Moving Morphable Components Using Strain-Based Beam Geometry Description for Topology Optimization

Abstract

In the moving-morphable-component topology optimization, morphable components are introduced as a geometrical model mapped onto the background finite elements, and their shape parameters are utilized as design variables for topology optimization. Whereas a complex curved geometry ensuring [Formula: see text] continuity can be generated using existing curved components, the component curvatures cannot be selected as design variables in the existing methods; thus geometric constraints associated with curvatures cannot also be directly imposed. To address this issue, this study proposes a curvature-based morphable component by introducing the curvilinear geometry representation in the strain-based beam formulation. Since the proposed component is parameterized by curvatures using the curvilinear equation, the component curvatures can be utilized as the design variables. This allows for directly imposing curvature constraints on structural members, thereby accounting for the manufacturability of an optimal topology. It is demonstrated that a symmetric placement of the design variables using the midpoint curvilinear coordinate system is critical in ensuring convergence of the proposed curvature-based component optimization. The symmetric curvature component is further extended to account for multiple curvatures within a single component while ensuring [Formula: see text] continuity. Several examples are presented to demonstrate the benefits of the proposed multicurvature component for topology optimization.