だ円座標による平面熱応力問題の解析解 : 第4報,共焦点中空だ円板の非定常熱応力

概要

論文の詳細を見る
Analytical solutions are presented for a transient heat conduction problem and an associated plane thermoelastic problem expressed in elliptical coordinates in a confocal hollow elliptical plate subjected to nonaxisymmetric heatings on the inner and outer elliptical boundaries. The transient heat conduction problem is confined to a symmetric one with respect to the x axis, and solved by proposing new integral transforms and their inverse transforms, the kernels of which are expressed in the form of Mathieu and modified Mathieu functions. The associated plane thermoelastic problem is formulated in terms of Airy's stress function. The formulation includes an assurance of single-valuedness of the rotation component based on Michell's condition in elliptical coordinates derived already by one of the present authors. The numerical calculations of the distributions of the transient temperature and circumferential thermal stress are carried out for three cases of partial heating on the outer elliptical boundary.
一般社団法人日本機械学会の論文
1990-11-25