Proportional topology optimisation with maximum entropy-based meshless method for minimum compliance and stress constrained problems

Abstract

In this paper, proportional topology optimisation (PTO) with maximum entropy (maxent)-based meshless method is presented for two-dimensional linear elastic structures for both minimum compliance (PTOc) and stress constraint (PTOs) problems. The computation of maxent basis functions is efficient as compared to the standard moving least square (MLS) and possesses a weak Kronecker delta property leading to straightforward imposition of Dirichlet boundary conditions. The PTO is a simple, non-gradient, accurate, and efficient method compared to the standard topology optimisation methods. A detailed and efficient implementation of the computational algorithms for both PTOc and PTOs is presented. The maxent basis functions are calculated only once at the start of simulation and used in each optimisation iteration. Young’s modulus for each background cells is calculated using the modified solid isotropic material with penalisation (SIMP) method. A parametric study is also conducted on the degree of proportionality and history dependence of both PTOc and PTOs algorithms. A variety of numerical examples with simple and complex geometries, and structured and unstructured discretisations are presented to show the accuracy, efficiency, and robustness of the developed computational algorithms. Both PTOc and PTOs algorithms can handle large topological changes, and provide excellent optimisation convergence characteristics.