James M. Greer

Singularities in Polynomial Representations of Transverse Shear in Finite Elements

Although many possible combinations of incomplete cubics are possible for representing the transverse displacements in a composite laminate, only a few make physical sense. Among these, a particualr choice was shown to be susceptible to irregularities and singularities, in that an unfortunate choice of ply thicknessses and shear moduli lead to laminates overly stiff in shear. Modifications to the displacement functions were shown to eliminate this behavior and yield a transverse shear stress distribution having some of th features associate with the elasticity solution, namely, continuous shear stresses and in plane displacements throughtou the lamniate thickess and th discontnuous transverse shear strains

A Corotational Total Lagrangian Finite Element Analysis with Application to the Aircraft Tire

A total Lagrangian finite element scheme for arbitrarily large displacements and rotations is applied to a section of an isotropic circular toroidal shell and an aircraft tire. The scheme decomposes the motion into stretches and rigid-body rotations, describing the deformed state in terms of local engineering measures: the Jaumann stresses and strains. Local and layer-wise thickness stretching and shear warping functions are used to model the three-dimensional behavior of the shells. The finite element model successfully models the bi-curved shell as well as the complex geometry of the aircraft tire under inflation and contact loads.