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AN INTEGRAL EQUATION METHOD FOR CUTOUT PROBLEMS IN SHELLS
Abstract
A method is described for the determination of the state of stress in a shallow shell with a single curvilinear hole. A system of two coupled integral equations is obtained using the Green's function method. Each of these equations includes a contour integral associated with the corresponding plate solution and a surface integral which yields the correction to the plate solution. A complex variable method is presented for the derivation of the Green's functions appearing in the integral equations. These functions are the Green's functions for plane stress and plate bending which satisfy the boundary conditions on the hole which eliminate the unknown boundary values from the contour integrals. Although the method is applicable to holes of arbitrary shape, the case of a circular hole with tractions prescribed on the edge is shown as an example. The formulation yields the direct solution to plate problems by simple contour integration. Closed form solutions are obtained for three selected plate problems. A numerical procedure for solving the equations is also described. The method involves representing certain derivatives of the Airy stress function and the normal deflection, which occur in the integral equations, by cubic B-splines with unknown coefficients. A system of equations corresponding to the number of spline coefficients is generated by evaluating the integral equations at the center point of each spline function and is solved by Gauss elimination. The numerical method is demonstrated for a circular cylindrical shell with a circular hole subjected to axial tension. The results confirm the viability of the formulation although the practicality of the numerical method was not demonstrated.
Subject Area
Mechanical engineering
Recommended Citation
GROVER, RICHARD LLOYD, "AN INTEGRAL EQUATION METHOD FOR CUTOUT PROBLEMS IN SHELLS" (1981). ETD collection for University of Nebraska-Lincoln. AAI8124512.
https://digitalcommons.unl.edu/dissertations/AAI8124512