NUMERICAL SOLVING OF A 3-D STIFFNESS MATRICES OF THE WOOD 1 BEAM USING THE FINITE ELEMENT METHOD

The interest of this article is to show the relevance of the non-linear geometric model to estimate and to simulate numerically the critical wooden beams buckling load. Base on the kinematic hypotheses of the Vlassov's theory, the consideration of the kinematic relationships associated with warping are presented in a coherent and unified geometric form. The virtual work principal in updated lagrangian description allowed us to determine the incremental equations of equilibrium. Polynomial interpolation helps us to reconstruct the main matrices of the problem of nonlinear geometry. The size of the rigidity matrices obtained takes into account the warping phenomenon. In a numerical plan, the resolution of the equations established allows us to appreciate relevance of the seventh degree of freedom on predicting the critical buckling load.