Application of ring elements in the nonlinear analysis of shells of revolution under nonaxisymmetric loading
Application of ring elements in the nonlinear analysis of shells of revolution under nonaxisymmetric loading
复制标题
环单元在非轴对称载荷下回转壳非线性分析中的应用
DOI：
10.1016/0045-7825(85)90036-2
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发表时间：
1985
影响因子：
7.2
通讯作者：
H. Obrecht
中科院分区：
文献类型：
--
作者：
W. Wunderlich;H. Cramer;H. Obrecht
提出了一种面向问题的非对称旋转壳非线性弹塑性分析方法。它是基于傅里叶级数对载荷和变量的周向分布的近似。轴向采用环形有限元。它们的刚度矩阵是通过精确的数值积分而不是试函数得到的。为了能够充分利用傅里叶分解和一维离散化，所有非线性都以伪载荷向量的形式进行迭代处理。因此，各种傅立叶谐波由不耦合的代数方程控制，不需要对非线性全局切刚度矩阵有明确的了解。采用一种共轭梯度法，在每个增量内都有特殊的预处理，避免了迭代过程的收敛性问题。给出了涉及强非线性行为和高度非对称应力和变形状态的数值算例，验证了该方法的有效性。
A problem-oriented method for the nonlinear elastic-plastic analysis of nonsymmetrically loaded shells of revolution is described. It is based on an approximation of the circumferential distribution of the loads and variables by Fourier series. Ring finite elements are used in the axial direction. Their stiffness matrices are obtained by accurate numerical integration rather than by trial functions. To be able to take full advantage of the Fourier decomposition and the one-dimensional discretization, all nonlinearities are treated iteratively in the form of pseudo-load vectors. Thus, the various Fourier harmonics are governed by uncoupled algebraic equations and no explicit knowledge of the nonlinear global tangent stiffness matrix is required. Convergence problems of the iterative procedure are avoided by employing a sort of conjugate gradient method with a special preconditioning within each increment. Numerical examples involving strongly nonlinear behavior and highly nonsymmetric states of stress and deformation are given which demonstrate the effectiveness of the method.