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Structural Engineering and Mechanics
  Volume 45, Number 6, March25 2013, pages 759-777
DOI: http://dx.doi.org/10.12989/sem.2013.45.6.759
 


A topology optimization method for multiple load cases and constraints based on element independent nodal density
Jijun Yi, Jianhua Rong, Tao Zeng and X. Huang

 
Abstract
    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.
 
Key Words
    topology optimization; element independent nodal density; Shepard interpolation scheme; multiple load cases; multiple constraints; parallel computation
 
Address
Jijun Yi: School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China; School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410004, China
Jianhua Rong: School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410004, China
Tao Zeng: School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China
X. Huang: School of Civil, Environmental and Chemical Engineering, RMIT University, GPO Box 2476, Melbourne3001, Australia
 

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