Geometrically nonlinear transient analysis of laminated composite plates

Abstract

Forced motions of laminated composite plates are investigated using a finite element that accounts for the transverse shear strains, rotary inertia, and large rotations (in the von Karman sense). The present results when specialized for isotropic plates are found to be in good agreement with those available in the literature. Numerical results of the nonlinear analysis of composite plates are presented showing the effects of plate thickness, lamination scheme, boundary conditions, and loading on the deflections and stresses. The new results for composite plates should serve as bench marks for future investigations. mation are assumed to remain straight and normal to the midsurface after deformation (i.e., transverse shear strains are zero), has been used to calculate frequencies, static response, and dynamic response under applied loads. Recent studies in the analysis of plates have shown that the effect of the transverse shear strains on the static and dynamic response of plates is significant. For example, the natural frequencies of vibration predicted by the classical plate theory are 25% higher, for plate side-to-thickness ratio of 10, than those predicted by a shear deformation theory (SDT). In transient analysis of plates the classical plate theory predicts unrealistically large phase velocities in the plate for shorter wavelengths. The Timoshenko beam theory,3 which includes transverse shear and rotary inertia effects, has been extended to isotropic plates by Reissner 4'5 and Mindlin,6 and to laminated anisotropic plates by Yang et al.7 A generalization of the von Karman nonlinear plate theory for isotropic plates to include the effects of transverse shear and rotary inertia in the theory of orthotropic plates is due to Medwadawski,8 and that for anisotropic plates is due to Ebcioglu.9 With the increased application of advanced fiber composite material to jet engine fan or compressor blades, and in high performance aircraft, studies involving transient response of plates made of such materials are needed to assess the capability of these materials to withstand the forces of impact due to foreign objects (e.g., the ingestion of stones, nuts and bolts, hailstones, or birds in jet engines). Previous in- vestigations into the linear transient analysis of composite plates include Moon's10'11 investigation of the response of infinite laminated plates subjected to transverse impact loads at the center of the plate; Chow's12 study of laminated plates (with transverse shear and rotary inertia) using the Laplace transform technique; the Wang et al. 13 investigation, by the method of characteristi cs, of unsymmetrical orthotropic laminated plates; and Sun and Whitney's14'15 study of plates under cylindrical bending. More recently, the present author16'17 investigated the linear transient response of layered anisotropic composite rectangular plates and presented extensive numerical results for center deflection and stresses.