Advanced Finite Element Analysis of Multilayered Composite Plates under Varied Boundary Conditions Using Least-Squares Formulation

Laminated composites are integral to numerous engineering industries, including aerospace, marine, automotive, and storage solutions. This chapter focuses on the three-dimensional deformations of a multilayered, linear elastic, anisotropic rectangular plate, which is subjected to arbitrary boundary conditions on one edge and simply supported on the opposite edge. The laminate comprises anisotropic and homogeneous layers of varying thicknesses.

We present an elastic analysis of these laminated composite plates under sinusoidal mechanical loading and diverse boundary conditions. Utilizing a state-space model, we employ the least-squares finite element method (LSFEM) to obtain solutions for displacements and stresses. This method ensures the continuity of field variables across the composite structure's domain and at the layer interfaces, thereby addressing common issues such as shear locking and improving the accuracy of the simulation.

The governing equations are formulated using LSFEM, which minimizes the residuals of the governing equations and side conditions across the computational domain. Our model incorporates layerwise variables, including displacements, out-of-plane stresses, and in-plane strains, treating them as independent variables. This approach allows for a more detailed and precise analysis of the composite's behavior under various loading conditions.

Numerical results illustrate the behavior of the laminated composite plates under various boundary conditions, demonstrating the effectiveness of the LSFEM approach. These results are compared with existing three-dimensional elasticity solutions in the literature, validating the accuracy of our method. The chapter also discusses the implications of different boundary conditions on the mechanical response of laminated composites, providing insights into optimal design strategies for engineering applications.