Plane Stress and Plane Strain in Orthotropic and Anisotropic Media
Abstract
Using the concepts embodied in the equations of stress equilibrium, strain compatibility and Hooke's law, the partial differential equations of plane stress and plane strain characteristic of homogeneous orthotropic bodies were derived. The plane stress problem requires the simultaneous solutions of five differential equations. Normally only one of the equations, that requiring compatibility of strain in the plane, is solved. In contrast, the plane strain problem requires the solution of but one differential equation.References
Hearmon, R. F. S. 1961. Applied anisotropic elasticity. Oxford Univ. Press. London.nJayne, B. A. and S. K. Suddarth. 1966. Matrix-tensor mathematics in orthotropic elasticity. Orientation effects in the mechanical behavior of anisotropic structural materials. A.S.T.M. Spec. Tech. Pub. 405. Philadelphia, Pennsylvania.nLekhnitskii, S. G. 1963. Theory of elasticity of an anisotropic body. Holden-Day, Inc., San Francisco.nShames, I. S. 1964. Mechanics of deformable solids. Prentice-Hall, Inc., Englewood Cliffs, New Jersey.nSokolnikoff, I. S. 1956. Mathematical theory of elasticity. McGraw-Hill, New York.nTimoshenko, S. P. 1953. Theory of elasticity. McGraw-Hill, New York.nWang, C. T. 1953. Applied elasticity. McGraw-Hill, New York.n
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