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The present work investigates the residual deformations arising from the curing process of composite curved parts and mitigation strategies to reduce them. Numerical simulations based on finite elements and refined structural theories are adopted and verified against closed-form solutions. The higher-order structural theories are based on the Carrera Unified Formulation, and one-dimensional models are built using layer-wise kinematics. The Cure-Hardening Instantaneously Linear Elastic constitutive model is used. The analytical formulation includes the effects of the final demolding and the in-plane deformations. Results consider spring-in and warping angles after the tool removal. The numerical efficiency of the one-dimensional model allows for thorough parametric analyses, and all the possible combinations of an eight-layer cross-ply laminate are considered. The results confirm that the in-plane deformation and the final demolding play a fundamental role in process-induced deformations. Furthermore, deformations can be significantly reduced by considering asymmetric laminates and localized composite patches. [ABSTRACT FROM AUTHOR]

AbstractHere, natural frequencies and mode shapes for axisymmetric vibration of the composite laminate shells of revolution have been considered using the Unified Carrera Formulation (CUF) approach. For the first time, results of natural frequencies and mode shapes of complex geometry shells such as spherical, parabolic, elliptical, hyperbolic, catenoidal, toroidal and pseudospherical have been presented. Calculations have been done for the first, second, third, fourth and fifth order models and a comparison with the classical Timoshenko model. We consider thick, moderately thick, moderately thin and thin composite laminate shells. The higher-order layer-wise models of elastic composite multilayer shells of revolution are developed using the variational principle of virtual power for the 3-D linear anisotropic elastodynamics and generalized series in the thickness coordinates. The higher-order composite axisymmetric spherical, paraboloidal, elliptical, hyperbolic, catenoidal, toroidal and pseudo-spherical shell fixed at the ends are considered. Numerical calculations were performed using the computer algebra software Mathematica. The resulting equations have been used for theoretical analysis and calculation of the eigenvalues and eigenmodes of the higher-order shells of revolution used in science, engineering, and technology. The results of calculation can be used as benchmark examples for finite element analysis of the higher-order composite laminate shells. [ABSTRACT FROM AUTHOR]

In this work, the wave propagation of Rayleigh type through a periodic elastic element covered with a T-plate is analyzed. Viscous-spring artificial boundaries are used to satisfy boundary conditions of a periodic structure. By using the Carrera Unified Formulation (CUF), the various kinematics of the three-dimensional structure are consistently expressed and the propagation of waves within the model is obtained. Lagrange expansion is employed to generate the mathematical model of the structure. The numerical evaluation and the comparison with the results obtained by the analytical method and COMSOL involving different structures reveal that the results of this study are reliable and show that the model developed provides accurate results for the analysis of the periodic elastic structure of T-plates. [ABSTRACT FROM AUTHOR]

Here, higher order models of elastic shells of revolution are developed using the variational principle of virtual power for 3-D equations of the linear theory of elasticity and generalized series in the coordinates of the shell thickness. Following the Carrera Unified Formulation (CUF), the stress and strain tensors, as well as the displacement vector, were expanded into series in terms of the coordinates of the shell thickness. As a result, all the equations of the theory of elasticity were transformed into the corresponding equations for the expansion coefficients in a series in terms of the coordinates of the shell thickness. All equations for shells of revolution of higher order are developed and presented here for cases whose middle surfaces can be represented analytically. The resulting equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. [ABSTRACT FROM AUTHOR]

Here, higher order models of elastic composite multilayer shells of revolution are developed using the variational principle of virtual power for the 3-D linear anisotropic theory of elasticity and generalized series in the shell thickness coordinates. Following the Unified Carrera Formula (CUF), the stress and strain tensors, as well as the displacement vector, were expanded into series in terms of the coordinates of the shell thickness. The higher-order cylindrical shell supported on the edges under axisymmetric loading, is considered and solved analytically using a Navier close form solution method. Also, composite axisymmetric circular plated as well as parabolic, hyperbolic and pseudo-spheric shell fixed ate the ends are considered. Numerical calculations were performed using the computer algebra software Mathematica. The resulting equations can be used for theoretical analysis and calculation of the stress-strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. The results of calculation can be used as benchmark examples for finite element analysis of the higher order elastic shells. [ABSTRACT FROM AUTHOR]

