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Xuan Q. Nguyen,Thanh T. Banh,Dongkyu Lee 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.79 No.1
This study presents an optimal topology material distribution method in the framework of minimum compliance with a constraint on the total amount of multi-material using constant strain triangle (CST) elements and Moved and Regularized Heaviside Function (MRHF) filters. The sensitivity formulations for objective function and sensitivity for structures are derived in terms of multiphase design variables through triangle elements. Mathematical formulations of topology optimization problem solving the minimum compliance by using multiple materials are an alternating active-phase algorithm with a Gauss-Seidel version as an optimization model of optimality criteria. Moreover, MRHF that has the role of a filter in multiple materials is considered to produce obvious material distributions and improve the convergence of objective values. Some optimal topology results under the influence of rmin and filter are also investigated and verify the CST element-based multi-material topology optimization is appropriate to the use of MRHF and produces reasonable optimal results.
Thanh T. Banh,Xuan Q. Nguyen,Michael Herrmann,Filip C. Filippou,Dongkyu Lee 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.35 No.1
In typical, structural topology optimization plays a significant role to both increase stiffness and save mass of structures in the resulting design. This study contributes to a new numerical approach of topologically optimal design of Mindlin-Reissner plates considering Winkler foundation and mathematical formulations of multi-directional variable thickness of the plate by using multi-materials. While achieving optimal multi-material topologies of the plate with multi-directional variable thickness, the weight information of structures in terms of effective utilization of the material at the appropriate thickness location may be provided for engineers and designers of structures. Besides, numerical techniques of the well-established mixed interpolation of tensorial components 4 element (MITC4) is utilized to overcome a well-known shear locking problem occurring to thin plate models. The well-founded mathematical formulation of topology optimization problem with variable thickness Mindlin-Reissner plate structures by using multiple materials is derived in detail as one of main achievements of this article. Numerical examples verify that variable thickness Mindlin-Reissner plates on Winkler foundation have a significant effect on topologically optimal multi-material design results.