Korn inequalities for elastic junctions of massive bodies, thin plates, and rods
Korn inequalities for elastic junctions of massive bodies, thin plates, and rods
复制标题
大质量物体、薄板和杆的弹性连接的科恩不等式
DOI：
10.1070/rm2008v063n01abeh004501
复制
发表时间：
2008
影响因子：
0.9
通讯作者：
S. Nazarov
中科院分区：
文献类型：
--
作者：
S. Nazarov
科恩不等式已经得到了大量的弹性体，薄板和杆在许多不同的组合的交界处。由于在位移及其导数的-范数中引入了各种权重因子，这些不等式是渐近尖锐的。由于薄体对拉伸和弯曲的反应不同，这种科恩不等式必然是各向异性的。弹性体的连接与对比刚度是允许的，但所获得的不等式中的常数是独立的相对厚度和相对刚度。对应于结构的刚性夹紧元件的规范与对应于不直接紧固而仅通过相邻元件紧固的硬移动或可移动元件的规范本质上不同;因此，加权各向异性规范的适当结构由整个连接的几何形状确定。每个变体的Korn不等式提供了一个例子，确认的最佳选择的权重因子。
Korn inequalities have been obtained for junctions of massive elastic bodies, thin plates, and rods in many different combinations. These inequalities are asymptotically sharp thanks to the introduction of various weight factors in the -norms of the displacements and their derivatives. Since thin bodies display different reactions to stretching and bending, such Korn inequalities are necessarily anisotropic. Junctions of elastic bodies with contrasting stiffness are allowed, but the constants in the inequalities obtained are independent of both the relative thickness and the relative rigidity . The norms corresponding to rigidly clamped elements of a structure are essentially different from the norms corresponding to hard-movable or movable elements that are not fastened directly, but only by means of neighbouring elements; therefore, an adequate structure of the weighted anisotropic norms is determined by the geometry of the whole junction. Each variant of Korn inequality is supplied with an example confirming the optimal choice of the weight factors.