Finite deformation of thin shells in the context of analytical mechanics of material surfaces
Finite deformation of thin shells in the context of analytical mechanics of material surfaces
复制标题
材料表面分析力学背景下薄壳的有限变形
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Y. Vetyukov
中科院分区：
文献类型：
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作者：
V. Eliseev;Y. Vetyukov
在直接法框架下，将壳体视为由质点组成的可变形曲面，用分析力学方法得到了理论关系式。在目前的工作中，我们分配给每个粒子五个自由度，即三个平移和两个面内旋转。虚功原理产生了壳体理论的所有关系：平衡方程、边界条件、力因子的定义和本构方程的一般形式。无论是在理论的关系，并在推导过程中实现了显着的一致性和清晰度。提出了一种新的壳的Piola张量公式，以便将方程转换为参考构型。为了分析屈曲或几何刚化的影响，我们在预变形构型附近将这些方程线性化。给出了轴压圆柱壳屈曲和超临界行为的一些新的半解析结果。方程和变分公式之间的对应关系进行了讨论，鉴于开发有效的数值模拟程序的非线性变形的外壳。壳结构的非线性变形的有限元建模的结果进行了讨论，与全三维解决方案的问题。
In the framework of the direct approach shells are considered as deformable surfaces consisting of particles, and the relations of the theory are obtained with the methods of analytical mechanics. In the present work we assign to each particle five degrees of freedom, namely three translations and two in-plane rotations. The principle of virtual work produces all the relations of the theory of shells: equations of equilibrium, boundary conditions, definition of the force factors and the general form of constitutive equations. Remarkable consistency and clarity is achieved both in the relations of the theory and in the derivation process. A new formulation of the Piola tensors for a shell is suggested in order to transform the equations to the reference configuration. To analyze the effects of buckling or geometric stiffening, we linearize these equations in the vicinity of a pre-deformed configuration. Some new semi-analytical results on buckling and supercritical behavior of an axially compressed cylindrical shell are presented. The correspondence between the equations and the variational formulation is discussed in view of development of efficient numerical procedures for modeling nonlinear deformations of shells. Results of finite element modeling of the nonlinear deformation of a shell structure are discussed in comparison with the fully three-dimensional solution of the problem.