Cubic b-splines to perform topology optimization with buckling load on carbon fiber nano reinforced simply supported cross ply laminated composite square plates using inverse buckling formulation

Abstract

Composite laminates are widely used in several civil engineering structures. Composite laminates are used in bridges, aircraft, and construction because of their light weight and high strength. The study on the behavior of these laminates is very important now. The main focus of this research is to propose a new method to perform topology optimization of nano-reinforced composite laminates carrying buckling loads. The goal is to present the optimal layout of the material, stress distribution at the optimal state, buckling load factors at the optimal state, and most importantly, the deformed profile of the composite laminate at the optimal state. The elastic stiffness matrix and the geometric stiffness matrix can be used to determine the buckling load. The reason for taking the reciprocal of the buckling load is that during optimization, the number of elements that are not participating in carrying the load increases, and hence the stress carried by these elements is minimal. Hence, we have considered the inverse value of the buckling load factor. The design domain is modelled using cubic b-splines. Higher-order shear deformation theory is used, and isogeometric analysis is performed to determine the buckling load. The deformed profile of the plate at the optimal state, the optimal layout of the material, stress distribution, buckling load factors, and the corresponding mode shapes are given as well. Only carbon fiber nano-reinforced, cross-ply square plates with a simple support structure have been considered. Three different types of loading conditions, namely uniaxial compressive loading, bi-axial compressive loading, and pure shear loading, are considered. Coding is done in MatLab®, and the buckling load factors are determined. Several examples from the literature are considered with different moduli ratios, laminae, and span to thickness ratios, and the non-dimensional buckling load is determined for each. The results obtained are in good agreement with those given in the literature.