Generalization Of Michell’s Solution To The Plane Problem Theory Of Elasticity In Polar Coordinates In The Event Of A Radially Inhomogeneous Body
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215 - 227
V. I. Andreev, N. Y. Cybin
In the plane problem of elasticity of inhomogeneous bodies problems are often found with the radial inhomogeneity occurring in the presence of axially symmetric physical fields (temperature, radiation, etc.). At the same time the plane problem itself can be two-dimensional. Of homogeneous bodies Michell’s solution for Airy’s stress function is the most well known. This solution is presented in the form of an infinite series in the trigonometric functions with constant coefficients. This article considers the statement of the problem in displacements, when the main unknown chosen functions are u(r, θ) and v(r, θ). The solution in displacements has the advantage that if the boundary conditions are in displacements it is not necessary to integrate Cauchy relations. Displacements are also represented in the form of series, but unlike in Michell’s solutions the coefficients of trigonometric functions are also functions that depend on the radius. They are also solved in the example.
Michell’s solution, theory of elasticity, plane problem, inhomogeneity