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Isogeometric analysis based topology optimization design with global stress constraint

机译:基于等几何分析的全局应力约束拓扑优化设计

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This paper presents an isogeometric analysis (IGA) based design method to address the stress-constrained topology optimization problem of plane stress and bending of thin plates. Based on the popular SIMP model, the integrated framework of geometry modeling, structural stress analysis and optimization is established. Owing to the geometry exactness and high-order continuity between elements, the IGA improves the computational accuracy of stress, and thus enhances the credibility of optimum design. Meanwhile, the obvious zigzag boundaries are avoided in the optimized results, and the stress function of IGA maintains the continuity for a relatively coarse discretization. Moreover, the IGA-SIMP method can easily meet the requirement of C-1-continuity for the Kirchhoff plate formulations, which also facilitates the stress analysis and sensitivity calculation. To overcome the convergence difficulty of highly nonlinear stress aggregation constraint, two STM (stability transformation method)-based stabilization schemes combining with the P-norm function for global stress constraint are developed to achieve the stable iterations and acceptable designs. Finally, representative examples illustrate the effectiveness and convenience of the proposed approach. It is indicated that the IGA-SIMP method shows superior performance for solution accuracy and efficiency, and the local stress level is well controlled. (C) 2018 Elsevier B.Y. All rights reserved.
机译:本文提出了一种基于等几何分析(IGA)的设计方法,以解决平面应力和薄板弯曲的应力约束拓扑优化问题。基于流行的SIMP模型,建立了几何建模,结构应力分析和优化的集成框架。由于几何精度和元素之间的高阶连续性,IGA提高了应力的计算精度,从而提高了最佳设计的可信度。同时,在优化结果中避免了明显的锯齿形边界,并且IGA的应力函数保持了相对粗略离散的连续性。此外,IGA-SIMP方法可以轻松满足Kirchhoff平板配方C-1连续性的要求,这也有助于应力分析和灵敏度计算。为了克服高度非线性应力聚集约束的收敛困难,开发了两种基于STM(稳定性转换方法)的稳定方案,并结合了用于全局应力约束的P-范数函数,以实现稳定的迭代和可接受的设计。最后,代表性的例子说明了该方法的有效性和便利性。结果表明,IGA-SIMP方法在求解精度和效率方面表现出优异的性能,并且局部应力水平得到了很好的控制。 (C)2018年Elsevier B.Y.版权所有。

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