It is shown that the classical theories of micropolar plates and shells can be obtained using the Carrera Unified Formulation (CUF) approach as a special case of approximation. The theory of micropolar plates and shells based on the hypotheses of Timoshenko–Mindlin and Kirchhoff–Love is considered in detail. The stress and strain tensors, as well as the displacement and rotation vectors are presented as linear expansion along the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including the generalized Hooke's law) were transformed into the corresponding equations for the expansion coefficients in the coordinates of the shell thickness. All equations of the theory of micropolar plates and shells based on the hypotheses of Timoshenko–Mindlin and Kirchhoff–Love are presented here. Micropolar plates in Cartesian and polar coordinates, as well as micropolar shells of cylindrical, conical, spherical and shallow geometry are considered in detail. The equations obtained can be used to calculate the stress-strain state and simulate thin-walled structures at the macro, micro and nanoscale, taking into account the micropolar stresses and the effects of rotation. [ABSTRACT FROM AUTHOR]

Starting from the variational principle of virtual power for the three-dimensional equations of the micropolar theory of elasticity and using generalized series in terms of the plate thickness coordinates a new higher order models of orthotropic micropolar plates have been developed here for the first time. Following carrera unified formulation, the stress and strain tensors, as well as the vectors of displacements and rotation, have been expanded into series in terms of the plate thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the series expansion on the plate thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the series expansion of the plate thickness coordinates have been obtained in the same way as in the classical theory of elasticity. All equations for the higher order theory of micropolar plates have been developed and presented here. The case of complete linear expansion has been considered in detail and compared with the theories based on shear deformation and Kirchhoff hypothesis. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

New higher-order models of orthotropic micropolar plates and shells have been developed using Carrera Unified Formulation (CUF). Here, a complete linear expansion case (CLEC) has been considered in detail. The stress and strain tensors, as well as the vectors of displacements and rotation, have been presented as linear expansion in terms of the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the expansion on the shell thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the expansion of the shell thickness coordinates has been obtained. All equations for the case of CLEC theory of micropolar plates and shells have been developed and presented here. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

Starting from the variational principle of virtual power for the 3-D equations of the micropolar theory of elasticity in orthogonal curvilinear coordinates and using generalized series in terms of the plate thickness coordinates a new higher order model of orthotropic micropolar plates and shells have been developed here. Following Carrera Unified Formulation (CUF), the stress and strain tensors, as well as the vectors of displacements and rotation, have been expanded into series in terms of the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the series expansion on the plate thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the series expansion of the shell thickness coordinates have been obtained in the same way as in the classical theory of elasticity. All equations for the higher order theory of micropolar plates and shells have been developed and presented here. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

New higher order models of micropolar beams, which is based on Carrera unified formulation have been developed here. The higher order theory is based on a variational principle of virtual power and the expansion of the 3D equations of the micropolar theory of elasticity into generalized series in terms of cross-section coordinates. The stress and strain tensors, as well as vectors of displacements and rotation, have been expanded into series in terms of cross-section coordinates. Thereby, all equations of the micropolar theory of elasticity (including generalized Hooke's law) have been transformed to the corresponding equations for the coefficients of the series of cross-section coordinates. Then, in the same way, as in the classical theory of elasticity, a system of differential equations in terms of displacements and rotation with boundary conditions for the coefficients of the series of cross-section coordinates have been obtained. All equations for higher order theory of micropolar plates have been developed and presented here. The case of complete linear expansion has been considered in detail. The obtained equations can be used for calculating the stress–strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects. [ABSTRACT FROM AUTHOR]

Here, higher order layer-wise models of elastic composite multilayer plates and shells of revolution are developed using the variational principle of virtual power for the 3-D linear anisotropic theory of elasticity and generalized series in the thickness coordinates. Following the Unified Carrera Formulation (CUF), the stress and strain tensors, as well as the displacement vector, were expanded into series in terms of the coordinates of the shell thickness. The higher-order rectangular plate and cylindrical shell supported on the edges under sinusoidal loading, are considered and solved analytically using a Navier close form solution method. Also, composite axisymmetric conical, spherical, elliptical and catenoidal shell fixed at the ends are considered. Numerical calculations were performed using the computer algebra software Mathematica. The resulting equations can be used for theoretical analysis and calculation of the stress–strain state, as well as for modeling thin-walled structures used in science, engineering, and technology. The results of calculation can be used as benchmark examples for finite element analysis of the higher order composite laminate shells. [ABSTRACT FROM AUTHOR]

