Topology optimization of structures under design-dependent pressure loads by a boundary identification-load evolution (B
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RESEARCH PAPER
Topology optimization of structures under design-dependent pressure loads by a boundary identification-load evolution (BILE) model Osezua Ibhadode 1 & Zhidong Zhang 1 & Pouyan Rahnama 1 & Ali Bonakdar 2 & Ehsan Toyserkani 1 Received: 9 January 2020 / Revised: 12 March 2020 / Accepted: 16 March 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract When a structure under design-dependent pressure loads is being topologically optimized, the magnitude and/or direction of these loads may change as the structure’s topology is being updated simultaneously. Therefore, two critical aspects in the optimization to be addressed are the identification of changing topological boundaries and the correct application of pressure loads to newly formed pressure surfaces. In this study, we present a simple boundary identification and load evolution (BILE) model to resolve these aspects. As the name suggests, a boundary identification step utilizes a threshold volume fraction to define topological boundaries and a load evolution step that occurs for a number of iterations between two successive boundary identification iterations. This model is particularly attractive because of its ease of application and computational costeffectiveness as most numerical results for 2D problems using 5000 to 13,000 isoparametric quad elements were obtained under 90 s and 100 iterations using the optimality criteria method (OCM). Based on the modified SIMP method, this model is compared with existing methodologies by presenting several numerical examples for validation. Keywords Topology optimization . Design-dependent loads . Pressure loads . Boundary identification . SIMP . OCM . MMA
1 Introduction We are in an era in science and technology where solutions to design problems call for minimal resources (energy, material, cost, time, even expertise). Topology optimization has been utilized and tested for over 30 years and has proven to be a viable means for optimizing structural design problems without predefining the structural layout. Topology optimization is the process of obtaining the best structural layout for a design problem constrained by several factors (e.g., mechanical properties, weight). The first known paper on topology Responsible Editor: YoonYoung Kim Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02582-8) contains supplementary material, which is available to authorized users. * Ehsan Toyserkani [email protected] 1
Multi-Scale Additive Manufacturing Lab, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
2
Siemens Canada Limited, 9505 Côte-de-Liesse, Montréal, Québec H9P 1A5, Canada
optimization was published by Michel, an Australian inventor, in 1904 (Rozvany, 2009). He derived an optimality criterion for the least weight layout of trusses (Rozvany, 2009). Since then, several efforts have made topology optimization an attractive and efficient tool within the design for manufacturing and pa
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