不均質材料に対する三次元熱弾性問題の定式化とその厚板への適用例

概要

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In this study, an analytical method of development of thermoelastic problems for a medium with nonhomogenous material properties is developed. For the isothermal problems of such a nonhomogeneous body, an analytical method of development has already given by Kassir under the assumption that the shear modulus of elasticity G changes arbitrarily with the variable z of the axial coordinate according to the relation G (z)=G_0z^m. However, no analytical procedure for the thermoelastic field has been established up to present. In this study, introducing the thermoelastic displacement potential function and two kinds of displacement functions, an analytical method of development of the three-dimensional thermoelastic field is proposed. Assuming that G, thermal conductivity λ and coefficient of linear thermal expansion a vary with the variable ζ connected with the dimensionless axial coordinate according to the relations G (ζ)=G_0ζ^m, λ(ζ)=λ_0ζ^l, α(ζ)=α_0ζ^k, the three-dimensional temperature solution in a steady state for a slab is obtained, and the associated thermal stress components are evaluated theoretically. Numerical calculations are carried out for several cases taking into account the variation of nonhomogeneous material properties, and the numerical results are shown graphically.
社団法人日本機械学会の論文
1999-05-25