The paper presents results on the elastoplastic analysis of compact and thin-walled structures via refined beam models. The application of Carrera Unified Formulation (CUF) to perform elastoplastic analysis of isotropic beam structures is discussed. Particular attention is paid to the evaluation of local effects and cross-sectional distortions. CUF allows formulation of the kinematics of a one-dimensional (1D) structure by employing a generalized expansion of primary variables by arbitrary cross-section functions. Two types of cross-section expansion functions, TE (Taylor expansion) and LE (Lagrange expansion), are used to model the structure. The isotropically work-hardening von Mises constitutive model is incorporated to account for material nonlinearity. A Newton–Raphson iteration scheme is used to solve the system of nonlinear algebraic equations. Numerical results for compact and thin-walled beam members in plastic regime are presented with displacement profiles and beam deformed configurations along with stress contour plots. The results are compared against classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory, reference solutions from literature, and three-dimensional (3D) solid finite element models. The results highlight: (1) the capability of the present refined beam models to describe the elastoplastic behavior of compact and thin-walled structures with 3D-like accuracy; (2) that local effects and severe cross-sectional distortions can be detected; (3) the computational cost of the present modeling approach is significantly lower than shell and solid model ones. [ABSTRACT FROM AUTHOR]

The present paper presents a refined one-dimensional finite element model with node-dependent kinematics. When this model is adopted, the beam theory can be different at each node of the same element. For instance, in the case of a 2-node beam element the Euler-Bernoulli theory could be used for node 1 and the Timoshenko beam theory could be used for node 2. Classical and higher-order refined models have been established with the Carrera Unified Formulation. Such a capability would allow the kinematic assumptions to be continuously varied along the beam axis, that is, no ad hoc mixing techniques such as the Arlequin method would be required. Different combinations of structural models have been proposed to account for different kinematic approximations of beams, and, beam models based on the Taylor and the Lagrange expansions have in particular been used. The numerical model has been assessed, and a number of applications to thin-walled structures have been proposed. The results have been compared with those obtained from uniform kinematic models and convergence analyses have been performed. The results show the efficiency of the proposed model. The high accuracy of refined one-dimensional models has been preserved while the computational costs have been reduced by using refined models only in those zones of the beam that require them. [ABSTRACT FROM AUTHOR]

This article deals with free vibration analysis of thin-walled structures reinforced by longitudinal stiffeners using refined one-dimensional (1D) models.The 1D theory, which is used in the present article, has hierarchical features and it is based on the Carrera Unified Formulation (CUF). The displacement field over the cross section is obtained by means of Taylor (TE) or Lagrange (LE) expansions. Finite element (FE) method is applied along the beam axis to obtain weak form solutions of the related governing equations. The obtained results are compared with those from classical finite element formulations based on plate and shell (2D), beam (1D), and solid (3D) elements that are available in commercial software. When solid formulation is used to build the FE solutions, stringers and skin are modeled with only 3D elements while, in the 2D-1D FE models, shell and beam elements are used for skin and stringers, respectively. Three benchmark problems are analyzed: a flat plate, a curved panel, and a thin-walled cylinder. When TE models are used, different orders of expansion, N, are considered, where N is a free parameter of the formulation. As far as Lagrange expansions are concerned, four-node (LE 4) and nine-node (LE 9) elements are used to build different meshes on the cross section. The results show that the present 1D models are able to analyze the dynamic behavior of complex structures and can detect 3D effects as well as very complex shell-like modes typical of thin-walled structures. Moreover, the 1D-CUF elements yield accurate results with a low number of degrees of freedom. [ABSTRACT FROM PUBLISHER]

The objective of the present work is to investigate progressive damage in fibre-reinforced composites under varying load conditions, and in particular transverse impact loads, using a global–local approach. The numerical models are built using higher-order structural theories based on the Carrera Unified Formulation (CUF). The Node-Dependent Kinematics (NDK) technique, an intrinsic feature of CUF models, is employed which enables the selective refinement of critical regions of interest within the structure and results in a global–local analysis. Progressive damage is governed by the CODAM2 material model, which is based on continuum damage mechanics. A series of numerical assessments are performed on composite laminates under varying load conditions, and predicted results of the global–local analysis are found to be in good agreement with experimental data, thereby validating the proposed approach. A comparison of its performance with reference high-fidelity CUF models of the full structure demonstrates the computational efficiency that can be achieved using the CUF-NDK global–local approach. [ABSTRACT FROM AUTHOR]

