A WEAK-WEAK FORMULATION FOR LARGE DISPLACEMENTS BEAM STATICS: A FINITE VOLUMES APPROXIMATION

This paper addresses the problem of the numerical solution of beam statics undergoing large displacements. A kinematic analysis outlines the beam geometrical model through the definition of its Lagrangian co-ordinate and strain parameters. A definition of the stress parameters, a constitutive law and an expression for the strain energy of the beam are then provided under the hypothesis of small strain. The equations governing the beam equilibrium are introduced and their weak form is derived. These equations are then proved to be equivalent to the primal and mixed form of Principle of Virtual Work. The numerical approximation is introduced by applying the bidiscontinuous finite elements method on the linearized weak form. The weak-weak formulation is attained by using the lowest interpolation order both for test and trial functions on two staggered decompositions of the space domain. Some numerical examples prove the capability of present formulation in handling actual problems.