Equilibrium of elastic nets
Equilibrium of elastic nets
复制标题
弹性网的平衡
DOI：
10.1098/rsta.1991.0056
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
A. Pipkin
中科院分区：
文献类型：
--
作者：
D. Steigmann;A. Pipkin
本文提出了由两类完全柔性弹性纤维构成的网的一般平衡理论。假设纤维是连续分布的，对剪切变形的阻力可以忽略不计。的网络被证明是最小化的变形的势能，只有当相关的纤维拉伸的纤维应变能函数的凸点和纤维中的应力是拉伸。这些结果被用来构建一个放松的能量密度，自动占网络的扭曲。得到了普遍的解。这些变形可以通过单独施加边缘牵引力和侧压力在每个弹性网中保持。一个详细的研究微分几何的网络，以帮助他们的解释。半松弛（褶皱）网的平衡理论的发展和应用的解决方案的一些代表性的例子。
A general equilibrium theory for nets constructed from two families of perfectly flexible elastic fibres is presented. The fibres are assumed to be continuously distributed and to offer negligible resistance to shear distortion. Configurations of nets are shown to be minimizers of the potential energy of deformation only if the associated fibre stretches are points of convexity of the fibre strain energy functions and the stresses in the fibres are tensile. These results are used to construct a relaxed energy density that automatically accounts for wrinkling of the network. Universal solutions are obtained. These are the deformations that can be maintained in every elastic net by the application of edge tractions and lateral pressure alone. A detailed study of the differential geometry of nets is included to aid in their interpretation. The equilibrium theory for half-slack (wrinkled) nets is developed and applied to the solution of some representative examples.