This article proposes a complex application of a refined electro-mechanical beam formulation. Lagrange-type polynomials are used to interpolate the unknowns over the beam cross section. Three- (L3), four- (L4), and nine-point (L9) polynomials, which lead to linear, bi-linear, and quadratic displacement field approximations over the beam cross-section, are considered. Finite elements are obtained by employing the principle of virtual displacement in conjunction with the Carrera unified formulation (CUF). With the CUF application, the finite element matrices and vectors are expressed in terms of fundamental nuclei whose forms do not depend on the assumption made (L3, L4, or L9). Additional refined beam models are implemented by introducing further discretizations over the beam cross-section. Some assessments from the bibliography have been considered in order to validate the electro-mechanical formulation. Complex three-dimensional geometries have been studied in order to demonstrate the capabilities of the present formulation. [ABSTRACT FROM PUBLISHER]

This paper proposes a refined electro-mechanical beam formulation. Lagrange-type polynomials are used to interpolate the unknowns over the beam cross section. Three-(L3), four-(L4), and nine-point(L9) polynomials are considered which lead to linear, bi-linear, and quadratic displacement field approximations over the beam cross-section. Finite elements are obtained by employing the principle of virtual displacements in conjunction with the Carrera Unified Formulation (CUF). The finite element matrices and vectors are expressed in terms of fundamental nuclei whose forms do not depend on the assumptions made. Additional refined beam models are implemented by introducing further discretizations, over the beam cross-section. Some assessments from bibliography have been solved in order to validate the electro-mechanical formulation. The investigations conducted show that the present formulation is able to detect the electro-mechanical interaction. [ABSTRACT FROM AUTHOR]

This work deals with a refined Finite Element (FE) analysis of multilayered plates. Various two-dimensional axiomatic assumptions in the thickness direction are illustrated and discussed by considering: 1-Taylor type expansion; 2-combinations of Legendre polynomials; 3-Lagrange polynomials. Both cases of an equivalent single layer description (the whole plate is seen as an equivalent single layer) and a layer-wise description (each layer is seen as an independent plate) have been implemented. The order N of the thickness expansions is a free parameter of the present formulation. A large variety of plate theories are therefore obtained. Related standard serendipity-type quadrilateral FEs are considered in this paper. FE matrices are written in a concise form by referring to the Carrera Unified Formulation and in terms of a few fundamental nuclei, whose form does not depend on the through-the-thickness polynomial assumption, order N, variable description or element number of nodes. The advantages and disadvantages of the various FEs are discussed by considering static and dynamic problems related to significant multilayered plate problems. [ABSTRACT FROM AUTHOR]

This paper presents numerical results on the micromechanical linear analysis of representative volume elements (RVE) containing voids. The modeling approach is the micromechanical framework within the Carrera Unified Formulation in which fibers and matrix are 1D finite elements (FE) with enriched kinematics and component-wise capabilities. RVE models are 3D and consider all six stress components. Such a modeling strategy leads to a twofold reduction of the degrees of freedom as compared to 3D FE. The numerical assessments address the influence of the volume fraction and distribution of voids, including comparisons with data from the literature and statistical studies regarding homogenized properties and stress fields. The proposed modeling approach can capture the local effects due to the presence of voids, and, given its computational efficiency, the present framework is promising for nonlinear analysis, such as progressive failure. [ABSTRACT FROM AUTHOR]

The present work deals with the progressive damage analysis of composite laminates subjected to low-velocity impact. We develop a numerical model using higher-order structural theories based on the Carrera Unified Formulation (CUF) with Lagrange polynomials and resulting in a 2D refined layer-wise model. To model damage, we use a combination of the continuum damage-based CODAM2 intralaminar damage model to account for fibre and matrix damage within the ply, and cohesive elements to account for delamination between successive composite plies. We carry out numerical assessments for the case of a linear elastic composite plate subjected to impact, to compare the current framework with standard approaches based on 3D finite element (FE) analysis. We, then, consider the elastoplastic analysis of a bimetallic laminated plate to compare the performance of the proposed layer-wise model and 3D-FE approaches, for the case of nonlinear impact analysis. The final assessment considers progressive damage due to low-velocity impact, and the results are compared with available literature data. The numerical predictions show a good correlation with reference experimental and simulation results, thus validating the current framework for impact analysis of composite structures. Comparisons of the proposed layer-wise structural models with those based on 3D finite elements demonstrate the improved computational efficiency of the CUF models in terms of model size and analysis time. • This work presents the progressive damage analysis of composite laminates subjected to low-velocity impact. • The emphasis is on the use of higher-order 2D elements with layer-wise capabilities. • The results show the ability of 2D models of accurately evaluating damage mechanisms. • The results are in good agreement with reference 3D finite element solutions with significantly lower computational costs. • There is a good agreement with experimental results. [ABSTRACT FROM AUTHOR]

