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Incorporating Stress Constraints in the Structural Topology Optimization Framework
Topology optimization (TO) is a design tool utilized during the conceptual phase, aiming to optimize the material distribution within a defined design domain while considering a specific set of loads and boundary conditions. Traditionally TO is employed for solving the problems with the formulation as minimizing compliance that increases the overall structural stiffness. However, from a practical point of view, stress is a significant concern ignored in the traditional compliance-based formulation. So, to make a TO a realistic approach, the involvement of the stress constraint is considered in the optimization formulation. When stress is incorporated into the optimization framework, a significant challenge arises due to the localized nature of stress, resulting in a considerable number of stress constraints. To address this issue, the global stress technique is adopted where stress constraint of each element is aggregated using some aggregation function. The von-mises failure criteria is used, and P-norm formulation is adopted to formulate the stress constraints. The SIMP method is used as an interpolation scheme to penalize the intermediate densities. A standard benchmark L-shape numerical problem is presented to study the influence of stress constraints in the traditional compliance-based optimization formulation. The results show that stress constraint consideration in the conventional compliance-based TO leads to a smooth round corner of the L-shape problem.
Incorporating Stress Constraints in the Structural Topology Optimization Framework
Topology optimization (TO) is a design tool utilized during the conceptual phase, aiming to optimize the material distribution within a defined design domain while considering a specific set of loads and boundary conditions. Traditionally TO is employed for solving the problems with the formulation as minimizing compliance that increases the overall structural stiffness. However, from a practical point of view, stress is a significant concern ignored in the traditional compliance-based formulation. So, to make a TO a realistic approach, the involvement of the stress constraint is considered in the optimization formulation. When stress is incorporated into the optimization framework, a significant challenge arises due to the localized nature of stress, resulting in a considerable number of stress constraints. To address this issue, the global stress technique is adopted where stress constraint of each element is aggregated using some aggregation function. The von-mises failure criteria is used, and P-norm formulation is adopted to formulate the stress constraints. The SIMP method is used as an interpolation scheme to penalize the intermediate densities. A standard benchmark L-shape numerical problem is presented to study the influence of stress constraints in the traditional compliance-based optimization formulation. The results show that stress constraint consideration in the conventional compliance-based TO leads to a smooth round corner of the L-shape problem.
Incorporating Stress Constraints in the Structural Topology Optimization Framework
Lecture Notes in Civil Engineering
Kumar, Ratnesh (editor) / Bakre, Sachin V. (editor) / Goel, Manmohan Dass (editor) / Gupta, Anurag (author) / Saurabh, Shubham (author) / Gupta, Abhinav (author) / Chowdhury, Rajib (author)
Structural Engineering Convention ; 2023 ; Nagpur, India
2024-11-24
7 pages
Article/Chapter (Book)
Electronic Resource
English
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