Some general results in the theory of large elastic deformations
Some general results in the theory of large elastic deformations
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大弹性变形理论的一些一般结果
DOI：
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发表时间：
1955
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通讯作者：
J. Adkins
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文献类型：
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作者：
J. Adkins
当弹性体的应变能函数表示为应变的六个分量的函数时，对于不同类型的材料，给定问题的解可能呈现出非常不同的形式。在本论文中，通过把应变能函数作为定义变形的参数的函数，得到的结果是有效的广泛的材料。每个问题的分析最初进行机构拥有一个合适的类型的曲线各向异性，并得出结果是独立的对称性的弹性材料。因此，这些结果是有效的，不仅对于一般类型的材料最初考虑，而且对于各向同性体和材料是正交各向异性或横向各向同性的曲线坐标系，它定义的各向异性。可压缩和不可压缩的机构被认为是。从这一点来看，一般类型的圆柱对称变形的检查，其中包括作为特殊情况下的问题的弯曲，膨胀，延伸和扭转的圆柱形管，和剪切的圆柱形环。这些特殊情况下的具体结果被认为是分开的，并为弯曲和扭转问题，表达式被发现的合力和夫妇需要保持变形。并对长方体的相应变形类型作了简要分析。在本文的最后一节中，考虑了广义剪切问题，其中，在变形过程中，弹性体的每个点平行于给定的轴移动一段距离，该距离是在垂直于该轴的平面中的位置的一般函数。
When the strain-energy function for an elastic body is expressed as a function of the six components of strain, the solution of a given problem for different types of material may assume very different forms. In the present paper, by regarding the strain-energy function as a function of the parameters defining the deformation, results are obtained which are valid for a wide range of materials. The analysis for each problem is performed initially for bodies possessing a suitable type of curvilinear aeolotropy, and results are derived which are independent of symmetries in the elastic material. These results are therefore valid, not only for the general type of material initially considered, but also for isotropic bodies and for materials which are orthotropic or transversely isotropic with respect to the curvilinear co-ordinate system which defines the aeolotropy. Both compressible and incompressible bodies are considered. From this point of view, a general type of cylindrically symmetrical deformation is examined which includes as special cases the problem of flexure, the inflation, extension and torsion of a cylindrical tube, and the shear of a cylindrical annulus. Particular results for these special cases are considered separately, and for the flexure and torsion problems, expressions are found for the resultant forces and couples required to maintain the deformation. A brief analysis is also given for the corresponding types of deformation for a cuboid. In the final section of the paper, a generalized shear problem is considered in which, during deformation, each point of the elastic body moves parallel to a given axis through a distance which is a general function of position in a plane normal to that axis.