THE CONSTRUCTION OF AN INTEGRAL-REPRESENTATION OF THE SOLUTION OF THEEQUILIBRIUM EQUATIONS OF TIMOSHENKO-TYPE THEORY FOR SHELLS OF COMPLEX-GEOMETRY

A method of constructing an integral representation of the solution of the equilibrium equations of Timoshenko-type theory for thin or shall ow isotropic shells of complex geometry is proposed. The method involv es the following steps: writing the equilibrium equations for a fundam ental solution of the three-dimensional theory of elasticity-the Kelvi n vector in a curvilinear system of coordinates, normally to the middl e surface of the shell; selecting a differential operator correspondin g to the given theory of shells from the exact equilibrium equations f or the Kelvin vector and constructing an integral representation of th e vector of displacements of elements of the shell using Green's formu la for the differential operator of the given theory of shells. It is shown that problems of determining the parameters of the stress-strain state of a shell in differential and integral formulations are equiva lent, with an error which is small in the context of approximations of the theory. One method of constructing integral equations for the dis placement vector of the elements of a shell of constant thickness is p roposed. (C) 1998 Elsevier Science Ltd. All rights reserved.