Stress-constrained volume minimization of structures undergoing design-dependent surface limit loads

Abstract

The work aims to propose a topological optimization based on stress-constrained volume minimization of structures undergoing design-dependent surface limit loads by adapting the Bi-directional Evolutionary Structural Optimization method (BESO). The initial stress-based version of the BESO method, including design-dependent loads, has been developed to minimize stress with a volume constraint. The optimization proposed in this work was obtained by transforming the restriction into an objective function. This solution is quite interesting in practical applications once it allows the reduction of structural weight to a prescribed maximum stress value, which could be associated with the mechanical properties of materials and can be applied to aeronautical, aerospace, civil, and mechanical structures. In load analysis, limit loads are those associated with material yield strength, and ultimate loads are those associated with tensile strength. As an example of using the methodology, in this article, the prescribed stress constraint has been selected based on the yield strength of the material in order to find the minimum structural volume for this limit condition. One advantage of using discrete methods is to avoid one of the main problems in optimisations based on a stress criterion, the density singularity. To the best of our knowledge, the stress-constrained volume minimization using the BESO method of structures undergoing design-dependent surface loads has not been explored before and is also a challenge in the field. The main demand is to allow increases and decreases in volume during the optimization process. To solve this challenge, an additional controlling parameter has been introduced. The P-norm has been used as an aggregation function of elemental von Mises stress, normalizing the sensitivity to stabilize the algorithm in order to increase the norm exponent, allowing a decrease in stress level and consequently a reduction in final volume. Four examples have been performed in order to analyze the benchmarks of stress criteria and design-dependent surface pressure loads: simple support systems (beams with and without a crack notch), double-clamped beam, and piston head. The examples evidence the convergence of the algorithm and its effectiveness in reducing the final volume.

Keywords:

• BESO method
• topological optimization
• stress constraints
• design-dependent loads
• surface pressure loads

Acknowledgments

The authors are grateful to the Brazilian National Council for Scientific and Technological Development (Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq grant number 152197/2022-2).

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

These data were derived from the following resources available in the public domain: https://github.com/gigarcez/Stress_Constraint_BESO

Additional information

Funding

This study was supported by the Brazilian National Council for Scientific and Technological Development (Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq grant number 152197/2022-2).