Marguerre shell type secant matrices for the postbuckling analysis of thin, shallow composite shells

Geometrically nonlinear analysis of shallow shells using higher order finite elements

In this thesis, an attempt is made at studying the dynamic characteristics of a composite-moving beam.;The model considered is an overhang beam on simple supports oscillating in the longitudinal direction. The lateral response of the beam is studied due to an initial lateral deflection. The beam is made-up of laminated composite materials. Both symmetric and unsymmetrical lay ups are considered. Since unsymmetrical lay ups introduce bending-axial coupling, axial deformation needs to be considered also. First Order Shear Deformation theory (FSDT) is used to formulate the problem since transverse shear deformations are important for composite beams. When reducing laminate plate theory to corresponding beams, plane strain and plane stress assumptions are considered. Within the plane stress approximation, two ways of reduction from (x,y) equations to x-equations are possible. One is to set all y-related forces and moment resultants zero; other is to keep the cross resultants non zero. Also, as a comparison, results are obtained based on Classical Laminate Plate theory (CLPT). (Abstract shortened by UMI.).

In this study, an enhanced first order shear deformation theory via the strain energy transformation (EFSDT) in Laplace domain is presented for the efficient yet accurate viscoelastic FEM analysis of laminated composite plates. The main objective herein is to systematically derive the improved strain energy expression of first order shear deformation theory (FSDT) based on a conventional Reissner-Mindlin’s plate theory. To this end, an efficient higher order plate theory (EHOPT) is utilized to obtain the in-plane warping functions and synthesized into the strain energy of FSDT to improve their performance. The relationships between the two independent theories are systematically established via the strain energy transformation and the least-square approximation of the mean displacement. And the convolution theorem of Laplace transformation is applied to circumvent the overwhelming complexity of dealing with visco-elastic materials which is expressed as the Bolzmann superposition integral equation. The proposed EFSDT in Laplace domain has the same computational advantage of the conventional FSDT, while allowing us to improve the local distributions of the visco-elastic responses via the recovery procedure. The numerical results obtained herein are compared to those available in literature.

Nonlinear forced response of doubly-curved laminated panels composed of cnt patterned layers within first order shear deformation theory

Meshless implementation of arbitrary 3D-shell structures based on a modified first order shear deformation theory

Spectral finite element for wave propagation analysis of laminated composite curved beams using classical and first order shear deformation theories

Wavenumber dynamic stiffness formulation for exact dispersion analysis of moderately thick symmetric cross-ply laminated plate built-up waveguides

High performance 3D-analysis of thermo-mechanically loaded composite structures

This study presents the development and validation of an open-source finite element framework implemented in Python for the analysis of laminated composite plates using First Order Shear Deformation Theory (FSDT). The formulation employs graded quadrilateral meshing with eight-noded serendipity elements and incorporates full laminate constitutive modeling through computation of the A, B, and D stiffness matrices along with transverse shear effects. The framework enables automated geometry generation for plates with geometric discontinuities, global stiffness assembly, displacement solution, plylevel stress recovery, and contour visualization. To assess numerical accuracy, the developed solver is benchmarked against the layered shell formulation (SHELL181) in ANSYS under identical geometry, mesh density, material properties, boundary conditions, and loading. Comparisons are performed for in-plane and transverse displacements as well as normal stress components in laminated plies for a composite plate containing a central circular cutout. The Python-based results demonstrate strong agreement with the commercial solver, with displacement deviations below 1% and stress deviations within 5%. The study highlights the feasibility of using open-source computational tools for small- to medium-scale composite structural analyses, reducing dependency on high-cost licensed software for preliminary design studies and parametric investigations. Furthermore, the developed framework is extended toward the generation of high-fidelity finite element datasets to enable data-driven modeling. Specifically, the solver infrastructure is being utilized to create structured simulation databases for training Graph Neural Network (GNN)-based predictive models aimed at replacing computationally expensive finite element simulations. This integration establishes a pathway toward rapid surrogate modeling of composite structures while preserving physics-informed accuracy

Mechanical and thermal buckling of functionally graded axisymmetric shells

PurposeThis paper aims to present development of a layer‐wise (LW) beam model for geometric nonlinear finite element analysis of laminated beams with partial layer interaction.Design/methodology/approachThe model is built assuming first order shear deformation theory (FSDT) at layer level and moderate interlayer slips. LW kinematic, strain and stress fields are established in view of co‐rotational finite element formulation. Laminated beam equilibrium relations are developed in strong, weak and matrix form. A notion of interface shear stress is used to define layer interactions.FindingsThrough suitable choice of kinematic model the co‐rotational approach is shown to provide means of obtaining robust finite element formulation for geometric nonlinear analysis of laminated structures with interlayer slips.Research limitations/implicationsThe proposed model is dedicated to geometric nonlinear finite element analysis of laminated beams undergoing large planar displacements, subject to small strains and moderate interlayer slips.Originality/valueNovelty of the proposed approach is based on encompassing shear deformations in geometric nonlinear analysis of laminated beams with interlayer slips. Arbitrary number of layers is considered.

A steady-state thermomechanical analysis model is established for the composite laminated plate with transverse cracks and delaminations based on the extended layerwise method. The one-dimensional weak and strong discontinuous functions are employed to simulate the interlaminar interfaces and the delaminations, respectively, while the transverse crack is simulated in the in-plane displacement fields by using the standard extended finite element method. The temperature field in the thickness direction is obtained by using a one-dimensional steady-state heat conduction equation and constructed with the linear Lagrange interpolation functions in the thickness direction. In several numerical examples, the proposed model is verified for the laminated plates with/without transverse crack and/or delaminations against the classic laminated plate theory, first-order shear deformation theory, Reddy’s layerwise theory or three-dimensional elastic model.

Large deformation analysis for anisotropic and inhomogeneous beams using exact linear static solutions

Wavelet spectral finite element for wave propagation in shear deformable laminated composite plates

A finite element method based approach is developed for studying the static, vibration and buckling behavior of curvilinearly stiffened plates in the presence of in-plane compressive and tensile stresses. The first order shear deformation theory (FSDT) is employed for both the plate and the Timoshenko beam modeling. Interpolation functions are used to build the displacement mapping between the stiffener and the plate nodes to allow the stiffener to be placed anywhere within the plate. One of the advantages of the present method is that the plate need not be re-meshed while the stiffener configuration is changed, and second, results obtained by the present method with much fewer number of elements match well with the results obtained by using a commercial FEM software. Several numerical examples are solved to study both the static and dynamic behaviors of stiffened plates. The effects of boundary conditions, stiffener eccentricity, stiffener curvature, stiffener-plate geometry parameters, in-plane load condition, stiffener-plate cross-section area ratio and stiffness ratio on the static and dynamic behaviors of curvilinearly stiffened plate are investigated. Results have shown that behavior of the natural frequency parameter as a function of applied in-plane stress could be affected by the plate thickness, in-plane load condition, stiffener-plate cross-section area ratio and stiffness ratio during compression only, but not when subjected to in-plane tension.