Polyconvexity and Existence Theorem for Nonlinearly Elastic Shells
Polyconvexity and Existence Theorem for Nonlinearly Elastic Shells
复制标题
非线性弹性壳的多凸性和存在定理
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
S. Anicic
中科院分区：
文献类型：
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作者：
S. Anicic
在涉及平均曲率和高斯曲率的二维理论框架下，给出了一大类低正则非线性弹性壳的存在性定理。我们的讨论仅限于超弹性材料，即具有储能功能的弹性材料。在储能函数的多凸性、强迫性和增长性等特殊条件下，证明了全局极小值的存在性。此外，我们还定义了一类满足强迫性不等式的一般多凸储能函数。
We present an existence theorem for a large class of nonlinearly elastic shells with low regularity in the framework of a two-dimensional theory involving the mean and Gaussian curvatures. We restrict our discussion to hyperelastic materials, that is to elastic materials possessing a stored energy function. Under some specific conditions of polyconvexity, coerciveness and growth of the stored energy function, we prove the existence of global minimizers. In addition, we define a general class of polyconvex stored energy functions which satisfies a coerciveness inequality.