Topology optimization with precise evolving boundaries based on IGA and untrimming techniques

Abstract

Abstract We present a new computational approach to topology optimization that includes precise representation of the boundaries as they evolve during optimization. The topology is defined following level set methods where a B-spline surface is used to parameterize the level set function. In each optimization cycle, the level set based topology is mapped into a spline-based representation that is constructed on an unstructured mesh. The mapping procedure is performed following untrimming techniques which lead to geometrical models whose boundaries are explicitly defined as cubic B-spline curves. The geometrical model is replicated precisely by mesh refinement to obtain a suitable model for subsequent Iso Geometric Analysis (IGA). It is shown that accurate stress evaluations are obtained on the untrimmed boundaries. Consistent sensitivity analysis is formulated to account for all mappings and refinements from the underlying level set function to the IGA-based solution of the mechanical response. Implementation of the proposed approach is demonstrated on compliance and maximum stress minimization problems. Several design aspects are examined, namely integrating a topological derivative technique for hole insertion; a control points mapping procedure; and imposing predefined fixed void regions. The results expose the capability of the proposed approach to generate optimized layouts while accurately modeling the boundaries throughout the optimization process. Furthermore, the outcomes are spline-based optimized topologies that are directly compatible with CAD environments.