Study of internal forces and displacements of beams by finite difference method

Abstract

In classical structural mechanics the main goal is to find continuous solutions, which is possible only for a very limited number of problems. Therefore, for each problem a separate method is applied to find its own solution. In contrast to the methods of classical structural mechanics, the application of a number of numerical methods according to a relatively unified scheme leads to universal electronic computer programs. The finite difference method is one of the two basic numerical methods along with the finite element method that is currently the most widely used, without question, for engineering problems in general and structural engineering problems in particular. The finite difference method solves most structural mechanics problems by solving differential equations or systems of differential equations. The exact solutions of these equations can be determined for some simple special cases with physical characteristics and pre-selected boundary conditions of the structure. In practice, applications are very diverse, and exact solutions in explicit form for most structural problems do not exist. Numerical methods then create rich possibilities for finding solutions. The difference method is a classical form in this direction.

Keywords: Finite difference method; internal forces and displacements of beams.