On the dynamic behavior of composite materials

Simple C” isoparametric finite element formulations based on a set ofhigher-order shear deformable theories are introduced for the analysis of symmetric/unsymmetric composite laminated and sandwich plates. The models account fornon-linear variation of in-plane displacements through the plate thickness, while thetransverse displacement variation may be constant, linear or non-linear. The assumedmodels eliminate the use of shear correction coefficients associated withReissner-Mindlin theory. A simple generalized coordinates/isoparametric finite elementformulation based upon Mindlin-Reissner theory is also presented for the analysis. Themethod of selective integration (uniform and reduced) is applied to evaluate elementstiffness matrix to prevent the appearance of the shear locking phenomenon. Theheterosis version of the proposed elements which shows neither spurious zero energymodes nor shear locking is evolved. An implicit time marching scheme is adopted forintegration of the dynamic equilibrium equation. A diagonalized-lumped mass matrix isemployed with a special procedure applicable to biquadratic isoparametric elements. Thesolutions obtained for deflections, stress resultants and stresses of rectangular laminatesas well as skew plates are compared with those obtained using the three-dimensionalelasticity solution, finite element and closed form solutions of higher-order shear theoriesand Mindlin-Reissner theory. Numerical results for deflections, stress resultants andstresses are presented showing the effects of plate aspect ratio, orthotropy, laminationscheme, skew angle, etc. on the transient response. The present formulation is the firstto deal with the transient response of skew plates. The results obtained herein should beof interest to composite-structure designers, and to experimentalists and numericalanalysts in the interpretation of their findings.