Shape preserving design with structural topology optimization

The purpose of this paper is to demonstrate a shape preserving topology optimization design approach to suppress the warping deformation of local structural domains. As structural deformation consists of rigid body motion and warping deformation, we propose using the elastic strain energy of the local domain to measure the warping deformation. Constraint on the local strain energy is then introduced into a standard compliance based topology optimization to obtain the shape preserving effect. Moreover, in the cases of shape preserving for multiple key points and cavities, i.e. when the local strain energies are unavailable, the idea of Artificial Weak Element (AWE) is introduced to measure and constrain the local warping deformation. Several numerical examples are tested here. The optimized results indicate that the local strain energy constraints on the shape preserving domains can suppress the warping deformation effectively in both simple illustrative examples and complicated engineering examples. Further discussions on the failure of structural load carrying path and the influence of the shape preserving constraint is also presented.