On the use of transverse shear stress homogeneous and non-homogeneous conditions in third-order orthotropic plate theory

2007 ◽  
Vol 77 (3) ◽  
pp. 341-352 ◽  
Author(s):  
Erasmo Carrera
Keyword(s):  
Shear Stress ◽  
Transverse Shear ◽  
Orthotropic Plate ◽  
Plate Theory ◽  
Transverse Shear Stress ◽  
Third Order

ASSESSMENT OF COMPUTATIONAL MODELS FOR LAMINATED COMPOSITE PLATES

2007 ◽  
Vol 04 (04) ◽  
pp. 633-644
Author(s):  
K. SUBHA ◽  
SHASHIDHARAN ◽  
S. SAVITHRI ◽  
V. SYAM PRAKASH
Keyword(s):  
Shear Stress ◽  
Stress Analysis ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Deformation Model ◽  
Transverse Shear Stress ◽  
Third Order ◽  
Stress Boundary

In this paper, results of the stress analysis of composite laminates subjected to mechanical load based on different higher order shear deformation theories are presented. Among the many equivalent single layer theories (ESL), the third-order shear deformation theory of Reddy is the most widely accepted model in the study of laminates. This model cannot represent shear stress continuity at the interfaces and zigzag nature of the displacement field. To improve the accuracy of transverse shear stress prediction, layer wise theories have proved to be very promising techniques. In all these theories, zero transverse shear stress boundary conditions at the top and the bottom of the plate are imposed. In many engineering applications, this requirement is not valid when the plate is subjected to shear traction parallel to the surface. To account for this, a displacement model which releases the zero transverse shear stress boundary condition is taken. The unconstrained third-order shear deformation theory (UTSDT) is useful where the boundary layer shear stress is significant. Navier solutions for bending and stress analysis of cross ply laminates are presented using layer wise model, unconstrained third-order shear deformation model and Reddy's ESL model, and compared with 3D elasticity solutions.

Evaluation of Various Laminated Plate Theories Accounting for Interlaminar Transverse Shear Stress Continuity

2013 ◽  
Vol 716 ◽  
pp. 119-126
Author(s):  
Xiao Dan Wang ◽  
Guang Yu Shi
Keyword(s):  
Finite Element ◽  
Shear Stress ◽  
Shear Deformation ◽  
Analytical Solutions ◽  
Transverse Shear ◽  
Plate Theory ◽  
Higher Order ◽  
Shear Stresses ◽  
Laminated Plate ◽  
Transverse Shear Stress

Based on a unified form of the plate kinematics in terms of the transverse shear functions and the Heaviside step function, the analytical solutions of laminated plates corresponding to a number of higher-order shear deformation plate theories are solved in this paper. The accuracy assessment of these higher-order laminated plate theories is conducted by comparing the resulting analytical solutions with the elasticity solutions and finite element results. The accuracy study shows that the interlaminar shear stress continuity condition is very important for the accurate prediction of the transverse shear stresses across the laminated plate thickness. The comparison study also indicates that the new laminated plate theory accounting for the interlaminar transverse shear stress continuity proposed by the authors yields both very accurate displacements and accurate stresses. This new higher-order laminated plate theory can be efficiently used in the finite element analysis of laminated composite plates since it uses the same five field variables as those used in the first-order shear deformation plate theory.

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.

Transverse shear stress within surface layer and its effects

2019 ◽  
Vol 25 (2) ◽  
pp. 166-180
Author(s):  
Ge Yan ◽  
Zaixing Huang
Keyword(s):  
Shear Stress ◽  
Surface Layer ◽  
Hydrostatic Pressure ◽  
Transverse Shear ◽  
Transverse Shear Stress ◽  
Middle Section ◽  
Nanoscale Solids ◽  
Maximal Stress

When the transverse shear stress within a surface layer is taken into account, what happens in the deformation of micro- or nanoscale solids? The relevant problems are investigated by analyzing the deformation of a micro- or nanosized solid ellipsoid. The results show that both the stress and the deformation of a micro- or nanosized ellipsoid increase after the transverse shear stress within the surface layer is introduced, and that the maximal stress always occurs at both ends of the long axis of the ellipsoid. Unlike the prediction given by the Gurtin–Murdoch model, the calculation coming from the model of this paper predicts that the micro- or nanosized ellipsoid subjected to hydrostatic pressure contracts radially in the middle section and expands radially on both sides of the middle section. This difference provides an experimental standard to verify two models.

