论文标题
使用动态弛豫表现出联合弯曲和拉伸的弹性板的同几何分析
Isogeometric Analysis of Elastic Sheets Exhibiting Combined Bending and Stretching using Dynamic Relaxation
论文作者
论文摘要
贝壳是无处不在的薄结构，可以在表现出弯曲和拉伸的组合模式并具有深刻的现代应用的同时，会经历大型非线性弹性变形。在本文中，我们提出了一种基于经典的Koiter非线性壳理论的新的等几何公式，以研究薄壳中的不稳定性问题，例如皱纹和屈曲。 NURBS-BASIS的使用提供无旋转的，构型的高阶空间连续性，从而可以直接从控制点的位置向量的插值来直接计算曲率和膜菌株。构建了伪，耗散和离散的动力系统，并通过动态弛豫方法（DR）获得静态平衡溶液。提出了基于高性能的DR的高性计算实现，并且针对几种现有的数值和实验结果对所提出的公式进行了标准。在评估壳的结构响应方面，这种表述的优势比传统的有限元方法。
Shells are ubiquitous thin structures that can undergo large nonlinear elastic deformations while exhibiting combined modes of bending and stretching, and have profound modern applications. In this paper, we have proposed a new Isogeometric formulation, based on classical Koiter nonlinear shell theory, to study instability problems like wrinkling and buckling in thin shells. The use of NURBS-basis provides rotation-free, conforming, higher-order spatial continuity, such that curvatures and membrane strains can be computed directly from the interpolation of the position vectors of the control points. A pseudo, dissipative and discrete, dynamical system is constructed, and static equilibrium solutions are obtained by the method of dynamic relaxation (DR). A high-performance computing-based implementation of the DR is presented, and the proposed formulation is benchmarked against several existing numerical, and experimental results. The advantages of this formulation, over traditional finite element approaches, in assessing structural response of the shells are presented.
