Topology optimization of structures under design-dependent pressure loads by a boundary identification-load evolution (BILE) model

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 cost-effectiveness 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.

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Funding

This work was supported by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Federal Economic Development Agency for Southern Ontario (FedDev Ontario), Siemens Canada Limited, and Petroleum Technology Development Agency (PTDF).

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Correspondence to Ehsan Toyserkani.

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The authors declare that they have no conflict of interest.

Replication of results

The steps in the BILE model have been elaborately explained and can be reproduced by following the workflow presented and ensuring the right values for volume fraction threshold, fth, and number of load evolution steps, nle, are chosen (these are also explained in the result section). Notwithstanding, a sample MATLAB code that implements Example 5.1 has been provided as supplementarymaterial.

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Responsible Editor: YoonYoung Kim

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Ibhadode, O., Zhang, Z., Rahnama, P. et al. Topology optimization of structures under design-dependent pressure loads by a boundary identification-load evolution (BILE) model. Struct Multidisc Optim 62, 1865–1883 (2020). https://doi.org/10.1007/s00158-020-02582-8

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Keywords

  • Topology optimization
  • Design-dependent loads
  • Pressure loads
  • Boundary identification
  • SIMP
  • OCM
  • MMA