Isogeometric topology optimization of shape memory alloy based structures

Abstract Topology optimization (TO) is an efficient numerical technique that enables the effective distribution of materials within the design domain, yielding the desired structural outcome. This approach depends on an analysis tool to calculate the responses of the altered domain. For history-dependent material like shape memory alloys (SMAs), a complete thermomechanical analysis comprises several load or time steps, each having multiple Newton–Raphson (NR) iterations. After the structural analysis is complete, the sensitivities of the objective function and the constraints are calculated following the adjoint method and are used to update the design variables. For SMAs, the calculation of sensitivities involves complex steps and is to be conducted at each of the Gauss quadrature points and for every time step. This demands huge computational time—to reduce this, while maintaining the required accuracy, isogeometric analysis (IGA) is utilized here. The developed IGA-based TO tool is then used to determine the effective topologies of the SMA structures, subjected to a variety of thermomechanical loading. A comparison study is carried out with a finite element method (FEM)-based TO tool and the outcomes are presented. The results reveal that the presented tool is capable of generating the converged material layout of the design domain while taking only 35% of the time taken by the FEM-based TO tool.