On regularization in parameter‐free shape optimization

Abstract

AbstractThis contribution is concerned with a parameter‐free approach to computational shape optimization of mechanically‐loaded structures. Thereby the term ’parameter‐free’ refers to approaches in shape optimization in which the design variables are not derived from an existing CAD‐parametrization of the model geometry but rather from its finite element discretization. One of the major challenges in using this type of approach is the avoidance of oscillating boundaries in the optimal design trials. This difficulty is mainly attributed to a lack of smoothness of the objective sensitivities and the relatively high number of design variables within the parameter‐free regime. To compensate for these deficiencies, Azegami introduced the concept of the so‐called traction method, in which the actual design update is deduced from the deformation of a fictitious continuum that is loaded in proportion to the negative shape gradient. We investigate a discrete variant of the traction method, in which the design sensitivities are computed with respect to variations of the design nodes for a given finite element mesh rather than on the abstract level by means of the speed method. Moreover, the design update process is accompanied by adaptive mesh refinement based on discrete material residual forces. Therein, we consider radaptive node relocation as well as hadaptive mesh refinement. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)