A BOUNDARY PROBLEM CONNECTED WITH THE CALCULATION OF A PRISMATIC ELASTIC SHELL OF VARIABLE THICKNESS,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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The article lists briefly the basic propositions of the mathematical theory of elasticity, and elucidates the mathematical difficulties connected with the calculation of shells. Using the method proposed by Professor I. N. Vekua, a system of equations is set up which characterizes approximately the stressed state of a prismatic elastic shell of variable thickness. This system of equations can be reduced, for the zero approximation, to the treatment of a boundary problem in some connected region S bounded by a smooth contour L. This problem can be divided into two boundary problems, one of which can be solved in the usual manner using Greens function for the Laplacian operator. The other problem can be solved by means of matrix-vector notation and, by applying Greens tensor, can be reduced to an integrodifferential equation in matrix-vector form. Finally, by integrating them by parts, the final equations are reduced to a system of integral equations of the Fredholm type.
- Numerical Mathematics