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| Phase-field based topology optimization with Drucker-Prager yield stress constraints |
| Received:November 19, 2019 Revised:December 25, 2019 |
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| DOI：10.7511/jslx20191119002 |
| KeyWord:topology optimization stress constraints phase-field function Drucker-Prager yield function |
| Author | Institution |
| 张晓鹏 |
大连理工大学 工程力学系, 工业装备结构分析国家重点实验室, 大连 |
| 康柯 |
大连理工大学 工程力学系, 工业装备结构分析国家重点实验室, 大连 |
| 杨东生 |
中国运载火箭技术研究院, 北京 |
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| Abstract: |
| Phase-field based topology optimization method is employed for finding the optimal layout of continuum structures exhibiting asymmetric strength behaviors in tension and compression.According to the Drucker-Prager yield criterion and the power rate interpolation scheme,the topology optimization problem is formulated to minimize the total material volume under the stress constraints.The qp relaxation method is used to solve the singularity problem of local stress constraints,and the stress constraints are condensed by the P-norm function.This method realizes the reduction of the number of the stress constraints.The STM(stability transformation method)is adopted to correct the highly nonlinear stress behavior and improve the convergence stability of optimization process.In the real application,the objective function and stress constraint are processed using the Lagrange multiplier method.Sensitivity analysis is performed with the adjoint variable method,and the design variables are updated by solving the Allen-Cahn equation.Numerical examples demonstrate the effectiveness of the proposed optimization model.The numerical examples also show that the design obtained with topology optimization considering Drucker-Prager yield constraints is obviously different from that obtained with topology optimization considering von-Mises strength constraints. |