A HIGHER-ORDER THEORY FOR FREE-VIBRATION OF UNSYMMETRICALLY LAMINATED COMPOSITE AND SANDWICH PLATES - FINITE-ELEMENT EVALUATIONS

This paper presents a refined higher-order theory for free vibration analysis of unsymmetrically laminated multilayered plates. The theory accounts for parabolic distribution of the transverse shear strains through the thickness of the plate and rotary inertia effects. A simple C0 finite element formulation is presented and the nine-noded Lagrangian element is chosen with seven degrees of freedom per node. Numerical results are presented showing the parametric effects of aspect ratio, length/thickness ratio, number of layers, and lamination angle. The present theory predicts the frequencies more accurately when compared with first-order and classical plate theories

NONLINEAR DYNAMICS OF LAMINATED PLATES WITH A HIGHER-ORDER THEORY AND CO FINITE-ELEMENTS

Impact responses of composite laminates are investigated with C0 finite elements. A ninenode isoparametric quadrilateral element based on a higher-order theory and the von Karman large deflection assumptions is developed. An experimentally established contact law which accounts for the permanent indentation is incorporated into the finite element program to evaluate the impact force. In the time integration, the explicit central difference technique is used in conjunction with the special mass matrix diagonalization scheme. Numerical results, including the contact force histories, deflections and strains in the plate, are presented

A critical-review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches

A critical review of literature pertinent to the subject matter of this paper was carried out under the following two broad headings: free vibration and transient dynamics. Each of these groups describes the various theoretical developments in fiber reinforced laminated composite and sandwich plates. The theoretical developments are further classified according to the refinement/accuracy of the theories developed, such as the classical theory, the first-order shear deformation theory, and the three-dimensional elasticity/higher-order shear deformation theories. The present literature review is limited to linear free vibration and transient dynamic analyses, and geometric nonlinear transient response of multilayer sandwich/fiber-reinforced composite plates. A comparative study of recently developed refined theories in conjunction with the C-degrees isoparametric finite element formulation has been made and the conclusions were drawn based on the literature review and the refined theories results. In order to compare the present results with the available results and to provide an easy means for future comparisons by other investigators, the numerical results are presented in tabular form

Effect of cross-sectional warping of anisotropic sandwich laminates due to dynamic loads using a refined theory and C° finite elements

An attempt has been made to study the effect of cross-sectional warping in the symmetrically laminated anisotropic composite sandwich plates for transient loads. A higher-order shear deformation theory (HOST) is used in conjunction with the simple displacement based C° finite element method (FEM). As is well-known, the classical first-order theories hitherto considered were inadequate to describe the propagation of waves in the highly orthotropic sandwich laminates. The present theory, which is more accurate than the Reissner-Mindlin theory, is applied herein, for the evaluation of plate response to different types of dynamic loads. An explicit central difference scheme is employed for the integration of dynamic equations of equilibrium with a diagonalized mass matrix obtained by a special procedure applicable to quadrilateral isoparametric elements. The numerical results of the present investigation have been compared with the first-order shear deformation theory (FOST) and the differences between HOST and FOST are examined. The results presented here should be useful in obtaining better correlation between theory and experiment, and to numerical analysts in verifying their results

EFFECT OF CROSS-SECTIONAL WARPING OF ANISOTROPIC SANDWICH LAMINATES DUE TO DYNAMIC LOADS USING A REFINED THEORY AND C(0) FINITE-ELEMENTS

An attempt has been made to study the effect of cross-sectional warping in the symmetrically laminated anisotropic composite sandwich plates for transient loads. A higher-order shear deformation theory (HOST) is used in conjunction with the simple displacement based C0 finite element method (FEM). As is well-known, the classical first-order theories hitherto considered were inadequate to describe the propagation of waves in the highly orthotropic sandwich laminates. The present theory, which is more accurate than the Reissner-Mindlin theory, is applied herein, for the evaluation of plate response to different types of dynamic loads. An explicit central difference scheme is employed for the integration of dynamic equations of equilibrium with a diagonalized mass matrix obtained by a special procedure applicable to quadrilateral isoparametric elements. The numerical results of the present investigation have been compared with the first-order shear deformation theory (FOST) and the differences between HOST and FOST are examined. The results presented here should be useful in obtaining better correlation between theory and experiment, and to numerical analysts in verifying their results

VIBRATIONS OF UNSYMMETRICALLY LAMINATED PLATES ANALYZED BY USING A HIGHER-ORDER THEORY WITH A C-DEGREES FINITE-ELEMENT FORMULATION

Recently developed shear deformation theory is used to analyze vibrations of laminated composite and sandwich plates in conjunction with a C° isoparametric finite element formulation. The present theory is based on a higher order displacement model and the three-dimensional Hooke's laws for plate material, giving rise to a more realistic representation of the cross-sectional deformation. The theory does not require the usual shear correction coefficients generally associated with Reissner-Mindlin theories. A special mass lumping procedure is used in the dynamic equilibrium equations. The numerical examples presented are compared with 3-D elasticity/analytical and Mindlin's plate solutions, and it is demonstrated that the present model predicts the frequencies more accurately when compared with the first order shear deformation theories and classical plate theories