Numerical treatment of a geometrically nonlinear planar Cosserat shell model
Numerical treatment of a geometrically nonlinear planar Cosserat shell model
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DOI：
10.1007/s00466-016-1263-5
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发表时间：
2014-12
影响因子：
4.1
通讯作者：
O. Sander;P. Neff;M. Bîrsan
中科院分区：
文献类型：
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作者：
O. Sander;P. Neff;M. Bîrsan
提出了一种新的几何非线性弹性平面Cosserat壳的离散方法。运动学模型类似于一般的六参数合成壳模型。离散化使用测地线有限元（GFE），这导致一个客观的离散模型，自然允许任意大的旋转。可以构造任何近似阶的GFE。由此产生的代数问题是一个非线性有限维黎曼流形上的最小化问题。我们解决这个问题，使用黎曼信赖域方法，这是一个推广的牛顿的方法，全局收敛，没有中间加载步骤。我们提出了连续模型和离散化，讨论了离散模型的性质，并给出了几个数值例子，包括剪切弹性薄板的扭曲。
We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton’s method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear.