On structural shape optimization using an embedding domain discretization technique

Abstract

Summary This contribution presents a novel approach to structural shape optimization that relies on an embedding domain discretization technique. The evolving shape design is embedded within a uniform finite element background mesh which is then used for the solution of the physical state problem throughout the course of the optimization. We consider a boundary tracking procedure based on adaptive mesh refinement to separate between interior elements, exterior elements, and elements intersected by the physical domain boundary. A selective domain integration procedure is employed to account for the geometric mismatch between the uniform embedding domain discretization and the evolving structural component. Thereby, we avoid the need to provide a finite element mesh that conforms to the structural component for every design iteration, as it is the case for a standard Lagrangian approach to structural shape optimization. Still, we adopt an explicit shape parametrization that allows for a direct manipulation of boundary vertices for the design evolution process. In order to avoid irregular and impracticable design updates, we consider a geometric regularization technique to render feasible descent directions for the course of the optimization. Copyright © 2016 John Wiley & Sons, Ltd.

Coupled topology and shape optimization using an embedding domain discretization method

“…On the other side, XFEM formulation does not suffer from these drawbacks. In our work, we employ a simple method of integration points oversampling (Riehl 2019) in which a larger amount of integration points, which are usually in the range n ip = (5. .10) d , is considered.…”

“…In the following work, we exploit the shape optimization method using an embedding domain technique, introduced by Riehl and Steinmann (2017), and couple it with a density-based topology optimization. The optimization problem now operates on design variables adopted from both methods, namely the pseudo-densities of the inner elements and the degrees of freedom of the vertices of the embedded boundary.…”

“…Thus, this article's contribution to the field of structural optimization can be understood twofold. (1) It extends the shape optimization approach of Riehl and Steinmann (2017) by introducing density design variables into the embedding domain. This allows to perform topological changes in a flexible manner, characteristic to density-based topology optimization.…”

Topography Optimization of Automobile Seat Belt Bracket

“…Disadvantages of traditional method is unreliable and always changing the installation environment of the original design. In order to make the optimization fast and efficient, the seat belt bracket is optimization designed with the topography optimization technique [2].…”

Structural shape optimization using Cartesian grids and automatic h-adaptive mesh projection

“…Among many other names used to describe these techniques where the mesh does not match the domain's geometry, we have the Immersed Boundary Method (IBM) [52] and the Immersed Finite Element Method (IFEM) [71]. These methods have been studied by a number of authors for very different problems including, of course, shape optimization [26,33,35,46,57].…”