus improving the prediction of the linear buckling loads of VAT composites. Full article

Variable Angle Tow (VAT) laminates offer a promising alternative to classical straight-fiber composites in terms of design and performance. However, analyzing these structures can be more complex due to the introduction of new design variables. Carrera’s unified formulation (CUF) has been successful in previous works for buckling, vibrational, and stress analysis of VAT plates. Typically, one-dimensional (1D) and two-dimensional (2D) CUF models are used, with a linear law describing the fiber orientation variation in the main plane of the structure. The objective of this article is to expand the CUF 2D plate finite elements family to perform free vibration analysis of composite laminated plate structures with curvilinear fibers. The primary contribution is the application of Reissner’s mixed variational theorem (RMVT) to a CUF finite element model. The principle of virtual displacements (PVD) and RMVT are both used as variational statements for the study of monolayer and multilayer VAT plate dynamic behavior. The proposed approach is compared to Abaqus three-dimensional (3D) reference solutions, classical theories and literature results to investigate the effectiveness of the developed models. The results demonstrate that mixed theories provide the best approximation of the reference solution in all cases. Full article

In this paper, we present a novel and unified model for studying the vibration of cylindrical shells based on the three-dimensional (3D) elastic theory and the Carrera Unified Formulation. Our approach represents a significant advancement in the field, as it enables us to accurately predict the vibrational behavior of cylindrical shells under arbitrary boundary conditions. To accomplish this, we expand the axial, circumferential, and radial displacements of the shell using Chebyshev polynomials and Taylor series, thereby reducing the dimensionality of the expansion and ensuring the precision and rigor of our results. In addition, we introduce three groups of artificial boundary surface springs to simulate the general end boundary conditions of the cylindrical shell and coupling springs to strongly couple the two surfaces of the cylindrical shell φ = 0 and φ = 2π to ensure continuity of displacements on these faces. Using the energy function of the entire cylindrical shell model, we obtain the characteristic equation of the system by finding the partial derivatives of the unknown coefficients of displacement in the energy function. By solving this equation, we can directly obtain the vibration characteristics of the cylindrical shell. We demonstrate the convergence, accuracy, and reliability of our approach by comparing our computational results with existing results in the literature and finite element results. Finally, we present simulation results of the frequency features of cylindrical shells with various geometrical and boundary parameters in the form of tables and figures. Overall, we believe that our novel approach has the potential to greatly enhance our understanding of cylindrical shells and pave the way for further advancements in the field of structural engineering. Our comprehensive model and simulation results contribute to the ongoing efforts to develop efficient and reliable techniques for analyzing the vibrational behavior of cylindrical shells. Full article

The present paper assessed the use of variable kinematic two-dimensional elements in the dynamic analysis of Lamb waves propagation in an isotropic plate with piezo-patches. The multi-field finite element model used in this work was based on the Carrera Unified Formulation which offers a versatile application enabling the model to apply the desired order theory. The used variable kinematic model allowed for the kinematic model to vary in space, thereby providing the possibility to implement a classical plate model in collaboration with a refined kinematic model in selected areas where higher order kinematics are needed. The propagation of the symmetric ($S_0$) and the antisymmetric ($A_0$) fundamental lamb waves in an isotropic strip was considered in both mechanical and piezo-elastic plate models. The convergence of the models was discussed for different kinematics approaches, under different mesh refinement, and under different time steps. The results were compared to the exact solution proposed in the literature in order to assess and further determine the effects of the different parameters used when dynamically modeling a Lamb wave propagating in such material. It was shown that the higher order kinematic models delivered a higher accuracy of the propagating wave evaluated using the corresponding Time Of Flight (TOF). Upon using the appropriate mesh refinement of 2000 elements and sufficient time steps of 4000 steps, the error between the TOF obtained analytically and numerically using a high order kinematics was found to be less than 1% for both types of fundamental Lamb waves $S_0$ and $A_0$. Node-dependent kinematics models were also exploited in wave propagation to decrease the computational cost and to study their effect on the accuracy of the obtained results. The obtained results show, in both the mechanical and the piezo-electric models, that a reduction in the computational cost of up to 50% can be easily attained using such models while maintaining an error inferior to 1%. Full article

This paper proposes a novel fully nonlinear refined beam element for pre-twisted structures undergoing large deformation and finite untwisting. The present model is constructed in the twisted basis to account for the effects of geometrical nonlinearity and initial twist. Cross-sectional deformation is allowed by introducing Lagrange polynomials in the framework of a Carrera unified formulation. The principle of virtual work is applied to obtain the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. In the nonlinear governing formulation, expressions are given for secant and tangent matrices with linear, nonlinear, and geometrically stiffening contributions. The developed beam model could detect the coupled axial, torsional, and flexure deformations, as well as the local deformations around the point of application of the force. The maximum difference between the present deformation results and those of shell/solid finite element simulations is 6%. Compared to traditional beam theories and finite element models, the proposed method significantly reduces the computational complexity and cost by implementing constant beam elements in the twisted basis. Full article

