Nonlinear Analysis of Thick Composite Plates Using a Cubic Spline Function

摘要

A non-linear thick composite shell theory is presented in which the through-the-thickness displacements are modeled using a variation of a cubic spline. The theory is developed by considering the Lagrangian strains in conjunction with the 2nd Piola-Kirchhoff stress. This formulation leads to a theory which encompasses large displacements with moderately large rotations but is restricted to small strains. The imposition of the cubic distribution through-the-thickness insures that the compatibility of the displacements and their first and second derivatives and thus the shear strains are maintained from lamina to lamina. The cubic distribution is seen as a higher order approximation than has been previously employed, but because of the nature of the spline, the theory is less cumbersome and more easily implemented than the parabolic theory. In addition, there is no introduction of additional degrees of freedom with the cubic theory. A family of 2-D isoparametric elements is employed in conjunction with the theory to solve a class of 3-D thick plate problems. Results are presented showing comparisons which are in good agreement with previous work. (Author)