A New C0 2D Fe Model Based on Improved Higher Order Zigzag Theory for the Analysis of Soft Core Sandwich Plate

An efficient C0 continuous finite element (FE) model is developed based on a combined theory (refine higher order shear deformation theory (RHSDT) and least square error (LSE) method) for the static analysis of a soft core sandwich plate. In this (RHSDT) theory, the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zig-zag linearly varying displacement field with a different slope in each layer. The transverse displacement assumes to have a quadratic variation within the core and it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C1 continuity requirement of the transverse displacements. In order to calculate the accurate through thickness transverse stresses variation, the Least Square Error (LSE) method has been used at the post processing stage. The proposed combined model (RHSDT and LSE) is implemented to analyze the laminated composites and sandwich plates. Many new results are also presented which should be useful for future research.

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VIBRATION AND BUCKLING ANALYSIS OF LAMINATED SANDWICH PLATE HAVING SOFT CORE

International Journal of Structural Stability and Dynamics ◽

10.1142/s021945541350034x ◽

2013 ◽

Vol 13 (08) ◽

pp. 1350034 ◽

Cited By ~ 20

Author(s):

RAVI PRAKASH KHANDELWAL ◽

ANUPAM CHAKRABARTI ◽

PRADEEP BHARGAVA

Keyword(s):

Shear Stress ◽

Free Vibration ◽

Displacement Field ◽

Transverse Shear ◽

Sandwich Plate ◽

Soft Core ◽

Transverse Displacement ◽

Fe Model ◽

Transverse Shear Stress ◽

The Core

Free vibration and buckling of laminated sandwich plate having soft core is studied by using an efficient C0 continuous finite element (FE) model based on higher-order zigzag theory (HOZT). In this theory, the in-plane displacement field for both the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zigzag linearly varying displacement field with a different slope in each layer. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the plate. The nodal field variables are chosen in an efficient manner to overcome the problem of C1 continuity requirement of the transverse displacement. Numerical examples on free vibration and buckling covering different geometric and material features of laminated composite and sandwich plates are presented. Many new results are also presented which should be useful for future research.

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Vibration of laminated sandwich beams having soft core

Journal of Vibration and Control ◽

10.1177/1077546311421947 ◽

2011 ◽

Vol 18 (10) ◽

pp. 1422-1435 ◽

Cited By ~ 10

Author(s):

Hanuman Devidas Chalak ◽

Anupam Chakrabarti ◽

Mohamad Asharaf Iqbal ◽

Abdul Hamid Sheikh

Keyword(s):

Shear Stress ◽

Free Vibration ◽

Transverse Shear ◽

Soft Core ◽

Future Research ◽

Transverse Displacement ◽

Beam Model ◽

Sandwich Beams ◽

Transverse Shear Stress ◽

The Core

Free vibration response of laminated sandwich beams having a soft core is studied by using a recently developed C0 finite element beam model. The model has been developed based on higher order zigzag theory where the in-plane displacement variation is considered to be cubic for both the face sheets and the core. The transverse displacement is assumed to be quadratic within the core while it remains constant in the faces beyond the core. The model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the beam. The nodal field variables are chosen in an efficient manner to overcome the problem of continuity requirement of the derivatives of transverse displacements. Numerical examples on free vibration covering different features of laminated composite and sandwich beams are presented. Many new results are also presented which should be useful for future research.

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A new formulation of continuous transverse shear stress field for static and dynamic analysis of sandwich beams with soft core

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.6289 ◽

2019 ◽

Vol 121 (8) ◽

pp. 1847-1876 ◽

Cited By ~ 1

Author(s):

Shanhong Ren ◽

Guozhong Zhao

Keyword(s):

Shear Stress ◽

Stress Field ◽

Dynamic Analysis ◽

Transverse Shear ◽

Soft Core ◽

Sandwich Beams ◽

Transverse Shear Stress ◽

Static And Dynamic Analysis ◽

New Formulation ◽

Shear Stress Field

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.716.119 ◽

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.

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Dynamic Response of Angle Ply Laminates with Uncertainties Using MARS, ANN-PSO, GPR and ANFIS

Materials ◽

10.3390/ma14020395 ◽

2021 ◽

Vol 14 (2) ◽

pp. 395

Author(s):

Bharat Mishra ◽

Ajay Kumar ◽

Jacek Zaburko ◽

Barbara Sadowska-Buraczewska ◽

Danuta Barnat-Hunek

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Shear Stress ◽

Transverse Shear ◽

Random Variable ◽

Fe Model ◽

Transverse Shear Stress ◽

Inference System ◽

Model Based ◽

Angle Ply Laminates

In the present work, for the first time, free vibration response of angle ply laminates with uncertainties is attempted using Multivariate Adaptive Regression Spline (MARS), Artificial Neural Network-Particle Swarm Optimization (ANN-PSO), Gaussian Process Regression (GPR), and Adaptive Network Fuzzy Inference System (ANFIS). The present approach employed 2D C0 stochastic finite element (FE) model based on the Third Order Shear Deformation Theory (TSDT) in conjunction with MARS, ANN-PSO, GPR, and ANFIS. The TSDT model used eliminates the requirement of shear correction factor owing to the consideration of the actual parabolic distribution of transverse shear stress. Zero transverse shear stress at the top and bottom of the plate is enforced to compute higher-order unknowns. C0 FE model makes it commercially viable. Stochastic FE analysis done with Monte Carlo Simulation (MCS) FORTRAN inhouse code, selection of design points using a random variable framework, and soft computing with MARS, ANN-PSO, GPR, and ANFIS is implemented using MATLAB in-house code. Following the random variable frame, design points were selected from the input data generated through Monte Carlo Simulation. A total of four-mode shapes are analyzed in the present study. The comparison study was done to compare present work with results in the literature and they were found in good agreement. The stochastic parameters are Young’s elastic modulus, shear modulus, and the Poisson ratio. Lognormal distribution of properties is assumed in the present work. The current soft computation models shrink the number of trials and were found computationally efficient as the MCS-based FE modelling. The paper presents a comparison of MARS, ANN-PSO, GPR, and ANFIS algorithm performance with the stochastic FE model based on TSDT.

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Determination of the transverse shear stress in layered composites

Industrial laboratory Diagnostics of materials ◽

10.26896/1028-6861-2020-86-2-44-53 ◽

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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A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

Journal of Sandwich Structures & Materials ◽

10.1177/1099636217729731 ◽

2017 ◽

Vol 21 (6) ◽

pp. 1820-1842

Author(s):

Wu Zhen ◽

Ma Rui ◽

Chen Wanji

Keyword(s):

Transverse Shear ◽

Equilibrium Equation ◽

Three Dimensional ◽

Higher Order ◽

Triangular Element ◽

Shear Stresses ◽

Sandwich Plates ◽

Transverse Shear Stress ◽

Transverse Shear Stresses ◽

Derivatives Of

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

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Transverse shear stress within surface layer and its effects

Mathematics and Mechanics of Solids ◽

10.1177/1081286519869418 ◽

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.

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