scholarly journals A Mindlin multilayered hybrid-mixed approach for laminated and sandwich structures without shear correction factors

2010 ◽  
pp. 725-742
Author(s):  
Achraf Tafla ◽  
Rezak Ayad ◽  
Lakhdar Sedira
Keyword(s):  
Transverse Shear ◽  
Order Theory ◽  
Shear Stresses ◽  
Correction Factors ◽  
Equilibrium Equations ◽  
First Order Theory ◽  
Static Condensation ◽  
Bending Stresses ◽  
Mixed Approach ◽  
Laminated Structures

A new hybrid-mixed variational approach for the linear analysis of laminated and sandwich plates, without transverse shear correction factors, is presented. It’s based on the first order theory of Reissner/Mindlin. A quadratic approximation through the thickness is proposed for transverse shear stresses (continuity C-1), and two equilibrium equations are used for their approximation. This reduces in consequence the number of interpolation parameters of bending stresses, which are eliminated using the static condensation technique. The proposed approach has been adapted to a quadrilateral 4-node finite element, free of locking, to which performances have been analyzed using some known problems of sandwich and laminated structures.

Rotating Moderately Thick Annular Disks via an Extension to Classical Theory

2012 ◽  
Vol 28 (2) ◽  
pp. 355-360 ◽  
Author(s):  
A. M. Zenkour
Keyword(s):  
Classical Theory ◽  
Order Theory ◽  
Equilibrium Equations ◽  
Annular Disk ◽  
First Order ◽  
First Order Theory ◽  
Distributed Load ◽  
Vertical Displacements ◽  
Bending Stresses ◽  
Annular Disks

AbstractThe problem of rotating annular disk subjected to a uniformly distributed load is treated in two ways. Stress is divided into a rotating part because of the angular velocity and a bending part due to force loading. New set of equilibrium equations with small deflections is developed. Solutions for radial displacement, deflection, forces and moment resultants, and the rotating and bending stresses of the first-order theory are presented in terms of corresponding quantities of annular disks based on the classical theory. The boundary conditions at the edges of the annular disk are roller supported, clamped or free. Several examples are presented to illustrate the use and accuracy of these relationships. The effects of several parameters on the radial and vertical displacements and rotating and bending stresses are studied. It is observed that the classical theory is sufficient to study the problem of rotating annular disks. However, the inclusion of the effect of shear deformation is necessary to study precisely the curvature of moderately thick annular disks.

Stress analysis of smart composite plate structures

2020 ◽  
pp. 095440622097544
Author(s):  
Aniket Chanda ◽  
Utkarsh Chandel ◽  
Rosalin Sahoo ◽  
Neeraj Grover
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Laminated Composite ◽  
Composite Plates ◽  
Higher Order ◽  
Hyperbolic Function ◽  
Solution Technique ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Equilibrium Equations

In the present study, the electro-mechanical responses of smart laminated composite plates with piezoelectric materials are derived using a two-dimensional (2 D) displacement-based non-polynomial higher-order shear deformation theory. The kinematics of the mathematical model incorporates the deformation of laminates which account for the effects of transverse shear deformation and a non-linear variation of the in-plane displacements using inverse sine hyperbolic function of the thickness coordinate. The equilibrium equations are obtained using the minimization of energy principle known as the principle of minimum potential energy (PMPE) which is also based on a variational approach and the solutions are obtained using Navier’s solution technique for diaphragm supported smart laminated composite plates. The responses obtained in the form of deflection and stresses are compared with three dimensional (3 D) solutions and also with different polynomial and non-polynomial based higher-order theories in the literature. The transverse shear stresses are obtained using 3 D equilibrium equations of elasticity to enhance the accuracy of the present results. Various examples are numerically solved to establish the efficiency of the present model.

Thermo-mechanical analysis of multilayered composite beams based on a new mixed global-local model

2019 ◽  
Vol 53 (28-30) ◽  
pp. 3963-3978 ◽  
Author(s):  
Qilin Jin ◽  
Ziming Mao ◽  
Xiaofei Hu ◽  
Weian Yao
Keyword(s):  
Transverse Shear ◽  
Order Theory ◽  
Mechanical Analysis ◽  
Composite Beams ◽  
Higher Order ◽  
Shear Stresses ◽  
Mixed Form ◽  
Multilayered Composite ◽  
Proposed Model ◽  
Higher Order Theory

