Validity improvement of evolutionary topology optimization: procedure with element replaceable method

Abstract

The aim of this paper is to enhance the validity of existing evolutionary topology optimization procedures. As this hard-killing scheme related to the element sensitivity values may lead to incorrect predictions of inefficient elements to be removed and the value of the objective function becomes sharply deteriorated during the iterations, a check position (CP) control is proposed to prevent the erroneous topology design generated by the rejection criteria of evolutionary methods. For this purpose, we introduce a sort of orthotropic cellular microstructure (OCM) element with moderate pseudodensity that acts as a compromising element between solid element and void OCM element. In this way, all inefficient elements removed previously are automatically replaced with the moderate OCM elements depending upon the deterioration of the objective function. Erroneously removed elements are then identified in the updated finite element model through a direct sensitivity computing of the moderate OCM elements and will be finally recovered by the bi-directional element replacement. Besides, detailed structures with checkerboard patterns are eliminated by controlling the local structural bandwidth with the so-called threshold method. Typical optimization examples of structural compliance and natural frequency that were difficult to tackle are solved by the proposed design procedure. Satisfactory numerical results are obtained.