Abstract

Using the support operator technique for two-dimensional problems of the elasticity theory we constructed integrally consistent approximations of the components of the strain tensor and the elastic energy of the medium for the equations of the elasticity theory in terms of displacements. Approximations are constructed for the case of irregular difference grids in the R–Z plane of a cylindrical coordinate system. We use the limiting process assuming that the azimuthal angle tends to zero for passing from the full three-dimensional approximations to the two-dimensional approximations in the R–Z plane. The used technique preserves the divergent form, self-adjointness, and sign-definiteness of the two-dimensional approximations. These properties are inherent in their 3D predecessors corresponding to the operators in the governing differential equations.

中文翻译：

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介质的应力应变状态和能量平衡一致逼近的差分方案

摘要

使用支持算子技术解决弹性理论的二维问题，我们建立了位移理论上的应变张量分量和介质弹性能的整体一致逼近。对于圆柱坐标系的R–Z平面中的不规则差异网格，可以构造近似值。我们使用限制过程，假设在R–Z平面中从完整的三维近似转换为二维近似时，方位角趋于零。使用的技术保留了二维近似的发散形式，自伴性和符号定性。