Reducing Computational Cost of Meso-Scale Analysis of Masonry Structures Using a Combination of Topology Optimization and the Drucker-Prager Yield Criterion

Document Type : Article

Authors

1 Faculty of Civil Engineering, University of Science and Culture, Tehran.

2 Faculty of Mechanical Engineering, University of Science and Culture, Tehran.

3 Faculty of Civil Engineering, Razi University, Kermanshah.

4 Faculty of Civil Engineering, Putra University, Malaysia.

10.24200/j30.2024.64683.3336

Abstract

Modeling masonry structures at the meso-scale, while yielding precise results, is often associated with significant computational costs. This paper introduces an innovative approach that mitigates these costs by integrating topology optimization with the Drucker-Prager yield criterion in meso-scale analysis. The proposed method commences with macro-scale numerical models, employing the Drucker-Prager criterion to account for material behavior under loading. The loading process is segmented into multiple incremental steps. At each step, a fraction of the total load is applied to the model, which subsequently undergoes topology optimization. This optimization aims to maximize structural stiffness while adhering to material distribution constraints. Throughout this process, the stress and strain results of each element are recorded at the conclusion of each step and utilized as inputs for the subsequent step. This iterative approach ensures that the stress and strain outcomes derived from the Drucker-Prager yield surface are incorporated into the stiffness maximization process, facilitating the identification of regions susceptible to damage from plastic strain. The regions pinpointed by the optimization algorithm are accumulated over the course of the analysis, highlighting areas within the masonry structure model that are prone to potential damage. These identified regions are then modeled separately at the meso-scale, while other areas remain modeled at the macro-scale. This dual-scale modeling technique drastically reduces computational costs by minimizing the number of meso-scale elements needed. The efficacy of the proposed method was validated through four numerical examples featuring varied boundary conditions and materials. The algorithm successfully identified potential damage zones, and the optimized models exhibited consistent behavior and crack patterns in comparison to fully meso-scale samples. The reductions in computational costs were significant: 21% in the validation model, 15.6% in the first numerical example, 63.5% in the second numerical example, and 58.6% in the third numerical example. This approach demonstrates a substantial advancement in efficiently modeling masonry structures at multiple scales.

Keywords

Main Subjects

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Sharif Journal of Civil Engineering
Volume 41, Issue 3 - Serial Number 3
December 2026
Pages 35-46

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