Efficient linear transverse normal stress analysis of layered composite plates

Two dimensional kinematic models for CNT reinforced sandwich cylindrical panels with accurate transverse interlaminar shear stress estimation

Combining a high‐order shear deformation theory and a layerwise theory, a laminate theory of zigzag type is presented. Like the high‐order shear deformation theories, the number of independent variables of the present theory is independent of layer number. The numerical efficiency is thus guaranteed. Similar to the layerwise theories, the in‐plane displacement components vary from layer to layer. Hence, the imposition of continuity conditions of interlaminar shear stresses on the laminate interfaces becomes possible. Consequently, the accuracy of displacement and stress components can be improved. Numerical studies on composite laminates made of alternate sequences based on 0° and 90° layers are performed. It can be concluded that the present theory gives accurate in‐plane displacement and stress for 6‐layer, 19‐layer and 32‐layer laminates. Its predictions on transverse displacement, transverse shear stress and transverse normal stress seem to be gradually improved as the number of alternate layers increases.

C0 triangular elements based on the Refined Zigzag Theory for multilayer composite and sandwich plates

High-order free vibrations of doubly-curved sandwich panels with flexible core based on a refined three-layered theory

Through-the-thickness stress distributions near edges of composite laminates using stress recovery scheme and third order shear and normal deformable theory

The objective of the paper is to present a simple analytical solution to study the flexural behaviour of intelligent (composite and sandwich) panels subjected to electromechanical loads. For this purpose, panels with simply supported edge restraints are considered, and a one-term solution, which is the exact solution for the cases considered, is developed. The first-order shear deformation theory is used in this study. The constitutive equations employed herein not only provide the requisite electromechanical coupling but also account for the stiffness of the actuator and sensor layers apart from substrate. The displacement field and sensor voltage are obtained by minimizing the total (electro-mechanical) potential. While constitutive relations are used to compute the inplane stress-state, the transverse normal and shear stresses are computed using 3-D elasticity equilibrium equations. A series of numerical examples is solved to study the influence of actuator loads (applied voltage) on these displacement and stress fields. A few interesting observations are made regarding the variation of interlaminar shear stresses at the actuator/substrate and sensor/substrate interface.

Axiomatic/asymptotic PVD/RMVT-based shell theories for free vibrations of anisotropic shells using an advanced Ritz formulation and accurate curvature descriptions

Thermal buckling of angle-ply laminated composite and sandwich plates according to a global higher-order deformation theory

In this study, an enhanced first order shear deformation theory via the strain energy transformation (EFSDT) in Laplace domain is presented for the efficient yet accurate viscoelastic FEM analysis of laminated composite plates. The main objective herein is to systematically derive the improved strain energy expression of first order shear deformation theory (FSDT) based on a conventional Reissner-Mindlin’s plate theory. To this end, an efficient higher order plate theory (EHOPT) is utilized to obtain the in-plane warping functions and synthesized into the strain energy of FSDT to improve their performance. The relationships between the two independent theories are systematically established via the strain energy transformation and the least-square approximation of the mean displacement. And the convolution theorem of Laplace transformation is applied to circumvent the overwhelming complexity of dealing with visco-elastic materials which is expressed as the Bolzmann superposition integral equation. The proposed EFSDT in Laplace domain has the same computational advantage of the conventional FSDT, while allowing us to improve the local distributions of the visco-elastic responses via the recovery procedure. The numerical results obtained herein are compared to those available in literature.

Nonlinear forced response of doubly-curved laminated panels composed of cnt patterned layers within first order shear deformation theory

