A mixed variational principle and its application to the nonlinear bending problem of orthotropic tubes—II. application to nonlinear bending of circular cylindrical tubes
A mixed variational principle and its application to the nonlinear bending problem of orthotropic tubes—II. application to nonlinear bending of circular cylindrical tubes
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DOI：
10.1016/0020-7683(94)90009-4
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发表时间：
1994-04
影响因子：
3.6
通讯作者：
A. Libai;C. Bert
中科院分区：
文献类型：
--
作者：
A. Libai;C. Bert
第一部分介绍了非线性壳分析的混合变分原理的推导过程，并对弱曲率壳和圆柱壳作了更详细的阐述。本文将圆柱壳原理推广到相容性方程中混合项的保留具有重要意义的特殊情况。重点放在相互作用的纵向拉伸应变与大的曲率周向变化。作为一个简单的第一个例子，它被应用到正交各向异性Brazier过程，其中的欧拉-拉格朗日方程和摄动解也被导出。变分原理在为高度非线性问题提供直接、近似的“工程解”方面有重要的用途。这样的解决方案补充了更精确，但繁琐的有限元或双级数技术。本文在推广原理中引入合理的简化假设，构造了有限长正交各向异性管强非线性非均匀弯曲问题的近似原理和近似方程。作为一个具体的例子，研究了固定，有限长管的纯弯曲。对失稳（或局部失稳）进行近似分析。一些局部屈曲的结果进行了比较，从文献的数值结果。
A procedure for deriving mixed variational principles for nonlinear shell analysis was presented in Part I and formulated in more detail for shells of weak curvatures and for circular cylindrical shells. The cylindrical shell principle is extended here to accommodate those special cases in which the retention of mixed terms in the compatibility equations is of significance. Emphasis is put on the interaction of longitudinal extensional strains with large circumferential changes of curvature. As a simple first example, it is applied to the orthotropic Brazier process, for which an Euler-Lagrange equation and perturbation solution are also derived. Variational principles have important uses for providing direct, approximate “engineering solutions” to highly nonlinear problems. Such solutions complement the more exact but cumbersome finite element or double series techniques. In the present case, reasonable simplifying assumptions are introduced in the extended principle to construct approximate principles and equations for the problem of strong, nonlinear, nonuniform bending of finite-length orthotropic tubes. As a specific example, the pure bending of a clamped, finite-length tube is studied. Approximate analysis is carried to collapse (or local buckling). Some of the local buckling results are compared with numerical results from the literature.