B.P. Patel

Hygrothermal effects on the structural behaviour of thick composite laminates using higher-order theory

Here, static and dynamic characteristics of thick composite laminates exposed to hygrothermal environment are studied using a realistic higher-order theory developed recently. The formulation accounts for the nonlinear variation of the in-plane and transverse displacements through the thickness, and abrupt discontinuity in slope of the in-plane displacements at any interface. The analysis is carried out employing a C 0 QUAD-8 isoparametric higher-order finite element. It is shown that the shear deformation theory without accounting for the thickness-stretching effect and slope discontinuity in the in-plane displacements may not be adequate for the analysis of fairly thick composite laminates exposed to hygrothermal loading. The significance of retaining various higher-order terms in the present model, in evaluating the deflection, buckling and natural frequency for composite laminates at different moisture concentration and temperature, is brought out through parametric study. 2002 Elsevier Science Ltd. All rights reserved.

Nonlinear free flexural vibrations/post-buckling analysis of laminated orthotropic beams/columns on a two parameter elastic foundation

Abstract Nonlinear free flexural vibrations and post-buckling of laminated orthotropic beams resting on a class of two parameter elastic foundation are studied using a three-noded shear flexible beam element. Geometric nonlinearity is considered using von Karman’s strain–displacement relations. The formulation includes the effects of transverse shear deformation, in-plane and rotary inertia terms. Exact numerical integration is employed for evaluating all the strain energy terms. The nonlinear governing equations are solved by employing the direct iteration technique. Numerical results are obtained for orthotropic and cross-ply laminated beams with simply supported boundary conditions. A detailed study is carried out to highlight the influences of different parameters on frequencies and buckling loads of laminated orthotropic beams.

Dynamic analysis of laminated composite plates subjected to thermal/mechanical loads using an accurate theory

Abstract This paper deals with the application of a new higher-order theory that accounts for the realistic variation of in-plane and transverse displacements through the thickness for the dynamic response analysis of thick multi-layered composite plates. The solutions are obtained employing the finite element procedure based on a C0 eight-noded serendipity quadrilateral element. The importance of various higher-order terms in the present model is highlighted through the numerical study of mechanical and thermal loads. A detailed study is also carried out considering the influences of ply angle, aspect ratio, number of layers and thermal coefficients on the global response of thick laminates.

Nonlinear dynamic analysis of thick composite/sandwich laminates using an accurate higher-order theory

Abstract Using a C0 eight-noded plate element developed based on an accurate higher-order theory, the nonlinear dynamics analysis of thick composite and sandwich plates are investigated. The formulation is based on a theory that accounts for the realistic variation of in-plane and transverse displacements through the thickness. It also includes the inertia terms pertaining to the higher-order terms involved in the displacement functions. The geometric nonlinearity is introduced in the formulation based on the relevant Greens strain vector for the laminate. The governing equations of motion obtained here are solved through eigenvalue solution for free vibration case whereas the direct integration technique is employed for the transient response analysis. The performance and the applicability of the proposed discrete model for the nonlinear free flexural and forced vibration responses of thick laminates are discussed among alternate models, considering multi-layered cross- and angle-ply, and sandwich plates.

Flexural loss factors of sandwich and laminated composite beams using linear and nonlinear dynamic analysis

The purpose of the article presented here is to analyze the flexural loss factors of beams with sandwich or constrained layer damping arrangements and laminated composite beams using a C 1 continuous, three-noded beam element. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects, and is applicable for both flexural and torsional studies. The geometric nonlinearity based on von Karman’s assumptions is incorporated in the formulation while retaining the linear behavior for the material. The finite element employed here is based on a sandwich beam theory, which satisfies the interface stress and displacement continuity and has zero shear stress on the top and bottom surfaces of the beam. The transverse shear deformation in the form of trigonometric sine function is introduced in the formulation to define the transverse shear strain. The governing equations of motion for the dynamic analysis are obtained using Lagrange’s equation of motion. The solution for nonlinear equations is sought by using an algorithmdirect iteration technique suitably modified for eigenvalue problems, based on the QR algorithm. A detailed numerical study is carried out to highlight the influences of amplitude of vibration, shear modulus and thickness of the core of the sandwich beam, aspect ratios, boundary conditions, and lay-up in the case of laminates on the system loss factors. q 1999 Elsevier Science Ltd. All rights reserved.

