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
37High performance 3D-analysis of thermo-mechanically loaded composite structures
High performance 3D-analysis of thermo-mechanically loaded composite structures
1Enhanced first order shear deformation theory for the improved visco-elastic FEM analysis of laminated composite plates
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.
Read more26Nonlinear forced response of doubly-curved laminated panels composed of cnt patterned layers within first order shear deformation theory
Nonlinear forced response of doubly-curved laminated panels composed of cnt patterned layers within first order shear deformation theory
Read more38Meshless implementation of arbitrary 3D-shell structures based on a modified first order shear deformation theory
Meshless implementation of arbitrary 3D-shell structures based on a modified first order shear deformation theory
58Spectral finite element for wave propagation analysis of laminated composite curved beams using classical and first order shear deformation theories
Spectral finite element for wave propagation analysis of laminated composite curved beams using classical and first order shear deformation theories
Read more12Mechanical and thermal buckling of functionally graded axisymmetric shells
Mechanical and thermal buckling of functionally graded axisymmetric shells
2Marguerre shell type secant matrices for the postbuckling analysis of thin, shallow composite 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.
Read more32Large deflections of laminated beams with interlayer slips
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.
Read more45Wavelet spectral finite element for wave propagation in shear deformable laminated composite plates
Wavelet spectral finite element for wave propagation in shear deformable laminated composite plates
2Finite Element Approach to the Static, Vibration and Buckling Analysis of Curvilinearly Stiffened 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.
Read more1Time-dependent creep analysis and life assessment of 304 L austenitic stainless steel thick pressurized truncated conical shells
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.
Read more2Modeling of the Lamb wave asymmetric modes with an improved two-dimensional thin plate theory
Modeling of the Lamb wave asymmetric modes with an improved two-dimensional thin plate theory
37Large deformation analysis for anisotropic and inhomogeneous beams using exact linear static solutions
Large deformation analysis for anisotropic and inhomogeneous beams using exact linear static solutions
1Laminated composites modeling in ADAGIO/PRESTO.
A linear elastic constitutive equation for modeling fiber-reinforced laminated composites via shell elements is specified. The effects of transverse shear are included using first-order shear deformation theory. The proposed model is written in a rate form for numerical evaluation in the Sandia quasi-statics code ADAGIO and explicit dynamics code PRESTO. The equation for the critical time step needed for explicit dynamics is listed assuming that a flat bilinear Mindlin shell element is used in the finite element representation. Details of the finite element implementation and usage are given. Finally, some of the verification examples that have been included in the ADAGIO regression test suite are presented.
Read more63Analytical solution of stability of FG-CNTRC conical shells under external pressures
Analytical solution of stability of FG-CNTRC conical shells under external pressures
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