Thermoelastic bending analysis of laminated composite plates according to various shear deformation theories

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Atteshamuddin Shamshuddin Sayyad ◽  
Bharati Machhindra Shinde ◽  
Yuwaraj Marotrao Ghugal
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Virtual Work ◽  
Plate Theory ◽  
Thermal Response ◽  
Laminated Composite ◽  
Composite Plates ◽  
Shear Stresses ◽  
Laminated Composite Plates

AbstractThis study presents the thermoelastic analysis of laminated composite plates subjected to sinusoidal thermal load linearly varying across the thickness. Analytical solutions for thermal displacements and stresses are investigated by using a unified plate theory which includes different functions in terms of thickness coordinate to represent the effect of shear deformation. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Governing equations of equilibrium and associated boundary conditions of the theory are obtained using the principle of virtual work. The Navier solution for simply supported laminated composite plates has been developed. Numerical results are presented to demonstrate the thermal response of the laminated composite plates.

Analytical Simulation of the Composite Ice Wall

1989 ◽  
Vol 111 (3) ◽  
pp. 174-180 ◽  
Author(s):  
P. Corder ◽  
T. Kozik
Keyword(s):  
Shear Stress ◽  
Closed Form ◽  
Normal Stress ◽  
Transverse Shear ◽  
Parametric Study ◽  
Beam Theory ◽  
Transverse Shear Stress ◽  
Transverse Normal Stress ◽  
Analytical Simulation ◽  
Sandwich Configuration

A system of linear, closed-form stress equations for a steel-concrete-steel sandwich configuration, i.e., the “Composite Ice Wall,” was derived incorporating a formulation of classical beam theory. The stress terms include the longitudinal normal stress, the transverse shear stress and the transverse normal stress. These equations were programmed using Pascal and a parametric study was conducted. Some of the results are included herein. The analytical model produces principal stress contours and centerline deflections very similar to those in the classical beam for comparable pressure loadings.

NONLINEAR BENDING ANALYSIS OF FUNCTIONALLY GRADED PLATES UNDER PRESSURE LOADS USING A FOUR VARIABLE REFINED PLATE THEORY

2014 ◽  
Vol 11 (04) ◽  
pp. 1350062 ◽  
Author(s):  
MOHAMED ATIF BENATTA ◽  
ABDELHAKIM KACI ◽  
ABDELOUAHED TOUNSI ◽  
MOHAMMED SID AHMED HOUARI ◽  
KARIMA BAKHTI ◽  
...  
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Plates ◽  
Refined Plate Theory ◽  
Von Karman ◽  
Von Kármán

The novelty of this paper is the use of four variable refined plate theory for nonlinear analysis of plates made of functionally graded materials. The plates are subjected to pressure loading and their geometric nonlinearity is introduced in the strain–displacement equations based on Von–Karman assumptions. Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The fundamental equations for functionally graded plates are obtained using the Von–Karman theory for large deflection and the solution is obtained by minimization of the total potential energy. Numerical results for functionally graded plates are given in dimensionless graphical forms; and the effects of material properties on deflections and stresses are determined. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the CPT, but are almost comparable to those obtained using higher order theories having more number of unknown functions.

Analysis of Sandwich Composite Beams with a New Transverse Shear Stress Continuity Model

1999 ◽  
Vol 1 (2) ◽  
pp. 96-110 ◽  
Author(s):  
S. Mistou ◽  
M. Karama ◽  
B. Lorrain ◽  
J. P. Faye
Keyword(s):  
Shear Stress ◽  
Transverse Shear ◽  
Composite Beams ◽  
Sandwich Composite ◽  
Transverse Shear Stress
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