A C1 finite element including transverse shear and torsion warping for rectangular sandwich beams

A new three-noded C1 beam finite element is derived for the analysis of sandwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. The transverse shear deformation is represented by a cosine function of a higher order. This allows us to avoid using shear correction factors. A warping function obtained from a three-dimensional elasticity solution is used in the present model. Since the field consistency approach is accounted for interpolating the transverse strain and torsional strain, an exact integration scheme is employed in evaluating the strain energy terms. Performance of the element is tested by comparing the present results with exact three-dimensional solu-tions available for laminates under bending, and the elasticity three-dimensional solution deduced from the de Saint-Venant solution including both torsion with warping and bending. In addition, three-dimensional solid finite elements using 27 noded-brick elements have been used to bring out a reference solution not available for sandwich structures having high shear modular ratio between skins and core. A detailed parametric study is carried out to show the effects of various parameters such as length-to-thickness ratio, shear modular ratio, boundary conditions, free (de Saint-Venant) and constrained torsion. Copyright

Dynamic analysis of laminated cross-ply composite non-circular thick cylindrical shells using higher-order theory

Abstract Here, the dynamic analysis of laminated cross-ply composite non-circular thick cylindrical shells subjected to thermal/mechanical load is carried out based on higher-order theory. The formulation accounts for the variation of the in-plane and transverse displacements through the thickness, abrupt discontinuity in slope of the in-plane displacements at the interfaces, and includes in-plane, rotary inertia terms, and also the inertia contributions due to the coupling between the different order displacement terms. The strain–displacement relations are accurately accounted for in the formulation. The shell responses are obtained employing finite element approach in conjunction with direct time integration technique. A detailed parametric study is carried out to bring out the effects of length and thickness ratios, eccentricity parameters and number of layers on the thermal/mechanical response characteristics of non-circular shells.

Non-linear dynamic stability characteristics of elastic plates subjected to periodic in-plane load

Abstract Using a C1 QUAD-8 shear-flexible plate element, based on a new kind of kinematics which allows one to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers in the laminates, the non-linear instability behaviour of plates subjected to periodic in-plane load has been studied. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects. Primarily, an attempt is made here to understand the geometrically non-linear parametric instability characteristics of isotropic and composite plates through a finite element formulation with dynamic response analysis. The non-linear governing equations obtained here are solved using the Newmark integration scheme coupled with a modified Newton–Raphson iteration procedure. The analysis brings out various characteristic features of the phenomenon, which are known from experiments, i.e. existence of beats, their dependency on the forcing frequency, the influence of initial conditions and load amplitudes, and the typical character of vibrations in the different regions.

Dynamic instability of layered anisotropic composite plates on elastic foundations

Abstract The dynamic instability of laminated composite plates supported on elastic foundations, subjected to periodic in-plane loads, is investigated using C 1 eight-noded shear-flexible plate element. The element is based on a new kind of kinematics which allows one to exactly ensure the continuity conditions for displacements and stresses at the interfaces between the layers of the laminate, and also the boundary conditions at the top and bottom surfaces of the laminate. The present model accounts for in-plane and rotary inertia effects. The boundaries of the principal instability region obtained here are conveniently represented in the non-dimensional excitation frequency—non-dimensional load amplitude plane. The influences of various parameters such as orthotropicity, ply-angle, static load factor, thickness and aspect ratios, and elastic foundation stiffness on dynamic stability are brought out.

Thermo-flexural analysis of thick laminates of bimodulus composite materials

Here, flexural analysis of laminated composite plates of bimodulus materials subjected to thermal load is carried out. The formulation is based on higher-order theory that accounts for the transverse shear and transverse normal deformations, and incorporates through the thickness approximations of the in-plane displacements. The governing equations obtained using the principle of minimum potential energy are solved through the finite element approach. The results obtained here are compared with those of the theory without thickness stretch/contraction terms and the first-order one. The combined influence of higher-order shear deformation, plate geometry, lay-up and ply-angle on the displacements/stresses and neutral surface locations of bimodulus composite laminate is examined.