Solution of two-dimensional problems of the statics of flexible shallow shells by spline approximation

Abstract

Spline functions have come into increasingly wide use recently in the solution of boundary-value problems of the theory of elasticity of plates and shells. This development stems from the advantages offered by spline approximations compared to other methods. Among the most important advantages are the following: (1) the behavior of the spline in the neighborhood of a point has no effect on the behavior of the spline as a whole; (2) spline interpolation converges well compared to polynomial interpolation; (3) algorithms for spline construction are simple and convenient to use. The use of spline functions to solve linear two-dimensional problems on the stress-strain state of shallow shells and plates that are rectangular in plan has proven their efficiency and made it possible to expand the range of problems that can be solved. The approach proposed in these investigations is based on reducing a linear two-dimensional problem to a unidimensional problem by the spline unidimensional problem by the method of discrete orthogonalization in the other coordinate direction. Such an approach makes it possible to account for local and edge effects in the stress state of plates and shells and obtain reliable solutions with complex boundary conditions. In the present study, wemore » take the above approach, employing spline functions to solve linear problems, and use it to also solve geometrically nonlinear problems of the statics of shallow shells and plates with variable parameters.« less