Micropolar Shells as Two-dimensional Generalized Continua Models
Micropolar Shells as Two-dimensional Generalized Continua Models
复制标题
DOI：
10.1007/978-3-642-19219-7_2
复制
发表时间：
2011-01-01
期刊：
影响因子：
--
通讯作者：
Lebedev, Leonid P.
中科院分区：
文献类型：
--
作者：
Altenbach, Holm;Eremeyev, Victor A.;Lebedev, Leonid P.
用直接法讨论了非线性微极壳理论的基本关系。在这一理论框架下，壳可以看作是一个带有三个单位正交矢量的可变形曲面，即所谓的指向矢。换句话说，微极壳是一个二维的Cosserat连续体或微极连续体。与刚体动力学一样，微极壳的每个点都有三个平移和三个转动自由度。在这个理论中，旋转在运动学上独立于平移。壳体任意两部分之间的相互作用仅用力和力矩来描述。因此，在壳的边界上，必须给出六个边界条件。与Kirchhoff-Love或Reissner的壳体模型相比，可以考虑作用在壳体表面的钻削力矩。本文利用虚功原理推导了壳体理论的平衡方程。介绍了基于帧无差异原理的应变测量方法。在拉格朗日和欧拉坐标下建立了边值问题的静力和动力方程。此外，还给出了一些变分原理。对于一般的本构方程，我们提出了一些本构约束，如Coleman-Noll不等式、Hadamard不等式等。最后，我们讨论了相变材料壳的平衡问题，并给出了相界上的相容条件。
Using the direct approach the basic relations of the nonlinear micropolar shell theory are considered. Within the framework of this theory the shell can be considered as a deformable surface with attached three unit orthogonal vectors, so-called directors. In other words the micropolar shell is a two-dimensional (2D) Cosserat continuum or micropolar continuum. Each point of the micropolar shell has three translational and three rotational degrees of freedom as in the rigid body dynamics. In this theory the rotations are kinematically independent on translations. The interaction between of any two parts of the shell is described by the forces and moments only. So at the shell boundary six boundary conditions have to be given. In contrast to Kirchhoff-Love or Reissner's models of shells the drilling moment acting on the shell surface can be taken into account.In the paper we derive the equilibrium equations of the shell theory using the principle of virtual work. The strain measures are introduced on the base of the principle of frame indifference. The boundary-value static and dynamic problems are formulated in Lagrangian and Eulerian coordinates. In addition, some variational principles are presented. For the general constitutive equations we formulate some constitutive restrictions, for example, the Coleman-Noll inequality, the Hadamard inequality, etc. Finally, we discuss the equilibrium of shells made of materials undergoing phase transformations, such as martensitic transformations, and formulate the compatibility conditions on the phase interface.