Multiphase material topology optimization of Mindlin-Reissner plate with nonlinear variable thickness and Winkler foundation
Multiphase material topology optimization of Mindlin-Reissner plate with nonlinear variable thickness and Winkler foundation
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DOI：
10.12989/scs.2020.35.1.129
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发表时间：
2020-04-10
影响因子：
4.6
通讯作者：
Lee, Dongkyu
中科院分区：
文献类型：
--
作者：
Banh, Thanh T.;Nguyen, Xuan Q.;Lee, Dongkyu
在典型的结构拓扑优化设计中，结构拓扑优化对提高结构刚度和节省结构质量起着重要的作用。本文提出了一种新的考虑Winkler地基的Mindlin-Reissner板拓扑优化设计的数值方法，给出了多材料多方向变厚度板的数学表达式。在实现具有多方向可变厚度的板的最佳多材料拓扑的同时，可以为结构的工程师和设计者提供关于在适当厚度位置处的材料的有效利用的结构的重量信息。此外，数值技术的成熟的混合插值张量分量4元（MITC 4）被用来克服一个著名的剪切锁定问题发生在薄板模型。作为本文的主要成果之一，详细推导了变厚度Mindlin-Reissner板结构多材料拓扑优化问题的数学表达式。数值算例验证了Winkler地基上的变厚度Mindlin-Reissner板对多材料拓扑优化设计结果的影响。
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.