NEW FORMULATION OF FEM FOR DETERMINISTIC AND STOCHASTIC BEAMS THROUGHGENERALIZATION OF FUCHS APPROACH

This paper proposes an alternative way of constructing the global stif fness matrix of the finite element method for bending beams, it also a pplies the new formulation to first and second moment analysis of stoc hastic beams, which involve spatially uncertain bending stiffness. Ori ginating from Fuchs' idea of decoupling the shear and bending componen ts in the bending beam, the element level stiffness matrix is diagonal ized. The generalized stress-strain, strain-displacement and equilibri um relationships are assembled, respectively, and then are combined to form the global stiffness matrix. The advantage of the new formulatio n is that the bending stiffness explicitly appears in the global stiff ness matrix. The mean vector and covariance matrix of the displacement of the beam are then obtained in terms of probabilistic characteristi cs of the uncertain bending stiffness. This is in contrast to the conv entional finite element method in stochastic setting, which is based o n the perturbation technique. The example is given to illustrate the e fficacy of the new formulation and its application to bending of stoch astic beams.