Static Analysis of Laminated Composite Plate Using First Order Shear Deformation Theory

Composites are used comprehensively in constructional company. Instead of conventional materials engineers are experimenting new materials every day in which composites are providing solution to many structural applications. MATLAB software is used in the investigation of static performance of laminated plates. Designing of composite laminate is very complex and requires lot of computational effort. It is very difficult to solve composite numerical problems manually. Developing MATLAB code for the analysis of laminated composite plate using finite element analysis. To determine the deflection and transverse shear stress of square laminated plate which is simply supported and subjected to uniform pressure. To explore the influence of modular ratio on deflection and transverse shear stress for different materials. Development of MATLAB code for the interpretation of first order shear deformation theory. Keywords: Laminated plate, composites, MATLAB, shear deformation theories, Finite element analysis

Dynamic Response of Angle Ply Laminates with Uncertainties Using MARS, ANN-PSO, GPR and ANFIS

In the present work, for the first time, free vibration response of angle ply laminates with uncertainties is attempted using Multivariate Adaptive Regression Spline (MARS), Artificial Neural Network-Particle Swarm Optimization (ANN-PSO), Gaussian Process Regression (GPR), and Adaptive Network Fuzzy Inference System (ANFIS). The present approach employed 2D C0 stochastic finite element (FE) model based on the Third Order Shear Deformation Theory (TSDT) in conjunction with MARS, ANN-PSO, GPR, and ANFIS. The TSDT model used eliminates the requirement of shear correction factor owing to the consideration of the actual parabolic distribution of transverse shear stress. Zero transverse shear stress at the top and bottom of the plate is enforced to compute higher-order unknowns. C0 FE model makes it commercially viable. Stochastic FE analysis done with Monte Carlo Simulation (MCS) FORTRAN inhouse code, selection of design points using a random variable framework, and soft computing with MARS, ANN-PSO, GPR, and ANFIS is implemented using MATLAB in-house code. Following the random variable frame, design points were selected from the input data generated through Monte Carlo Simulation. A total of four-mode shapes are analyzed in the present study. The comparison study was done to compare present work with results in the literature and they were found in good agreement. The stochastic parameters are Young’s elastic modulus, shear modulus, and the Poisson ratio. Lognormal distribution of properties is assumed in the present work. The current soft computation models shrink the number of trials and were found computationally efficient as the MCS-based FE modelling. The paper presents a comparison of MARS, ANN-PSO, GPR, and ANFIS algorithm performance with the stochastic FE model based on TSDT.

Determination of the transverse shear stress in layered composites

An engineering approach to estimation of the transverse shear stresses in layered composites is developed. The technique is based on the well-known D. I. Zhuravsky equation for shear stresses in an isotropic beam upon transverse bending. In general, application of this equation to a composite beam is incorrect due to the heterogeneity of the composite structure. According to the proposed method, at the first stage of its implementation, a transition to the equivalent model of a homogeneous beam is made, for which the Zhuravsky formula is valid. The transition is carried out by changing the shape of the cross section of the beam, provided that the bending stiffness and generalized elastic modulus remain the same. The calculated shear stresses in the equivalent beam are then converted to the stress values in the original composite beam from the equilibrium condition. The main equations and definitions of the method as well as the analytical equation for estimation of the transverse shear stress in a composite beam are presented. The method is verified by comparing the analytical solution and the results of the numerical solution of the problem by finite element method (FEM). It is shown that laminate stacking sequence has a significant impact both on the character and on the value of the transverse shear stress distribution. The limits of the applicability of the developed technique attributed to the conditions of the validity of the hypothesis of straight normal are considered. It is noted that under this hypothesis the shear stresses do not depend on the layer shear modulus, which explains the absence of this parameter in the obtained equation. The classical theory of laminate composites is based on the similar assumptions, which gives ground to use this equation for an approximate estimation of the transverse shear stresses in in a layered composite package.

Investigation of a Cross-Section with a Constant Transverse Shear Stress Distribution Using a Numerical Approach

A structural beam which is subjected to shear forces acting perpendicularly to its longitudinal axis will experience longitudinal and transverse shear stresses. In beams where failure in the transverse direction is plausible, it is desirable to maintain a constant transverse shear stress over the beam cross-section to avoid stress concentrations and to use the least amount of material. A numerical approach to the inverse problem of solving for a beam cross-section with a constant transverse shear stress distribution was investigated in this study using Microsoft Excel’s Solver and Matlab. The efficiency and shape of the developed cross-section were dependent on the number of elements used to discretize the cross-section. As the number of elements approached infinity, the shape of the cross-section became infinitely thin at the top and infinitely wide at the neutral axis, while also approaching an efficiency of 100%. It is therefore determined that this is an ill-posed inverse problem and no such perfect cross-section exists.

Transverse shear stress within surface layer and its effects

When the transverse shear stress within a surface layer is taken into account, what happens in the deformation of micro- or nanoscale solids? The relevant problems are investigated by analyzing the deformation of a micro- or nanosized solid ellipsoid. The results show that both the stress and the deformation of a micro- or nanosized ellipsoid increase after the transverse shear stress within the surface layer is introduced, and that the maximal stress always occurs at both ends of the long axis of the ellipsoid. Unlike the prediction given by the Gurtin–Murdoch model, the calculation coming from the model of this paper predicts that the micro- or nanosized ellipsoid subjected to hydrostatic pressure contracts radially in the middle section and expands radially on both sides of the middle section. This difference provides an experimental standard to verify two models.

A Modern Technique to Solve the Problem of the Failure of Layers of Multilayer Cylindrical Shells

Depending on the theory of the discrete-structure of the thin walls structures, an arithmetical model was proposed for elements of thin, multilayered walls for set layers anisotropic rigid. Assuming that the transverse shear stress is equal to the compression stress at the contact boundary. An elastic slip on the contact surface of adjacent layers is assumed. The problem was solved in a geometrically nonlinear formula with allowance for transverse deformations landslide and compression. The stressed-deformed state of two-layer transversally isotropic cylindrical shells with interphase defects of the structure of the material is studied. The numerical results were compared with the experimental results. The study proved numerically and experimentally data, the change in the kinetic and static conditions of contact on mating surfaces in the solid layers of the various elements of the fine wall structures greatly influences the distribution of compression stress and transverse shear stress deformations. Its ends are rigidly fixed, the work experience of the internal pressure of the uniform intensity of P = 1.11 MPa.