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

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.

Interlaminar stress analysis of multilayered composites based on the Hu-Washizu variational theorem

2017 ◽  
Vol 52 (13) ◽  
pp. 1765-1779 ◽  
Author(s):  
Wu Zhen ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Beam Element ◽  
Composite Beams ◽  
Higher Order ◽  
Shear Stresses ◽  
Interlaminar Stresses ◽  
Beam Elements ◽  
Transverse Shear Stresses ◽  
Derivatives Of

Up to date, accurate prediction of interlaminar stresses is still a challenging issue for two-node beam elements. The postprocessing approaches by integrating the three-dimensional equilibrium equation have to be used to obtain improved transverse shear stresses, whereas the equilibrium approach requires the first-order derivatives of in-plane stresses. In-plane stresses within two-node beam element are constant, so the first-derivatives of in-plane stresses are close to zero. Thus, two-node beam elements encounter difficulties for accurate prediction of transverse shear stresses by the constitutive equation or the equilibrium equation, so a robust two-node beam element is expected. A two-node beam element in terms of the global higher-order zig-zag model is firstly developed by employing the three-field Hu-Washizu mixed variational principle. By studying the effects of different boundary conditions, stacking sequence and loading on interlaminar stresses of multilayered composite beams, it is shown that the proposed two-node beam element yields more accurate results with lesser computational cost compared to various higher-order models. It is more important that accurate transverse shear stress has active impact on displacements and in-plane stresses of multilayered composite beams.

Higher Order Global-Local Theory Coupled Bending and Extension for Laminated Composite Plates and Refined Element Methods

2006 ◽  
Author(s):  
Wanji Chen ◽  
Zhen Wu
Keyword(s):  
Transverse Shear ◽  
Composite Plates ◽  
Higher Order ◽  
Laminated Plates ◽  
Triangular Element ◽  
Local Theory ◽  
Weak Continuity ◽  
Shear Stresses ◽  
Thickness Direction ◽  
Transverse Shear Stresses

In this paper an augmented higher order global-local theories are presented to analyze the laminated plate problems coupled bending and extension. The in-plane displacement field is composed of a mth-order (9 > m > 3) polynomial of global coordinate z in the thickness direction and 1,2-3 order power series of local coordinate ζk in the thickness direction of each layer and a nth-order (5 > n >= 0) polynomial of global coordinate z in the thickness direction of transverse deflection. The transverse shear stresses can satisfy continuity at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this theory, a refined three-node triangular element satisfying the requirement of C1 weak-continuity is presented. Numerical results show that present theory can be used to predict accurately in-plane stresses and transverse shear stresses from direct use of the relations of stresses and strains without any postprocessing method. However, to accurately obtain transverse normal stresses, the local equilibrium equation approach in one element is employed herein. It is effective when the number of layers of laminated plates is more than five and up to fourteen, and it can solve the problems for coupling bending and extension. It is also shown that the present refined triangular element possesses higher accuracy.

Vibration characteristic of laminated sandwich plates with soft core based on an improved higher-order zigzag theory

2008 ◽  
Vol 222 (8) ◽  
pp. 1443-1452 ◽  
Author(s):  
M K Pandit ◽  
A H Sheikh ◽  
B N Singh
Keyword(s):  
Transverse Shear ◽  
Plate Theory ◽  
Three Dimensional ◽  
Higher Order ◽  
Thickness Variation ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Displacement ◽  
Zigzag Theory ◽  
Three Dimensional Elasticity

This paper presents an improved higher order zigzag theory for vibration of laminated sandwich plates. It ensures continuity of transverse shear stresses at all the layer interfaces and transverse shear stress-free condition at the top and bottom surfaces apart from core compressibility. The through-thickness variation of in-plane displacements is assumed to be cubic, whereas transverse displacement varies quadratically across the core, which is modelled as a three-dimensional elastic continuum. An efficient C0 finite element is developed for the implementation of the plate theory. The model is validated using three-dimensional elasticity solutions and some other relevant results available in the literature.

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.

Bending Analysis of SMA Embedded Rectangular Laminated Sandwich Plates with Soft Core Using 3D Finite Element Method

2011 ◽  
Vol 110-116 ◽  
pp. 1458-1465 ◽  
Author(s):  
M. Khadem ◽  
M. M. Kheirikhah
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transverse Shear ◽  
Soft Core ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
3D Finite Element ◽  
Bending Analysis ◽  
Transverse Shear Stresses ◽  
3D Finite Element Method

Nowadays Shape Memory Alloys (SMAs) are used as actuators in many applications such as aerospace structures. In sandwich structures, the SMA wires or plates are used in the skins for shape control of the structure or vibration damping. In this paper, bending behavior of sandwich plates with embedded SMA wires in their skins is studied. 3D finite element method is used for construction and analysis of the sandwich plate with a flexible core and two stiff skins. Some important points such as continuity conditions of the displacements, satisfaction of interlaminar transverse shear stresses, the conditions of zero transverse shear stresses on the upper and lower surfaces and in-plane and transverse flexibility of soft core are considered for accurate modeling and analysis of sandwich structures. Solution for bending analysis of sandwich plates under various transverse loads are presented and the effect of many parameters such as plate dimensions, loading conditions, material properties of core, skins and SMA wires are studied. Comparison of the present results in special case with those of the three-dimensional theory of elasticity and some plate theories confirms the accuracy of the proposed model.

