On the performance of higher order theories for transient dynamic analysis of sandwich and composite beams

Abstract

Abstract-Higher-order shear-deformable refined theories, based on isoparametric elements, are adopted for transient dynamic analysis of symmetric and unsymmetric sandwich and composite beam constructions. These shear-correction coefficient free theories model cross sectional warping using nonlinear variation of inplane displacements across the depth. They also incorporate transverse shear stress in the formulation. A special lumping scheme is employed for the evaluation of diagonal mass matrix, and a central difference scheme is used for carrying out the integration of the equation of motion, to obtain the response history. Through numerical experiments, the efficacy of higher-order models in predicting displacements and stress, resultants over from the first-order theory, with respect to time, is clearly brought out in this paper. 0 1997 Elsevier Science Ltd.

Assessment of zigzag theory for static loading, buckling, free and forced response of composite and sandwich beams

“…Eqs. (12) imply that the three natural frequencies x n and thickness modes U n ¼ U n 0 cos x n t for given longitudinal mode n are obtained from KU n 0 ¼ x 2 n MU n 0 . For longitudinally sinusoidal harmonic load P n ¼ P n 0 cos xt, let the steady state response be U n ¼ A n cos xt þ B n sin xt.…”

“…Several 1D models exist to account for the shear deformation in moderately thick laminated beams. The smeared beam theories with global expansion of displacements across the thickness, like the first order shear deformation theory (FSDT) [6], third order theory (TOT) [7][8][9][10] arid higher order theories (HOT) [11][12][13][14] have been developed. Shear correction factor is needed only for FSDT.…”

Dynamic response of aerospace structures by means of refined beam theories

“…The use of refined 1D models is relevant to predict the time-dependent response of thin-walled slender structures, as those considered in [62]. In this paper, 1D CUF is employed along with mode superposition method to conduct dynamic response analysis on various structures.…”

Free vibration analysis of third-order shear deformable composite beams using dynamic stiffness method

“…Khdeir [6] developed an analytical solution of the classical, first-and third-order laminated beam theories to study the dynamic response of antisymmetric cross-ply laminated beams with generalized boundary conditions and for arbitrary loadings. Marur and Kant [7] compared the higher-order refined theories on the transient response of laminated composite beams, showing the effects of shear deformation and rotary inertia. Kant et al [8] presented an analytical method for the dynamic analysis of laminated beams using higher-order refined theory.…”