ON APPLICATIONS OF GENERALIZED FUNCTIONS TO CALCULATION OF THIN CYLINDRICAL SHELLS

Abstract eng:
The mathematical model of a thin cylindrical shell according to Timoshenko and Love bending theory contains derivatives of generalized internal forces and deformation components. However these derivatives are not defined at such points between ends of the shell where a concentrated loading or an internal support or coupling is located. In order that the mathematical model of a thin cylindrical shell subjected to axisymmetric loading may hold true at the points of discontinuity mentioned, which are common in calculating experience, we have used the distributional derivative for the unknown quantities, and developed a generalized mathematical model in the form of a system of ordinary differential equations (SODE). We have found the general solution to the SODE by using the Laplace transform method and symbolic programming approach. The solution found is a generalization of Krylov functions method.

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