だ円座標による平面熱応力問題の解析解 : 第1報,だ円板の非定常熱応力

概要

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As an example of transient thermal stress problems expressed in rectangular curvilinear coordinates for which no analytical solutions have been reported, analytical solutions are presented for a transient two-dimensional temperature field and an associated thermal stress problem in an elliptical plate expressed in elliptical co-ordinates. The transient temperature function of the elliptical plate subjected to an abrupt change in temperature on the elliptic boundary can be expressed in the form of an infinite series, including Mathieu and modified Mathieu functions of the first kind of even integral order. The associated thermal stress problem can be formulated in terms of thermoelastic displacement potential and Papkovich-Neuber's stress functions. Numerical calculations are carried out for the distributions of circumferential thermal stress on the elliptic boundary and the major and minor axes in the elliptical plate for three cases of eccentricity.
一般社団法人日本機械学会の論文
1987-11-25