LARGE DEFLECTION OF DEEP BEAMS ON ELASTIC FOUNDATIONS

This research deals with the geometric nonlinear behavior of beams resting on Winkler foundation. Timoshenko’s deep beam theory is extended to include the effect of large deflection theory. The finite difference method was used to solve the problem deep beams and the obtained results were compared. An incremental load approach with Newton-Raphson iteration computational technique was used for solving the nonlinear sets of node equilibrium equations in the finite difference method. In the finite element method (ANSYS program), the element SHELL 43 incorporated in ANSYS 5.4 was used. The element has four nodes with six degrees of freedom at each node: translations in the nodal x, y, and z- directions and rotations about the nodal x, y, and zdirections. Several important parameters were incorporated in the analysis to study the effects of vertical subgrade reaction, beam width, and beam depth to length ratio on the deflections, bending moments and shear forces. The results obtained from this method were compared with exact and numerical methods to check the accuracy of the solutions. Good agreements were found, the maximum difference in deflection at midspan from the finite elements and the finite differences was (0.79%). Also, the difference between the exact solution and the present finite difference was found to be (0.86%).