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

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.

This paper is concerned with the coupled thermo-mechanical stress analysis of functionally graded (FG) gas turbine rotor shaft system. Gas turbine shaft may expose in high temperature environments which demands to use functionally graded materials (FGMs). The aim of the present work is to study the stresses developed in the FG turbine shaft due to temperature variations and mechanical loading due to unbalance masses. For the present analysis aluminum oxide (Al2O3) and stainless steel (SUS304) are taken as shaft materials, power law gradation is used for the determination of FG material properties of the turbine shaft. Three nodded Timoshenko beam element with six degree of freedom (DOF) per node is considered for the finite element modelling of FG shaft. First order shear deformation theory (FSDT) is used with rotary inertia, strain and kinetic energy. Solution for governing equation of motion is obtained by the Hamilton principle. Complete MATLAB code has been developed for thermosmechanical stress analysis. Comparative study between steel shaft and FG shaft have been carried out. Normal stress (σxx) on plane perpendicular to axial direction, shear stress (τxr) on plane perpendicular to axial direction in radial direction and shear stress (τxθ) on plane perpendicular to axial direction in circumferential direction are obtained against time and along radius of shaft. Also these stresses are obtained for different parameters like power law indexes and speed of rotation of shaft.

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

The failure mechanisms of air‐plasma‐sprayed ZrO 2 thermal barrier coatings with various microstructures were studied by microscopic techniques after thermal cycling. The elastic modulus ( E ) and hardness ( H ) of the coatings were measured as functions of the number of thermal cycles. Initially, both E and H increased by ∼60% with thermal cycling because of sintering effects. However, after ∼80 cycles (0.5 h at 980°C), the accumulated damage in the coatings led to a significant decrease of ∼20% of the maximum value in both E and H . These results were correlated with stresses measured by a spectroscopic technique to understand specific damage mechanisms. Stress measurement and analysis revealed that the stress distribution in the scale was a complex function of local interface geometry and damage in the top coat. Localized variations in geometry could lead to variations in measured hydrostatic stresses from −0.25 to −2.0 GPa in the oxide scale. Protrusions of the top ZrO 2 coat into the bond coat were localized areas of high stress concentration and acted as damage‐nucleation sites during thermal and mechanical cycling. The net compressive hydrostatic stress in the oxide scale increased significantly as the scale spalled during thermal cycling.

Mechanical and thermal buckling of functionally graded axisymmetric shells

The postbuckling behaviour of thin shells has fascinated researchers because the theoretical prediction and their experimental verification are often different. In reality, shell panels possess small imperfections and these can cause large reduction in static buckling strength. This is more relevant in thin laminated composite shells. To study the postbuckling behaviour of thin, imperfect laminated composite shells using finite elements, explicit incremental or secant matrices have been presented in this paper. These incremental matrices which are derived using Marguerre's shallow shell theory can be used in combination with any thin plate/shell finite element (Classical Laminated Plate Theory - CLPT) and can be easily extended to the First Order Shear deformation Theory (FOST). The advantage of the present formulation is that it involves no numerical approximation in forming total potential energy of the shell during large deformations as opposed to earlier approximate formulations published in the literature. The initial imperfection in shells could be modeled by simply adjusting the ordinate of the shell forms. The present formulation is very easy to implement in any existing finite element codes. The secant matrices presented in this paper are shown to be very accurate in tracing the postbuckling behaviour of thin isotropic and laminated composite shells with general initial imperfections.

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 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.

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

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.).

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

This paper presents a semi-analytical solution for the creep analysis and life assessment of 304L austenitic stainless steel thick truncated conical shells using multilayered method based on the first order shear deformation theory (FSDT). The cone is subjected to the non-uniform internal pressure and temperature gradient. Damages are obtained in thick truncated conical shell using Robinson's linear life fraction damage rule, and time to rupture and remaining life assessment is determined by Larson-Miller Parameter (LMP). The creep response of the material is described by Norton's law. In the multilayer method, the truncated cone is divided into n homogeneous disks, and n sets of differential equations with constant coefficients. This set of equations is solved analytically by applying boundary and continuity conditions between the layers. The results obtained analytically have been compared with the numerical results of the finite element method. The results show that the multilayered method based on FSDT has an acceptable amount of accuracy when one wants to obtain radial displacement, radial, circumferential and shear stresses. It is shown that non-uniform pressure has significant influences on the creep damages and remaining life of the truncated cone.