This work presents a refined beam model based on the Carrera Unified Formulation for the free-vibration analyses of variable stiffness composite laminate characterized by layers with curvilinear fibers. These models introduce a refined kinematic description over the cross-section to obtain a 3D displacement field. Taylor and Lagrange polynomials have been used to describe the cross-sectional variables that is, equivalent single layer and layer-wise approaches have been considered. Variable stiffness composite materials have been introduced considering a continuous variation of the lamination angle thanks to an ad hoc integration scheme. Extensive validation of the models has been performed including convergence analyses and comparisons with commercial codes. The results obtained using the present models have been compared with those from open literature considering composites with different values of thickness, lamination, and boundary conditions. The results show that the use of refined models is mandatory for the analysis of such structures where complex laminations may create strong mechanical couplings. [ABSTRACT FROM AUTHOR]

This work presents the free vibration analysis of tapered aircraft structures made of composite and metallic materials, with reference to global and local damage. A refined one-dimensional model, developed in the framework of the Carrera Unified Formulation, has been used to provide a detailed description of structures. Multi-component aeronautical structures have been modeled adopting Lagrange polynomials to evaluate the displacement field over the cross-section. Each component has been described through the component-wise approach, with its own geometrical and mechanical characteristics. The effects of localized damage have been investigated, thanks to the accuracy of the layer-wise models adopted. The model has been assessed by comparing the results with classical FE models. The results show that the present approach provides an accurate solution for the free vibration analyses of complex structures and is able to predict the consequences of a global or local failure of a structural component. The computational efficiency and the accuracy of the model used in this work can be exploited to characterize the dynamic response of complex composite structures considering a large number of damage configurations. [ABSTRACT FROM AUTHOR]

This paper presents the results of a static analysis on reinforced thin-walled tapered structures using refined one-dimensional models. The structural model is based on a one-dimensional formulation derived from the Carrera Unified Formulation. This formulation provides a quasi three-dimensional solution, thanks to the use of polynomial expansions to describe the displacement field over the cross-section. According to which type of expansion is used, various classes of refined one-dimensional elements are obtained. Lagrange expansions were used in this work. The use of these models allows each structural component to be considered separately; this methodology is called the component-wise approach. After an initial assessment of the structural model, different kinds of aeronautical structures, which gradually become more complex, have been studied. The stress and displacement fields have been obtained. The results have been compared with those obtained using commercial tools. Three- and two-dimensional models have been used for comparison purposes. The results show the capability of the present advanced one-dimensional models to achieve accurate results while avoiding high computational costs. [ABSTRACT FROM AUTHOR]

The present work applies the global–local technique to the progressive damage analysis of fiber-reinforced composite laminates. A one-way, loosely-coupled global–local approach is developed as a combination of a low-fidelity linear global analysis and a high-fidelity local nonlinear analysis of specific regions within the structure, where damage is expected to occur. The local model is based on higher-order structural theories derived using the Carrera Unified Formulation (CUF), and specifically, Lagrange polynomials are used to model each ply through its thickness, leading to a layer-wise model. Composite damage is described using the CODAM2 material model, which is based on continuum damage mechanics. Initial assessments compare the relative performance of 3D finite elements (FE), 1D-CUF, and the proposed global–local approach via the free-edge stress analysis of a stiffened composite plate. The proposed technique is then used to predict the tensile strength of an open-hole specimen. The last assessment simulates damage progression within an over-height compact tension specimen using the global–local approach. Verification and validation of results are carried out via refined models and experiments from literature. The results demonstrate the accurate evaluation of 3D stress fields and composite laminates' mechanical response in the progressive damage regime. A multi-fold improvement in the computational cost is shown when compared to full-scale CUF analyses and indicates this technique's strong potential towards the computationally-efficient high-fidelity analysis of complex and large-scale composite structures. • A global–local approach is used to evaluate damage onset and propagation in composite laminates. • The global model is 3D-FE from ABAQUS with coarse meshes. • The local model is 2D or 1D with layer-wise capabilities, and CODAM2 is used for the damage modeling. • Linear and nonlinear cases were considered. • The global–local approach has similar accuracy as a full global model but leads to significant reductions in the computational time. [ABSTRACT FROM AUTHOR]

