A topology optimization method for multiple load cases and constraints based on element independent nodal density

作者：Yi, Jijun; Rong, Jianhua^*; Zeng, Tao; Huang, X.

来源：Structural Engineering and Mechanics, 2013, 45(6): 759-777.

DOI：10.12989/sem.2013.45.6.759

• topology optimization
• element independent density
• Shepard interpolation scheme
• multiple load cases
• multiple constraints
• parallel computation

In this paper, a topology optimization method based on the element independent nodal density (EIND) is developed for continuum solids with multiple load cases and multiple constraints. The optimization problem is formulated as minimizing the volume subject to displacement constraints. Nodal densities of the finite element mesh are used as the design variables. The nodal densities are interpolated into any point in the design domain by the Shepard interpolation scheme and the Heaviside function. Without using additional constraints (such as the filtering technique), mesh-independent, checkerboard-free, distinct optimal topology can be obtained. Adopting the rational approximation for material properties (RAMP), the topology optimization procedure is implemented using a solid isotropic material with penalization (SIMP) method and a dual programming optimization algorithm. The computational efficiency is greatly improved by multithread parallel computing with OpenMP to run parallel programs for the shared-memory model of parallel computation. Finally, several examples are presented to demonstrate the effectiveness of the developed techniques.

• 出版日期2013-3-25
• 单位中南大学; 长沙理工大学