Asymptotically accurate 3-D recovery from Reissner-like composite plate finite elements

Abstract

An accurate stress/strain recovery procedure for laminated, composite plates that can be implemented in standard finite element programs is developed. The formulation is based on an asymptotic analysis and starts from a three-dimensional, anisotropic elasticity problem that takes all possible deformation into account. After a change of variable, which introduces intrinsic two-dimensional description for the deformation of the reference plane, the variational asymptotic method is then used to rigorously split this three-dimensional problem into two reduced-dimensional problems: a nonlinear, two-dimensional analysis of the reference surface of the deformed plate (an equivalent single-layer plate model), and a linear, one-dimensional analysis of the normal-line element through the thickness. The latter is solved by a one-dimensional finite element method and provides a constitutive law between the generalized, two-dimensional strains and stress resultants for the plate analysis, and a set of recovering relations to approximately express the three-dimensional displacement, strain and stress fields in terms of two-dimensional variables determined from solving the equations of the plate analysis. The strain energy functional that is asymptotically correct through the second-order in the small parameters is then cast into the form of Reissner’s theory. Although it is not in general possible to construct an asymptotically correct Reissner-like composite plate theory, an optimization procedure is used to drive the present theory as close as possible to being asymptotically correct, while maintaining the simplicity and beauty of the Reissner-like formulation. A computer program based on the present procedure, called variational asymptotic plate and shell analysis, has been developed. Its utility is demonstrated by inserting the recovery procedure into the plate element of a general-purpose finite element code. Numerical results obtained for a variety of laminated, composite plates show that three-dimensional field variables recovered from the present theory agree very well with those from exact solutions.