A level set approach for topology optimization with local stress constraints

Abstract

SUMMARYThe purpose of this work is to present a level set‐based approach for the structural topology optimization problem of mass minimization submitted to local stress constraints. The main contributions are threefold. First, the inclusion of local stress constraints by means of an augmented Lagrangian approach within the level set context. Second, the proposition of a constraint procedure that accounts for a continuous activation/deactivation of a finite number of local stress constraints during the optimization sequence. Finally, the proposition of a logarithmic scaling of the level set normal velocity as an additional regularization technique in order to improve the minimization sequence. A set of benchmark tests in two dimensions achieving successful numerical results assesses the good behavior of the proposed method. In these examples, it is verified that the algorithm is able to identify stress concentrations and drive the design to a feasible local minimum. Copyright © 2014 John Wiley & Sons, Ltd.

Topology optimization with mixed finite elements on regular grids

“…Most of the numerical methods presented in the literature consist of approaches that resort to displacement-based finite elements, see e.g. [4,5,6,7,8]. When displacements are main variables of the formulation the stress field is computed through post-processing techniques and is not among the direct variables of the problem.…”

Topology optimization of continuum structures with stress constraints and uncertainties in loading

“…[23][24][25][26][27][28][29][30][31][32][33][34][35][36] There are two main difficulties associated with stress constraints when the solid isotropic material with penalization (SIMP) approach is used for material parameterization. The first difficulty consists in the local nature of material failure constraints, which provides a major challenge due to the large number of stress constraints and their high nonlinearity.…”

“…One can use an augmented Lagrangian algorithm, which proved to be a mathematically consistent alternative with reasonable computational cost. [24][25][26]33,35 The other important issue that must be considered is the singularity phenomenon. There are 2 main techniques used to relax the design space: the qp approach 27 and the -relaxed approach.…”

Sustainable Design-Oriented Level Set Topology Optimization

“…It has demonstrated the adaptability subjected to different engineering disciplines. For instance, Wang et al [1] and Allaire et al [2] solved the compliance-minimization problems; and later, many other researchers investigated the stress-minimization and stress-constrained problems [3][4][5][6][7][8]; in Refs. [9][10][11], the multimaterial design problems were addressed.…”