A new quasi-linearization finite difference scheme for large deflection analysis of prismatic and non-prismatic inextensible slender beams

A new scheme called quasi-linearization finite differences is developed for large deflection analysis of prismatic and non-prismatic inextensible slender beams with different boundary conditions subjected to various types of continuous and discontinuous external loads in horizontal and vertical global directions. Simultaneous equations of highly nonlinear and linear terms are obtained when casting the derived exact highly nonlinear governing differential equation using central finite differences on the nodes along the beam. A quasi-linearization scheme is used to solve these equations based on successive corrections of the nonlinear terms in the simultaneous equations. The nonlinear terms in the simultaneous equations are assumed constant during each correction (iteration). Several representative numerical examples of prismatic and non-prismatic slender beams with different loading and boundary conditions are analyzed to illustrate the merits of the new adopted numerical scheme as well as its validity, accuracy and efficiency. The results of the present scheme are checked using large displacement finite element analysis of MSC/NASTRAN program. A comparison between present scheme and MSC/NASTRAN results reveals excellent agreements. The advantage of the new scheme is that the load can be applied in one step with few iterations (3 to 6 iterations).