Bending Analysis for Stress and Deflection for Cross-Ply Laminated Composite Plate Using Higher Order Shear Deformation Theory Subjected to Sinusoidal Loading using Finite Element Method

Abstract

Background: Laminated composite plates find extensive applications across aerospace, military, civil infrastructure, and automotive industries due to their advantageous properties, including superior fatigue resistance, high strength and stiffness resulting in reduced weight, and customizable fiber orientation, materials, and stacking patterns. Consequently, it becomes imperative to conduct analyses of deflections and stress levels. Objectives: In this current research, a mathematical formulation based on the higher-order deformation theory (HSDT) is employed, featuring 12 degrees of freedom per node. The focus of the analysis involves studying stress and deflection in two-layer crossply laminate plates. The obtained results are then compared with established findings in existing literature. Furthermore, a parametric investigation is conducted, exploring different side-to-thickness ratios at values of a/h equal to 4, 5, 10, 20, 40, 50, and 100. Methodology: In this research, the finite element analysis was performed with HSDT using MATLAB software. A twolayer laminate with material properties from category 2 was employed. The deflection and in-plane stresses were subsequently compared to analytical solutions provided by Kant & Manjunath, Pandya & Kant, and Pagano. Findings: The non-dimensional deflection values for a two-layer cross-ply configuration under sinusoidal loading conditions are 0.2133 for an a/h ratio of 4 and 0.1220 for an a/h ratio of 10. Additionally, the non-dimensional in-plane stress values, when considering an a/h ratio of 10, are as follows: σ x at the top fiber is 0.7202, σ y at the top fiber is 0.0857, and τ xy at the top fiber is -0.0543. Conversely, σ x at the bottom fiber is -0.0879, σ y at the bottom fiber is -0.7206, and τ xy at the bottom fiber is 0.0546. Detailed results are presented in tables, and they exhibit a high degree of agreement with established standard results.