An adaptive bubble method for structural shape and topology optimization

An adaptive bubble method is presented in this paper for shape and topology optimization design of stiffest structures and compliant mechanisms. With the aim of overcoming the shortcomings of the traditional bubble method and retaining all its advantages, the proposed method achieves a comprehensive integration of topological derivative, implicit model and fixed grid. The topological derivative is devoted to the iterative positioning of new holes inside the design domain. Each of the holes is described by smoothly deformable implicit curve (SDIC) characterized by very few parameters and high deformation capacity. Since the structural model could be implicitly constructed using the SDICs, the finite cell method (FCM) is applied to facilitate the mechanical analysis of the implicit model with fixed Eulerian mesh. Two new concepts, i.e., the topological derivative threshold and the total influence region of inserted holes, are further introduced to adaptively control the numbers and positions of new holes so that the numerical stability of topology optimization could be well guaranteed. It is shown that the adaptive bubble method no longer needs the mesh updating process and can perform the merging and separating operations of holes straightforwardly. Numerical examples concerning the stiffest structure design and the compliant mechanism synthesis are tested to demonstrate the universality of the present method, especially its capability of being integrated within CAD systems directly without post-processing.