Cylindrical shell subject to local loads applied on an arbitrarily shaped area

problem of a cylindrical shell subject to local loads over an arbitrary shaped base is being analysed. Governing equations for the cylindrical shell are solved by the double Fourier series expansion technique, yielding solutions for stresses and displacements in terms of Fourier load coefficients. The load coefficients are double integral functions, which have variable integral limits when the load has a non-rectangular base profile. To evaluate the load coefficients, two methods are studied. In the first method, the discrete Fourier approximation technique is employed. In the second method, the double integral expression is converted into a boundary line integral by means of Green’s Theorem. For a boundary with no analytical expression, it can be approximated by a series of line segments and integration is carried out along each line segment. The numerical integration is accomplished by the Clenshaw-Curtis quadrature rule. The boundary integral method is simpler and easier to implement in the computer than the discrete Fourier approximation method.