Discrete-Continual Finite Element Method for Semianalytical Analysis of Plates on Two-Parameter Elastic Foundation. Part 1: Continual Formulations of the Problem and Approximations

This paper is proposed discrete-continual finite element method (DCFEM) for semianalytical analysis of plates on two-parameter elastic foundation. First of all, the operational and discrete-continual formulations of the problem are described, then the approximation of unknown functions and its partial derivatives are obtained. Later the internal forces, local stiffness matrices and local load vectors are evaluated, then these local vectors and matrices are assembled to obtain resultant multipoint boundary problem and in the final step the problem is solved by the exact analytical method. This method allowed to obtain exact analytical solutions of boundary problems along the regular direction, and these solutions remain exact for arbitrary influences such as any force or moment, soil parameters, intermediate constraints and connections. Using this method, the problem remains continual in the one direction (basic), while the discrete (finite element) approximation is carried out with respect to the non-basis direction. The structural discontinuities in the analytical direction can be taken into account, by addition of new appropriate boundary conditions at the relevant section. The DCFEM increases the accuracy of the solution and significantly reduces the computational efforts, especially within analysis of extended plates such as strip foundations. (paper)