Isogeometric Analysis for Topology Optimisation of Two Dimensional Planar and Laminated Composite Plate Continuum Structures

Abstract

Isogeometric analysis is the recent development in the field of engineering analysis with high performance computing and greater precision.  This current research has opened a new door in the field of structural optimisation.  The main focus of this research study is to perform topology optimisation of continuum structures in civil engineering using Isogeometric analysis. The continuum structures analysed here in this study are reinforced concrete, steel and laminated composite plates.  Reinforced concrete is a rational union of concrete and steel.  Topology optimisation of reinforced concrete structures is an emerging area of study to determine the optimal layout of material in the concrete domain.  Laminated structures are made of several layers of material and bonded to achieve high stiffness and low weight to strength ratio. The deformed shape at the optimal state can be determined with topology optimisation of laminated composites.  The formulation for composite plates is done using kirchoff thin plate theory without any shear contribution.  B-splines are used to model the geometry.  The objective is to optimise the energy of the structure and optimality criteria is used to calculate the newer values of relative densities.  First order sensitivity analysis is performed to determine the newer values of objective function.  The code is written in MatLab® and a few problems have been solved with different domains.  The results are verified and have shown a good agreement with those in the literature.