An accurate mixed-form global-local higher-order theory including transverse normal thermal deformation is developed for thermo-mechanical analysis of multilayered composite beams. Although transverse normal deformation is considered, the number of displacement parameters is not increased. The proposed mixed-form global-local higher-order theory is derived using the displacement assumptions of global-local higher-order theory in conjunction with the Reissner mixed variational theorem. Moreover, the mixed-form global-local higher-order theory retains a fixed number of displacement variables regardless of the number of layers. In order to obtain the improved transverse shear stresses, the three-dimensional equilibrium equation is used. It is significant that the second-order derivatives of in-plane displacement variables have been eliminated from the transverse shear stress field, such that the finite element implementation is greatly simplified. The benefit of the proposed mixed-form global-local higher-order theory is that no post-processing integration procedure is needed to accurately calculate the transverse shear stresses. The equilibrium equations and analytical solution of the proposed model can be obtained based on the Reissner mixed variational equation. The performance of the proposed model is assessed through different numerical examples, and the results show that the proposed model can better predict the thermo-mechanical responses of multilayered composite beams.

Higher-Order Zig-Zag Theory for Laminated Composites With Multiple Delaminations

2000 ◽  
Vol 68 (6) ◽  
pp. 869-877 ◽  
Author(s):  
M. Cho ◽  
J.-S. Kim
Keyword(s):  
Displacement Field ◽  
Transverse Shear ◽  
Dynamic Equilibrium ◽  
Composite Plates ◽  
Present Theory ◽  
Higher Order ◽  
Bottom Surface ◽  
Shear Stresses ◽  
Equilibrium Equations ◽  
Natural Frequency Analysis

A higher-order zig-zag theory has been developed for laminated composite plates with multiple delaminations. By imposing top and bottom surface transverse shear stress-free conditions and interface continuity conditions of transverse shear stresses including delaminated interfaces, the displacement field with minimal degree-of-freedoms are obtained. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Through the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. The delaminated beam finite element is implemented to evaluate the performance of the newly developed theory. Linear buckling and natural frequency analysis demonstrate the accuracy and efficiency of the present theory. The present higher-order zig-zag theory should work as an efficient tool to analyze the static and dynamic behavior of the composite plates with multiple delaminations.

Static buckling and vibration analysis of continuously graded ceramic-metal beams using a refined higher order shear deformation theory

2019 ◽  
Vol 15 (6) ◽  
pp. 1152-1169 ◽  
Author(s):  
Ahmed Bekhadda ◽  
Ismail Bensaid ◽  
Abdelmadjid Cheikh ◽  
Bachir Kerboua
Keyword(s):  
Shear Deformation ◽  
Power Law ◽  
Transverse Shear ◽  
Axial Load ◽  
Higher Order ◽  
Geometrical Parameters ◽  
Shear Stresses ◽  
Beam Model ◽  
Correction Factors ◽  
Content Type

Purpose The purpose of this paper is to study the static buckling and free vibration of continuously graded ceramic-metal beams by employing a refined higher-order shear deformation, which is also the primary goal of this paper. Design/methodology/approach The proposed model is able to catch both the microstructural and shear deformation impacts without employing any shear correction factors, due to the realistic distribution of transverse shear stresses. The material properties are supposed to vary across the thickness direction in a graded form and are estimated by a power-law model. The equations of motion and related boundary conditions are extracted using Hamilton’s principle and then resolved by analytical solutions for calculating the critical buckling loads and natural frequencies. Findings The obtained results are checked and compared with those of other theories that exist in the literature. At last, a parametric study is provided to exhibit the influence of different parameters such as the power-law index, beam geometrical parameters, modulus ratio and axial load on the dynamic and buckling characteristics of FG beams. Originality/value Searching in the literature and to the best of the authors’ knowledge, there are limited works that consider the coupled effect between the vibration and the axial load of FG beams based on new four-variable refined beam theory. In comparison with a beam model, the number of unknown variables resulting is only four in the general cases, as against five in the case of other shear deformation theories. The actual model represents a real distribution of transverse shear effects besides a parabolic arrangement of the transverse shear strains over the thickness of the beam, so it is needless to use of any shear correction factors.

scholarly journals Bending of functionally graded plates via a refined quasi-3D shear and normal deformation theory

2018 ◽  
Vol 5 (1) ◽  
pp. 190-200 ◽  
Author(s):  
Asharf M. Zenkour ◽  
Rabab A. Alghanmi
Keyword(s):  
Transverse Shear ◽  
Deformation Theory ◽  
Virtual Work ◽  
Three Dimensional ◽  
Present Theory ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Normal Strain ◽  
Equilibrium Equations ◽  
Normal Deformation

