| A total Lagrangian finite element scheme for arbitrarily large displacements and rotations is applied to a wide range of shell geometries. The scheme decomposes the deformation into stretches and rigid-body rotations, examining the deformed state with respect to an orthogonal, rigidly translated and rotated triad located at the point of interest on the deformed structure. The Jaumann stresses and strains, which are resolved along the axes of this triad, are employed in the algorithm. Local and layer-wise thickness stretching and shear warping functions are used to model the three-dimensional behavior of the shell. These functions are developed through the use of the constitutive equations, certain stress and displacement continuity requirements at ply interfaces and laminate surfaces, and the behavior of the shell reference surface. Two finite elements are employed in the analyses: an eight-noded, 36 degree-of-freedom (DOF) element, and a four-noded, 41 DOF element. The 36 DOF element, which is not a compatible element with respect to the derivatives of in-plane deformations (i.e., {dollar}usb{lcub},x{rcub}, usb{lcub},y{rcub}, vsb{lcub},x{rcub}, {lcub}rm and{rcub} vsb{lcub},y{rcub}{dollar} are not forced to be continuous along interelement boundaries) proves adequate for moderate rotation problems, but fails in modeling very large rotation problems. The use of the 44 DOF element provides dramatically improved results in the large rotation problem. The scheme is used to analyze isotropic and anisotropic beams, plates, arches, and shells. As a special application, a detailed finite element model of an aircraft tire is analyzed with regard to deformations resulting from inflation pressure. Finally, the feasibility of static contact analysis is also demonstrated. |
