Method of Solving Geometrically Nonlinear Bending Problems of Functionally Graded Shallow Shells of Complex Shape

A new numerical-analytical method for solving geometrically nonlinear bending problems for thin shallow shells of complex shape in plan made of functionally graded materials is developed. The method is based on the R-functions method and the parameter continuation method. Test problems for clamped homogeneous and hinged functionally graded plates under uniformly distributed load of different intensity are solved. The results for deflections and stresses obtained with the developed method are compared with those obtained with other methods. The bending problem for a functionally graded shell of complex shape is solved. The influence of the gradient properties of the material and geometric shape on the stress–strain state is studied.