Abstract Bending of functionally graded plate with two reverse simply supported edges is studied based upon a refined quasi three-dimensional (quasi-3D) shear and normal deformation theory using a third-order shape function. The present theory accounts for the distribution of transvers shear stresses that satisfies the free transverse shear stresses condition on the upper and lower surfaces of the plate. Therefore, the strain distribution does not include the unwanted influences of transverse shear correction factor. The effect of transverse normal strain is included. Unlike the traditional normal and shear deformation theories, the present theory have four unknowns only. The equilibrium equations are derived by using the principle of virtual work. The influence of material properties, aspect and side-to-thickness ratios, mechanical loads and inhomogeneity parameter are discussed. The efficiency and correctness of the present theory results are established by comparisons with available theories results.

scholarly journals A Predictor-Corrector Layerwise Model for Thick Laminated Composite Plates and Shells: Bending and Vibration

1997 ◽  
Author(s):  
K. H. Lee ◽  
L. Cao
Keyword(s):  
Transverse Shear ◽  
Laminated Composite ◽  
Composite Plates ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Equilibrium Equations ◽  
Model Account ◽  
Transverse Shear Stresses ◽  
Plates And Shells ◽  
Predictor Corrector

This paper describes a predictor-corrector theory based on a general higher-order layerwise model for the accurate prediction of the linear static and dynamic response of thick laminated composite plates and shells. The general polynomials introduced in the model account for the arbitrary variation of the transverse shear stresses across the thickness of each layer. The main purpose of the approach is to reduce the differences between the assumed variation of the transverse shear stresses provided by the constitutive equations and the computed variation of the same stresses from the equilibrium equations of elasticity. The present predictor-corrector layerwise model satisfies the continuity of the in-plane displacements and the transverse shear stresses at the interfaces. The numerical results for the bending and vibration of thick laminated composite plates and shells show that a high level of accuracy can be achieved with the same number of variables as that in Mindlin’s theory.

Accurate stress analysis of laminated composite and sandwich plates

2020 ◽  
pp. 030932472092129
Author(s):  
Aniket Chanda ◽  
Rosalin Sahoo
Keyword(s):  
Transverse Shear ◽  
Solid Mechanics ◽  
Mechanical Load ◽  
Laminated Composite ◽  
Flexural Behavior ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Essential Condition ◽  
Transverse Shear Stresses

This article is devoted to derive the analytical solution for flexural behavior of general symmetric and anti-symmetric cross-ply laminated composite and sandwich plates subjected to transverse mechanical load using the recently developed trigonometric zigzag theory. The inter-laminar continuity conditions of transverse shear stresses at the layer interfaces of the plate are enforced which is an essential condition for any zigzag model. The governing equations of equilibrium of the boundary value problem derived from the principle of minimum potential energy is reduced to a system of five partial differential equations whose solutions are obtained by Navier’s method. Attempt is made to demonstrate number of numerical problems to compare the results of the zigzag model with the elasticity solutions and with the results of other researchers in one common platform. Though in any solid mechanics problem, the displacement components are the primary unknowns, more attention is paid to the stress determination. Hence, the transverse shear stresses are evaluated using both the constitutive and equilibrium equations.

Determination of the transverse shear stress in layered composites

2020 ◽  
Vol 86 (2) ◽  
pp. 44-53
Author(s):  
Yu. I. Dudarkov ◽  
M. V. Limonin
Keyword(s):  
Shear Stress ◽  
Transverse Shear ◽  
Composite Beam ◽  
Layered Composite ◽  
Equivalent Model ◽  
Shear Stresses ◽  
Transverse Shear Stress ◽  
Layered Composites ◽  
Laminate Composites ◽  
Transverse Shear Stresses

An engineering approach to estimation of the transverse shear stresses in layered composites is developed. The technique is based on the well-known D. I. Zhuravsky equation for shear stresses in an isotropic beam upon transverse bending. In general, application of this equation to a composite beam is incorrect due to the heterogeneity of the composite structure. According to the proposed method, at the first stage of its implementation, a transition to the equivalent model of a homogeneous beam is made, for which the Zhuravsky formula is valid. The transition is carried out by changing the shape of the cross section of the beam, provided that the bending stiffness and generalized elastic modulus remain the same. The calculated shear stresses in the equivalent beam are then converted to the stress values in the original composite beam from the equilibrium condition. The main equations and definitions of the method as well as the analytical equation for estimation of the transverse shear stress in a composite beam are presented. The method is verified by comparing the analytical solution and the results of the numerical solution of the problem by finite element method (FEM). It is shown that laminate stacking sequence has a significant impact both on the character and on the value of the transverse shear stress distribution. The limits of the applicability of the developed technique attributed to the conditions of the validity of the hypothesis of straight normal are considered. It is noted that under this hypothesis the shear stresses do not depend on the layer shear modulus, which explains the absence of this parameter in the obtained equation. The classical theory of laminate composites is based on the similar assumptions, which gives ground to use this equation for an approximate estimation of the transverse shear stresses in in a layered composite package.

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