Extension of Koiter’s linear shell theory to materials exhibiting arbitrary symmetry
Extension of Koiter’s linear shell theory to materials exhibiting arbitrary symmetry
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DOI：
10.1016/j.ijengsci.2011.09.012
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发表时间：
2012-02
影响因子：
6.6
通讯作者：
D. Steigmann
中科院分区：
文献类型：
--
作者：
D. Steigmann
Koiter 的线性壳理论适用于各向同性弹性材料和各向异性材料，这些材料表现出相对于壳中表面的弹性特性的反射对称性。就此类壳的特殊性而言，经典线性壳理论是不完整的。这里通过一个系统程序解决了这个缺陷，该程序同样适用于所有类型的材料对称性，这需要将壳的势能以其厚度的幂进行扩展，这让人想起 Koiter 的工作。这些变量是壳体中表面的位移场和膨胀过程中出现的某些导向场。根据精确三维理论中出现的必要条件对指向矢进行约束，从而在小厚度下得到三阶势能的最佳表达式。对于缺乏反射对称性的材料，发现除了传统理论中常见的应变和弯曲应变外，壳的应变能还对应变的切向梯度敏感。
Koiter’s linear shell theory applies to isotropic elastic materials and to anisotropic materials that exhibit reflection symmetry of the elastic properties with respect to the shell mid-surface. To the extent that such shells are exceptional, classical linear shell theory is incomplete. This lacuna is addressed here through a systematic procedure, applicable equally to all kinds of material symmetry, which entails an expansion of the potential energy of the shell in powers of its thickness in a manner reminiscent of Koiter’s work. The variables are the displacement field of the shell mid-surface and certain director fields that arise in the course of the expansion procedure. The directors are constrained in accordance with necessary conditions arising in the exact three-dimensional theory, yielding the optimal expression for the potential energy among those of third order in the small thickness. For materials lacking reflection symmetry, it is found that the strain energy of the shell is sensitive to tangential gradients of strain in addition to the usual strain and bending strain of the conventional theory.