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A mathematical analysis method for bending problem of clamped shallow spherical shell on elastic foundation

Last modified: 2020-07-14

#### Abstract

A mathematical analysis method is employed to solve the bending problem of slip clamped shallow spherical shell on elastic foundation. The differential equations of the problem are simplified to a biharmonic equation using the slip clamped boundary conditions. A function is established by using the R-function, the fundamental solution and the boundary equation of the biharmonic equation. This function satisfies the homogeneous boundary condition of the biharmonic equation. The biharmonic equation of the bending problem of slip clamped shallow spherical shell on elastic foundation is transformed to Fredholm integral equation of the second kind by using Green formula. The vector expression of the integral equation kernel is derived. The singularity of the integral equation kernel is overcome by choosing a suitable form of the normalized boundary equation. To obtain numerical results, the discretization of the integral equation of the bending problem is conducted. The treatment of singular term in the discretization equation is using the integration by parts. Two numerical results show high accuracy of the method given by the present paper. The results show fine agreement with the ANSYS finite element method(FEM) solution, and which shows the method is an effective mathematical analysis method.

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