Structural theories based on 1D component-wise models are proposed to investigate the progressive disbonding in sandwich structures. The structural framework adopts the Carrera Unified Formulation to generate higher-order theories of structures via a variable kinematic approach. The component-wise approach, formulated within the Lagrange polynomial based CUF models, permits modelling of various components of a complex structure through 1D CUF models at reduced computational costs and 3D accuracy. The disbonding constitutive models are retrieved from well-established works in the literature and based on cohesive elements. The results verify the accuracy of 1D models with some 10–20% computational time as compared to 3D finite elements. [ABSTRACT FROM AUTHOR]

This work focuses on deriving guidelines for choosing structural theories for composite shells using Convolutional Neural Networks (CNN). The Axiomatic/Asymptotic Method (AAM) is used to evaluate higher-order structural theories' accuracy and computational efficiency based on polynomial expansions. AAM exploits the Carrera Unified Formulation to derive the finite element matrices and obtain natural frequencies. The outcomes of AAM concerning the accuracy and computational cost are used to train CNN for various composite shell configurations. The trained network can then be used as a substitute for finite element models to estimate the accuracy of a given structural theory. The results are provided via Best Theory Diagrams (BTD), in which the set of generalized displacement variables to retain the best accuracy can be read for a given amount of nodal degrees of freedom. Verification is carried out using results from FEM. The results proved the computational efficiency of CNN and highlighted the influence of the shell thickness for the proper choice of the structural theory. Third-order terms and transverse stretching are often necessary to obtain acceptable accuracy. • The accuracy of a structural theory is problem-dependent. • The selection process for the optimal modeling strategy can be a challenging task. • The synergistic use of machine learning and Carrera Unified Formulation can reduce the complexity of the selection process. [ABSTRACT FROM AUTHOR]

This work presents contact problems of laminated structures via the Carrera Unified Formulation (CUF). The modeling approach makes use of higher-order 1D elements accounting for transverse shear and stretching. The current work considers normal, frictionless contact based on a node-to-node formulation, and the penalty approach to enforce the contact constraints. Numerical assessments compare classical beam theories, higher-order CUF, and 3D finite element models regarding solution accuracy, computational size, and time required for the analysis. The results show the validity of Layer-Wise CUF models to capture both global and local deformations accurately, which is a shortcoming of classical beam theories, and require at least an order of magnitude fewer degrees of freedom and computational time than a full 3D finite element analysis. Particularly relevant are the accurate distributions of transverse shear stress and stretching along the thickness in the perspective of failure analyses. [ABSTRACT FROM AUTHOR]

• This work presents the numerical analysis of elastoplastic contact problems of compact and thin-walled metallic structures. • The emphasis is on the use of higher-order 1D elements with pure displacement variables to capture localized effects and cross-sectional distortions. • The results show the ability of 1D models of accurately evaluating localized deformations and plasticity. • The results are in good agreement with reference 3D finite element solutions and require an order of magnitude fewer degrees of freedom and analysis time. This work presents the numerical analysis of elastoplastic contact problems of compact and thin-walled metallic structures. The emphasis is on the use of higher-order 1D elements with pure displacement variables and based on the Carrera Unified Formulation (CUF) to capture localized effects and cross-sectional distortions. Contact interactions are normal and frictionless via a node-to-node contact algorithm with the penalty approach for contact enforcement. The analysis considers the material nonlinearity via the von Mises constitutive law. Numerical assessments compare the CUF solutions with 3D finite element analysis concerning the solution quality, computational size, and analysis time. The results show the ability of 1D CUF models of accurately evaluating localized deformations and plasticity. The CUF results are in good agreement with reference 3D finite element solutions, and require an order of magnitude fewer degrees of freedom and analysis time, making them computationally efficient. [ABSTRACT FROM AUTHOR]

