Topology Optimization Using Strain Energy Distribution for 2D Structures

Abstract

Optimization is carried out to achieve the best out of given resources while satisfying constraints on performance, state variables, and resources thus avoiding the excessive use of resources and decrease the cost associated. Structural systems need to be designed for a minimum of weight, compliance, displacement, frequency, etc., to save cost and get optimal performance. For this, structural optimization is carried out. Topology optimization is one type of structural optimization in which topology of the structure is changed. Generally, topology optimization is performed using methods like solid isotropic material with penalization (SIMP), level set-based methods, phase field method, evolutionary structural optimization (ESO), and bidirectional evolutionary structural optimization (BESO). In the present work, a modified evolutionary algorithm is proposed for structural optimization with consideration to strain energy distribution. Addition of material is performed on a partially void space instead of material removal. As the final optimum structure bears only a fraction of initial structure, the method of structure growth using addition approach is better for computational efficiency. This method initially takes a void input design domain but to make numerical computation easy, negligible density is assumed. The objective is to achieve critical strain energy per unit volume which is less than the modulus of resilience according to the maximum strain energy criterion. According to the maximum strain energy theory, a safe structure should have strain energy per unit volume less than the modulus of resilience. Hence, the objective is to find a structure satisfying the above criterion with minimum weight. The main focus of the work is to find optimum topology. Effect of multiple loads, rate of material addition, and effect of the magnitude of loads are also considered for structural optimization. The results are close to the results reported in the literature.