In the current research, variable angle tow composites are used to improve the buckling and free vibration behavior of a structure. A one-dimensional (1D) Carrera Unified Formulation (CUF) is employed to determine the buckling loads and natural frequencies in Variable Angle Tow (VAT) square plates by taking advantage of the layerwise theory (LW). Subsequently, the Genetic Algorithm (GA) optimization method is applied to maximize the first critical buckling load and first natural frequency using the definition of linear fiber orientation angles. To show the power of the genetic algorithm for the VAT structure, a surrogate model using Response Surface (RS) method was used to demonstrate the convergence of the GA approach. The results showed the cost reduction for optimized VAT performance through GA optimization in combination with the 1D CUF procedure. Additionally, a Latin hypercube sampling (LHS) method with RS was used for buckling analysis. The capability of LHS sampling confirmed that it could be employed for the next stages of research along with GA. Full article

In this study, the geometrically nonlinear behaviour caused by large displacements and rotations in the cross sections of thin-walled composite beams subjected to axial loading is investigated. Newton–Raphson scheme and an arc length method are used in the solution of nonlinear equations by finite element method to determine the mechanical effect. The Carrera-Unified formulation (CUF) is used to solve nonlinear, low or high order kinematic refined structure theories for finite beam elements. In the study, displacement area and stress distributions of composite structures with different angles and functionally graded (FG) structures are presented for Lagrange polynomial expansions. The results show the accuracy and computational efficiency of the method used and give confidence for new research. Full article

New concepts of lightweight components are conceived nowadays thanks to the advances in the manufacture of composite structures. For instance, mature technologies such as Automatic Fibre Placement (AFP) are employed in the fabrication of structural parts where fibres are steered along curvilinear paths, namely variable angle tow (VAT), which can enhance the mechanical performance and alleviate the structural weight. This is of utmost importance in the aerospace field, where weight savings are one of the main goals. For that reason, shell structures are commonly found in the aerospace industry because of their capabilities of supporting external loadings. Straight-fibre composite shell structures have been studied in recent decades and, now, spatially varying composite shells are attracting the attention of manufacturers. This work analyses the mechanical behaviour of VAT composite shells subjected to different external loadings and boundary conditions. The Carrera Unified Formulation (CUF) is employed to obtain the different structural models in a systematic and hierarchic manner. The outcomes of such numerical models are discussed and compared with commercial software Abaqus. Full article

It is well known that fabrication processes inevitably lead to defects in the manufactured components. However, thanks to the new capabilities of the manufacturing procedures that have emerged during the last decades, the number of imperfections has diminished while numerical models can describe the ground truth designs. Even so, a variety of defects has not been studied yet, let alone the coupling among them. This paper aims to characterise the buckling response of Variable Stiffness Composite (VSC) plates subjected to spatially varying fibre volume content as well as fibre misalignments, yielding a multiscale sensitivity analysis. On the one hand, VSCs have been modelled by means of the Carrera Unified Formulation (CUF) and a layer-wise (LW) approach, with which independent stochastic fields can be assigned to each composite layer. On the other hand, microscale analysis has been performed by employing CUF-based Mechanics of Structure Genome (MSG), which was used to build surrogate models that relate the fibre volume fraction and the material elastic properties. Then, stochastic buckling analyses were carried out following a multiscale Monte Carlo analysis to characterise the buckling load distributions statistically. Eventually, it was demonstrated that this multiscale sensitivity approach can be accelerated by an adequate usage of sampling techniques and surrogate models such as Polynomial Chaos Expansion (PCE). Finally, it has been shown that sensitivity is greatly affected by nominal fibre orientation and the multiscale uncertainty features. Full article

This paper aims to investigate the effect of the Winkler-Pasternak elastic foundation on the natural frequencies of Carbon Nanotube (CNT)-reinforced laminated composite plates and shells. The micromechanics of reinforcing CNT particles are described by a two-parameter agglomeration model. CNTs are gradually distributed along the thickness direction according to various functionally graded laws. Elastic foundations are modeled according to the Winkler-Pasternak theory. The theoretical model considers several Higher-order Shear Deformation Theories (HSDTs) based on the so-called Carrera Unified Formulation (CUF). The theory behind CNTs is explained in detail. The theoretical model presented is solved numerically by means of the Generalized Differential Quadrature (GDQ) method. Several parametric studies are conducted, and their results are discussed. Full article