A computational framework for polyconvex large strain elasticity for geometrically exact beam theory
A computational framework for polyconvex large strain elasticity for geometrically exact beam theory
复制标题
几何精确梁理论的多凸大应变弹性计算框架
DOI：
10.1007/s00466-015-1231-5
复制
发表时间：
2015
影响因子：
4.1
通讯作者：
C. Hesch
中科院分区：
文献类型：
--
作者：
R. Ortigosa;A. J. Gil;J. Bonet;C. Hesch
本文提出了一种新的计算框架，用于分析大应变下的非线性梁有限元。具体而言，在三维多凸弹性的背景下，最近在Bonet等人（Comput Methods Appl Mech Eng 283：1061-1094，2015）中引入的方法被扩展到Simo的几何精确梁模型（Comput Methods Appl Mech Eng 49：55-70，1985），许多其他有限元梁类型公式的起点。这个新的变分框架可以被看作是一个连续退化的制定，而且，增强了三个关键的新颖性。首先，为了便于实现特别与经受大应变的梁相关联的复杂的多凸本构律，采用了Bonet等人的新颖的张量叉积代数（Comput Methods Appl Mech Eng 283：1061-1094，2015），从而产生了对否则复杂的计算框架的优雅且物理上有意义的表示。其次，本文展示了如何新的代数方便的变形梯度的任何不变量的重新表达，其余因子和行列式的经典梁应变措施。后者是非常有用的，当一个经典的梁实现是首选。这是particularised的情况下，穆尼-里夫林模型，虽然该技术可以直接推广到其他更复杂的各向同性和各向异性的多凸模型。第三，在三维弹性和梁的本构模型的定义的两个最被接受的限制之间的连接被示出，桥接连续体和其退化梁描述之间的差距。这是通过一个新的有见地的表示正切算子。
In this paper, a new computational framework is presented for the analysis of nonlinear beam finite elements subjected to large strains. Specifically, the methodology recently introduced in Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) in the context of three dimensional polyconvex elasticity is extended to the geometrically exact beam model of Simo (Comput Methods Appl Mech Eng 49:55–70, 1985), the starting point of so many other finite element beam type formulations. This new variational framework can be viewed as a continuum degenerate formulation which, moreover, is enhanced by three key novelties. First, in order to facilitate the implementation of the sophisticated polyconvex constitutive laws particularly associated with beams undergoing large strains, a novel tensor cross product algebra by Bonet et al. (Comput Methods Appl Mech Eng 283:1061–1094, 2015) is adopted, leading to an elegant and physically meaningful representation of an otherwise complex computational framework. Second, the paper shows how the novel algebra facilitates the re-expression of any invariant of the deformation gradient, its cofactor and its determinant in terms of the classical beam strain measures. The latter being very useful whenever a classical beam implementation is preferred. This is particularised for the case of a Mooney–Rivlin model although the technique can be straightforwardly generalised to other more complex isotropic and anisotropic polyconvex models. Third, the connection between the two most accepted restrictions for the definition of constitutive models in three dimensional elasticity and beams is shown, bridging the gap between the continuum and its degenerate beam description. This is carried out via a novel insightful representation of the tangent operator.