Strain-rate-dependent failure criteria for composites

This paper addresses the problem of multilayered plates with embedded piezoelectric layers by finite element method (FEM). Original ideas in previous papers (Int. J. Numer. Methods Eng. 2002; 195: 191–231, 253–291) have been extended to the static and dynamic analysis of coupled electro‐mechanical problems. Two variational statements, the Principle of Virtual Displacements (PVD) and the Reissner Mixed Variational Theorem (RMVT) are employed to derive classical and mixed finite element matrices, respectively. Transverse stress assumptions are made in the framework of RMVT and the resulting finite elements describe a priori interlaminar continuous transverse shear and normal stresses. The unified formulation (UF) has been referred to in order to derive hierarchical finite elements (FEs) in term of a few fundamental nuclei for a large variety of piezoelectric plate theories. Both modellings that preserve the number of variables independent from the number of layers (equivalent single layer models, ESLM) and layer‐wise models (LWM) in which the same variables are independent in each layer have been treated. The expansion order N assumed for displacement, transverse stress and electrical potential fields in the plate thickness direction z as well as the number of the element nodes Nn have been taken as free parameters of the considered formulations. By varying N, Nn, variable treatment (LW or ESL) as well as variational statements (PVD and RMVT), a large number of FEs have been presented. Compliances and/or stiffness are accumulated from layer to multilayered level according to the corresponding variable treatment.The numerical evaluations and assessment for the presented plate elements have been provided. The superiority of RMVT applications with respect to classical ones based on PVD has been confirmed for piezolectric plates. The proposed RMVT elements, in fact, are able to give a quasi‐three‐dimensional description of stress/strain mechanical and electrical fields in multilayered thick and thin piezolectric plates. Copyright © 2006 John Wiley & Sons, Ltd.

This paper deals with the problem of stress distribution in orthotropic and laminated plates subjected to central concentrated load. An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is used to obtain in-plane normal and transverse shear stresses through the thickness of plate. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. A simply supported plate with central concentrated load is considered for the numerical analysis. Anomalous behavior of inplane normal and transverse shear stresses is observed due to effect of stress concentration compared to classical plate theory and first order shear deformation theory.

A three-dimensional mixed variational principle is used toderive a Kth-order two-dimensional lineartheory for an anisotropichomogeneouspiezoelectric(PZT)plate.Themechanicaldisplacements, theelectricpotential,theinplane components of the stress tensor, and the in-plane components of the electric displacement are expressed as a e niteseries of orderK inthethickness coordinate bytakingLegendrepolynomialsas thebasisfunctions. However, the transverse shear stress, the transverse normal stress, and the transverse electric displacement are expressed as a e nite series of order (K +2) in the thickness coordinate. The formulation accounts for the double forces without moments that may change the thickness of the plate. Results obtained by using the plate theory are given for the bending of a cantilever thick plate loaded on the top and the bottom surfaces by uniformly distributed 1) normal tractions and 2) tangential tractions. Results are also computed for the bending of a cantilever thick PZT beam loaded by 1) a uniformly distributed charge density on the top and the bottom surfaces and 2) equal and opposite normal tractions distributed uniformly only on a part of the beam. The seventh-order plate theory captures well the boundary-layer effects near the clamped and the free edges and adjacent to the top and the bottom surfaces of a thick orthotropic cantilever beam with the span to the thickness ratio of two. Also, through-the-thickness variation of the transverse shear and the transverse normal stresses agree well with those computed from the analytical solution of the three-dimensional elasticity equations. The governing partial differential equations are second order, so that Lagrange basis functions can be used to solve the problem by the e nite element method.

: This report covers three topics in mechanics of advanced composites: effect of fiber cross-section on stiffness and strength of laminated composites; failure criteria for composites under combined loading; and stress analysis models for thick composites. In the area of fiber cross-sectional effect, micromechanics analysis addresses the effect of elliptical fibers on the stiffness and in-plane stress concentrations. Numerical results show that fiber cross-sectional geometry has only a modest influence on laminate elastic constants. The second topic addresses the interaction between longitudinal compression and transverse loading (tension and compression). Data obtained with a mini-sandwich beam are used to generate failure stresses. Classical lamination theory, including thermal residual stresses due to cure, is utilized for determining play stresses. Experimental results reveal little interaction between longitudinal compression and transverse stresses as long as the transverse load is below uniaxial transverse failure. Under the topic of thick composites, the effect of shear deformation and transverse normal stress on the cylindrical bending of laminated, anisotropic plates subjected to a uniform lateral load is investigated. closed form solutions indicate that the effect of transverse normal stress on maximum deflection is small, even for relatively thick plates.