Eigen theory of elastic mechanics for anisotropic solids

来源期刊：中国有色金属学报(英文版)2000年第2期

论文作者：郭少华

文章页码：217 - 219

Key words：anisotropic solid; elastic mechanics; eigen form; standard space

Abstract: Eigen characters of the fundamental equations, equilibrium equation of stress and harmony equation of deformation, of the traditional elastic mechanics under geometrical space were testified by means of the concept of standard space, and the modal equilibrium equation and the modal harmony equation under mechanical space were obtained. Based on them and the modal Hooke’s law, a new system of the fundamental equation of elastic mechanics is given. The advan- tages of the theory given here are as following: the form of the fundamental equation is in common for both isotropy and anisotropy, both force method and displacement method, both force boundary and displacement boundary; the number of stress functions is equal to that of the anisotropic subspaces, which avoids the man-made mistakes; the solution of stress field or strain field is given in form of the modal superimposition, which makes calculation simplified greatly; no matter how complicated the anisotropy of solids may be, the complete solutions can be obtained.