Layout optimization with h‐adaptivity of structures

Abstract

SUMMARYIn this paper, we propose a new procedure for the layout optimization of structures making use of h-adaptive methods. The method combines the topology optimization and the existing h-adaptive ÿnite element methods in order to: (i) improve the deÿnition of the material boundary, i.e. the contour between the material and void regions; (ii) reduce the e ective number of design variables; and (iii) bound the relative solution error. The reÿnement strategy is applied to a given element if: (a) the measure of the quality of the element is below a given lower bound; (b) the element is a 'material element' or has a side which forms the 'material boundary' of the given optimum layout; and (c) the element average error estimate is larger than a multiple of the average error of the mesh. After the h-adaptive reÿnement, the mesh quality is improved with the application of a conditional Laplacian smoothing process. The formulation of the optimization problem is deÿned by the minimization of the compliance of the structure subjected to a volume and side constraints. The design variable is then the average density of the material, which is considered to be constant within each ÿnite element.

Improving multiresolution topology optimization via multiple discretizations

“…In the second part of this paper, we propose an adaptive multiresolution topology optimization (AMTOP) scheme to further increase the efficiency. The adaptive mesh refinement approach has been proposed to reduce the total number of finite elements by representing the void with fewer (coarser) elements and the solid with more (finer) elements. Lin and Chou proposed a two‐stage approach in which the first‐stage is performed with coarse finite elements and the optimal topology at the end of the first stage is used as the starting point for the second stage, which uses a fine FE mesh.…”

Adaptive multiresolution refinement with distance fields

“…These approaches are known as p and h refinements, respectively [2]. Although increasing the degree p of the basis functions results in better convergence of the solution [3], h refinement remains quite popular [4,5]. It is usually achieved by either global or local remeshing of the underlining geometric model or by introducing additional grids of finer resolution.…”

Using artificial reaction force to design compliant mechanism with multiple equality displacement constraints

“…A dense mesh density is often required over the physical domain to resolve physical phenomena accurately. Adaptive meshing, which maintains a high mesh density locally in regions of material boundaries, or large solution variations, is attractive and will obviously improve the computational accuracy [21,32]. In this paper, the design domain is discretized using linear triangular elements in 2D and tetrahedral elements in 3D, and the h-adaptive method is implemented to locally capture the boundary position.…”