A C-1 finite element including transverse shear and torsion warping for rectangular sandwich beams

A new three-noded C-1 beam finite element is derived for the analysis of sa ndwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper an d lower surfaces of the beam. The transverse shear deformation is represent ed by a cosine function of a higher order. This allows us to avoid using sh ear correction factors. A warping function obtained from a three-dimensiona l elasticity solution is used in the present model. Since the field consist ency approach is accounted for interpolating the transverse strain and tors ional strain, an exact integration scheme is employed in evaluating the str ain energy terms. Performance of the element is tested by comparing the present results with exact three-dimensional solutions available for laminates under bending, an d the elasticity three-dimensional solution deduced from the de Saint-Venan t solution including both torsion with warping and bending. In addition, th ree-dimensional solid finite elements using 27 noded-brick elements have be en used to bring out a reference solution not available for sandwich struct ures having high shear modular ratio between skins and core. A detailed par ametric study is carried out to show the effects of various parameters such as length-to-thickness ratio, shear modular ratio, boundary conditions, fr ee (de Saint-Venant) and constrained torsion. (C) 1999 John Wiley & Sons, L td.