The use of Cauchy-Krylov functions for the calculation of stresses and strains in plates and shells

Solving the boundary value problems in the theory of plates and shells is topical for low-weight thin-walled structures used in aerospace systems. In this case, the problem is to develop computationally efficient and robust algorithms for solving strength problems for thin-walled structural elements. An example of a solution to this problem is the fundamental system of functions suggested by A. Krylov to solve differential equations of the 4-th order describing a beam on an elastic foundation under arbitrary initial conditions. The approach is based on the Cauchy method applied to a system of ordinary differential equations with constant coefficients. In this paper, a similar set of functions called the Cauchy-Krylov functions is determined by the matrix algebra for a given arbitrary fundamental system of functions. A simple computer-adaptive technique is constructed to determine the Cauchy-Krylov functions for differential equations with constant and variable coefficients in the mechanics of deformation of plates and shells. To overcome the problem of robustness of algorithms in the mechanics of plates and shells, a multiplicative method is used to transfer boundary conditions to an arbitrarily given point and to form a system of algebraic equations. Solving this system yields strength parameters of a plate or shel l . A new analytical method is suggested for solving boundary value problems of mechanics of plates, shells and a certain class of thin-walled structures.

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