Axisymmetric problem of a nonhomogeneous elastic layer
The paper is devoted to the elastic behaviour of nonhomogeneous materials defined by the relation \(G(\overline z)= G_0\overline z^m\), i.e. the shear modulus of elasticity \(G\) varies with the power of the dimensionless axial coordinate \(\overline z\). The fundamental differential equation governing such nonhomogeneous medium was proposed by \textit{K. M. Kassir} in [Proc. of the ASCE, Mechanic Division 98, 457-470 (1972)]. Here the authors show that these fundamental equations are not sufficient for formulating several types of boundary value problems. It is shown in this paper that fundamental equations derived in an earlier paper [J. Thermal stress. 5, No. 1, 1-11 (1982)] can be used to formulate axisymmetric problems for a thick plate subjected to an arbitrary distributed load or a concentrated load on its surface. Numerical calculations are made for several values of the non-homogeneous parameter \(m\), and numerical variations of stress and displacement components are shown graphically.
scientific article; zbMATH DE number 1192774
scientific article