Abstract The objective of the current work is to perform a failure evaluation of fiber composite structures based on failure indices computed using the Hashin 3D failure criterion. The analysis employs 1D and 3D finite elements. 1D elements use higher-order structural theories from the Carrera Unified Formulation based on Lagrange expansions of the displacement field. The 3D model analysis exploits ABAQUS. Attention is paid to the free-edge effects, the mode of failure initiation - matrix or fiber tension, delamination -, and the loads at which first ply failure occurs. The results underline the paramount importance of out-of-plane stress components for accurate prediction and the computational efficiency of refined 1D models. In fact, 1D models lead from one to twofold reductions of the CPU time if compared to 3D models. [ABSTRACT FROM AUTHOR]

A computationally efficient framework has been developed for the elastoplastic analysis of compact and thin-walled structures using a combination of global-local techniques and refined beam models. The theory of the Carrera Unified Formulation (CUF) and its application to physically nonlinear problems are discussed. Higher-order models derived using Taylor and Lagrange expansions have been used to model the structure, and the elastoplastic behavior is described by a von Mises constitutive model with isotropic work hardening. Comparisons are made between classical and higher-order models regarding the deformations in the nonlinear regime, which highlight the capabilities of the latter in accurately predicting the elastoplastic behavior. The concept of global-local analysis is introduced, and two versions are presented - the first where physical nonlinearity is considered for both the global and local analyses, and the second where nonlinearity is considered only for the local analysis. The second version results in reasonably accurate results compared to a full 3D finite element analysis, with a twofold reduction in the number of degrees of freedom. [ABSTRACT FROM AUTHOR]

This paper presents Best Theory Diagrams (BTDs) constructed from various non-polynomial terms to identify best plate theories for metallic and functionally graded plates. The BTD is a curve that provides the minimum number of unknown variables necessary to obtain a given accuracy or the best accuracy given by a given number of unknown variables. The plate theories that belong to the BTD have been obtained using the Axiomatic/Asymptotic Method (AAM). The different plate theories reported are implemented by using the Carrera Unified Formulation (CUF). Navier-type solutions have been obtained for the case of simply supported plates loaded by a bisinusoidal transverse pressure with different length-to-thickness ratios. The BTDs built from non-polynomial functions are compared with BTDs using Maclaurin expansions. The results suggest that the plate models obtained from the BTD using non-polynomial terms can improve the accuracy obtained from Maclaurin expansions for a given number of unknown variables of the displacement field. [ABSTRACT FROM AUTHOR]

A refined progressive damage analysis of fiber-reinforced laminated composites subjected to compressive loads is presented here. The numerical analysis exploits higher-order theories developed using the Carrera Unified Formulation, specifically 2D plate theories with Lagrange polynomials to enhance the kinematic approximation through each ply's thickness resulting in a layer-wise structural model. The CODAM2 material model, based on continuum damage mechanics, governs the intralaminar composite damage. The Hashin criteria and the crack-band approach provides failure initiation and propagation, respectively. Fiber micro-buckling and kinking is taken into account via the use of nonlinear post-peak softening models. It is shown that linear-brittle stress-strain softening is effective for accurate compressive strength predictions. A series of numerical assessments on coupon-level composite laminates is carried out to verify the proposed numerical framework while its validation is demonstrated by successfully applying the numerical tool to test cases for which experimental data is available from the literature. Various through-the-thickness structural models are evaluated to provide insights for proper modeling. Numerical assessments considered quasi-isotropic laminates, the compressive strength and size-effects under brittle fracture of notched laminates, and progressive damage characteristics due to stable crack growth in compact compression tests. The results show the possibility of using coarser meshes than those used in standard FEM approaches as the accuracy of predictions is preserved through the use of higher-order structural theories. [ABSTRACT FROM AUTHOR]

The objective of the current work is the development of a numerical framework for the simulation of damage in composite structures using explicit time integration. The progressive damage is described using a Continuum Damage Mechanics (CDM) based material model, CODAM2, in which the damage initiation and progression are modelled using Hashin's failure criteria and crack-band theory, respectively. The structural modelling uses higher-order theories based on the Carrera Unified Formulation (CUF). The current work considers 2D-CUF models where Lagrange polynomials are used to represent the displacement field through the thickness of each ply, resulting in a layer-wise element model. Numerical assessments are performed on coupon-level specimens, and the results are shown to be in good agreement with reference numerical predictions and experimental data, thus verifying the current implementation for progressive tensile damage. The capability of the proposed framework in increasing the polynomial expansion order through the ply thickness, and its influence on the global behaviour of the structure in the damaged state, is demonstrated. The advantages of using higher-order structural models in achieving significant improvements in computational efficiency are highlighted. [ABSTRACT FROM AUTHOR]