First order basis splines to perform isogeometric topology optimization of three dimensional structures

Abstract

Topology optimization is at the heart of the design process. With the increasing availability of computational power at cheaper prices the research work in this field has been growing steadily in recent years. Isogeometric analysis using basis splines can be very useful to represent the design domain with good precision. The main focus of this research is to use first-order basis spline functions to represent the design domain in three dimensions and to perform topology optimization and to determine the optimal distribution of material. The principal stresses at the centroid of each element are calculated and compared with the permissible stress of the given material. The nodal displacements are computed at each control point and checked with the permissible displacement for the given material. A few problems from the existing work have been solved using isogeometric topology optimization and shown good agreement with the results obtained using Finite Element Analysis (FEA).