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Non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the strength constraint parameterized level set method and interval mathematics
Abstract In this paper, a study on non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the parameterized level set method (PLSM) is conducted. The P-norm is used to replace the local stress constraint with a single comprehensive stress constraint that approximates the maximum stress to optimize the structure model with minimum volume. In the interval-set model, the stress constraint is transformed into the non-probabilistic reliability-based scheme and the reliability is evaluated by the optimization feature distance (OFD). In the NRBTO scheme, the unknown-but-bounded (UBB) uncertainties of the material and external load of the optimized structure are considered. By interpolating the level set function (LSF) with the multiquadric (MQ) splines, the partial differential equation (PDE) is transformed into an ordinary differential equation (ODE). In addition, the interval parameter vertex method is employed to obtain the stress constraint interval, and the shape derivative and adjoint vector methods are used to obtain the evolution velocity field of LSF. The optimality criterion (OC) method is used to solve the optimization problem. Finally, three examples are given, and the optimization model of stiffness constraint is introduced, which not only verifies the applicability of the topology optimization scheme based on non-probabilistic reliability but also compares the difference between the topology optimization with strength constraint and the topology optimization with stiffness constraint.
Highlights The calculation method of comprehensive stress is proposed, the optimal value of P parameter is discussed, and the solution of volume minimization optimization problem under the constraints of comprehensive stress is given, which improves the calculation efficiency. From the perspective of LSM, the relationship between interval vertex method and LSF is established, and then a new topology optimization model is established. The evolution velocity field of uncertain topology optimization is derived. A new NRBTO based on PLSM and NRBM is established and solved by OC method.
Non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the strength constraint parameterized level set method and interval mathematics
Abstract In this paper, a study on non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the parameterized level set method (PLSM) is conducted. The P-norm is used to replace the local stress constraint with a single comprehensive stress constraint that approximates the maximum stress to optimize the structure model with minimum volume. In the interval-set model, the stress constraint is transformed into the non-probabilistic reliability-based scheme and the reliability is evaluated by the optimization feature distance (OFD). In the NRBTO scheme, the unknown-but-bounded (UBB) uncertainties of the material and external load of the optimized structure are considered. By interpolating the level set function (LSF) with the multiquadric (MQ) splines, the partial differential equation (PDE) is transformed into an ordinary differential equation (ODE). In addition, the interval parameter vertex method is employed to obtain the stress constraint interval, and the shape derivative and adjoint vector methods are used to obtain the evolution velocity field of LSF. The optimality criterion (OC) method is used to solve the optimization problem. Finally, three examples are given, and the optimization model of stiffness constraint is introduced, which not only verifies the applicability of the topology optimization scheme based on non-probabilistic reliability but also compares the difference between the topology optimization with strength constraint and the topology optimization with stiffness constraint.
Highlights The calculation method of comprehensive stress is proposed, the optimal value of P parameter is discussed, and the solution of volume minimization optimization problem under the constraints of comprehensive stress is given, which improves the calculation efficiency. From the perspective of LSM, the relationship between interval vertex method and LSF is established, and then a new topology optimization model is established. The evolution velocity field of uncertain topology optimization is derived. A new NRBTO based on PLSM and NRBM is established and solved by OC method.
Non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the strength constraint parameterized level set method and interval mathematics
Wang, Lei (author) / Liu, Yingge (author) / Li, Zeshang (author) / Hu, Juxi (author) / Han, Bing (author)
Thin-Walled Structures ; 188
2023-05-12
Article (Journal)
Electronic Resource
English
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