Structural Topology Optimization Based On Topological Derivatives

This paper introduces the derivation of topological derivatives.In this paper,we prove the first-order convergence of the finite element discrete scheme of the topolog-ical derivative expression of Poisson problem,and give the corresponding numerical examples.For the shape design of plane elastic mechanics,the topological derivative of shape functional is calculated,and the level set method combined with topological derivative is used to realize the topological optimization of plane elastic structure.Com-pared with the traditional level set method,it is found that the level set method combined with topological derivative is more effective.