An accurate zigzag theory for bending and buckling analysis of thick laminated sandwich plates with soft core

2020 ◽  
Vol 54 (18) ◽  
pp. 2473-2488
Author(s):  
Qilin Jin ◽  
Weian Yao
Keyword(s):  
Transverse Shear ◽  
Buckling Analysis ◽  
Soft Core ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Plate Element ◽  
Proposed Model ◽  
Transverse Shear Stresses ◽  
Zigzag Theory ◽  
Benchmark Solutions

An accurate and computationally attractive zigzag theory is developed for bending and buckling analysis of thick laminated soft core sandwich plates. The kinematic assumptions of the proposed zigzag theory are obtained by superimposing a nonlinear zigzag function on the first-order shear deformation theory. In order to obtain the accurate transverse shear stresses, a preprocessing approach based on the three-dimensional equilibrium equations and the Reissner mixed variational theorem is used. It is significant that the second-order derivatives of in-plane displacement variables have been removed from the transverse shear stresses, such that the finite element implementation is greatly simplified. Thus, based on the proposed zigzag model, a computationally efficient four-node C0 quadrilateral plate element with linear interpolation function is proposed for bending and buckling analysis of soft core sandwich plates. The advantage of the present formulation is that no post-processing approach is needed to calculate the transverse shear stresses while maintaining the computational accuracy of a linear plate element. Moreover, the accurate transverse shear stresses can be involved in the strain energy which can actively improve the accuracy of critical loads. Performance of the proposed model is assessed by comparing with several benchmark solutions. Agreement between the present results and the reference solutions is very good, and the proposed model only includes the seven displacement variables which can demonstrate the accuracy and effectiveness of the proposed model.

Bending analysis of soft core sandwich plates with embedded shape memory alloy wires using three-dimensional finite element method

2012 ◽  
Vol 226 (3) ◽  
pp. 186-202 ◽  
Author(s):  
Mohammad M Kheirikhah ◽  
Mahdi Khadem ◽  
Peyman Farahpour
Keyword(s):  
Finite Element Method ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Sandwich Plate ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Dimensional Finite Element ◽  
Transverse Shear Stresses ◽  
Three Dimensional Finite Element

In this article, bending behavior of the sandwich plates with embedded shape memory alloy wires in their face sheets is studied. Three-dimensional finite element method is used for constructing and analyzing the sandwich plates with flexible core and two stiff face sheets. Some important points such as continuity conditions of the displacements, satisfaction of inter-laminar transverse shear stresses, conditions of zero transverse shear stresses on the upper and lower surfaces and in-plane and transverse flexibility of the soft core are considered for the accurate modeling of the sandwich plate. Solutions for bending analysis of shape memory alloy wire-reinforced sandwich plates under various transverse loads are presented and the effects of plate dimensions, shape memory alloy wires diameter, boundary conditions and shape memory alloy wires embedding positions are studied. Comparison of the present results in special case with those of the three-dimensional theory of elasticity and some plate theories confirms the accuracy of the proposed model. According to the obtained numerical results, the local behavior of the sandwich plate in bending against various loading conditions was significantly improved by employing the shape memory alloy wires in the face sheets.

scholarly journals Buckling Analysis of Functionally Graded Material Plates Using Higher Order Shear Deformation Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
B. Sidda Reddy ◽  
J. Suresh Kumar ◽  
C. Eswara Reddy ◽  
K. Vijaya Kumar Reddy
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Plates ◽  
Transverse Shear Stresses

The prime aim of the present study is to present analytical formulations and solutions for the buckling analysis of simply supported functionally graded plates (FGPs) using higher order shear deformation theory (HSDT) without enforcing zero transverse shear stresses on the top and bottom surfaces of the plate. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. Material properties of the plate are assumed to vary in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The equations of motion and boundary conditions are derived using the principle of virtual work. Solutions are obtained for FGPs in closed-form using Navier’s technique. Comparison studies are performed to verify the validity of the present results from which it can be concluded that the proposed theory is accurate and efficient in predicting the buckling behavior of functionally graded plates. The effect of side-to-thickness ratio, aspect ratio, modulus ratio, the volume fraction exponent, and the loading conditions on the critical buckling load of FGPs is also investigated and discussed.

Bending Analysis of Composite Sandwich Plates with Flexible Core Using 3D Finite Element Method

2011 ◽  
Vol 110-116 ◽  
pp. 1229-1236
Author(s):  
Mohammad Mahdi Kheirikhah ◽  
Seyyed Mohammad Reza Khalili
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Transverse Shear ◽  
Sandwich Plate ◽  
Element Model ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Normal Strain ◽  
Bending Analysis ◽  
Transverse Shear Stresses

Sandwich plates have been extensively used in many engineering applications such as automotive and aerospace. In the present paper, an accurate finite element model is presented for bending analysis of soft-core rectangular sandwich plates. The sandwich plate is composed of three layers: top and bottom skins and core layer. The core is assumed as a soft orthotropic material and skins are assumed generally unequal laminated composites. Finite element model of the problem has been constructed in the ANSYS 11.0 standard code area. Continuity conditions of transverse shear stresses at the interfaces are satisfied as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of plate. Also transverse flexibility and transverse normal strain and stress of core are considered. The effect of geometrical parameters of the sandwich plate are studied. Comparison of the present results with those of plate theories confirms the accuracy of the proposed model.

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.

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