Non-polynomial zigzag theories with C° finite element formulation for buckling analysis of laminated composite and sandwich plates

2021 ◽  
pp. 095440622110200
Author(s):  
Suganyadevi Sarangan ◽  
BN Singh
Keyword(s):  
Transverse Shear ◽  
Laminated Composite ◽  
Buckling Analysis ◽  
Laminated Plates ◽  
Load Parameter ◽  
Shear Stresses ◽  
Element Formulation ◽  
Sandwich Plates ◽  
Plane Displacement ◽  
Zigzag Theory

In this present work, non-polynomial zigzag theories (algebraic zigzag theory (AZT), exponential zigzag theory (EZT), hyperbolic zigzag theory (HZT), inverse hyperbolic zigzag theory (IZT), logarithmic zigzag theory (LZT) and trigonometric zigzag theory (TZT)) are performed for buckling response of laminated composite and sandwich plates. The present models assume parabolic variation of out – plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag models able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. An efficient eight noded C° continuous isoparametric serendipity element is established and employed to examine the buckling analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical examples are carried out to study the effects of span to thickness ratio, ply orientation, lay-up number, modular ratio, loading condition and boundary condition on the buckling response. To ensure the capability of the proposed models, higher modes of buckling are obtained for laminated plates and sandwich plates. Further, the efficiency and superiority of the proposed models is ascertained by comparing it with 3 D elasticity solution and also with various existing shear deformation theories in the literature. Most remarkably, the present models are accurately estimates the buckling load parameter and they are insensitive of shear-locking.

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.

Analytical modeling of laminated composite plates integrated with piezoelectric layer using Trigonometric Zigzag theory

2020 ◽  
Vol 54 (29) ◽  
pp. 4691-4708
Author(s):  
Aniket Chanda ◽  
Rosalin Sahoo
Keyword(s):  
Transverse Shear ◽  
Piezoelectric Layer ◽  
Composite Plate ◽  
Laminated Composite ◽  
Composite Plates ◽  
Solution Technique ◽  
Shear Stresses ◽  
Smart Composite ◽  
Laminated Composite Plate ◽  
Zigzag Theory

The analytical solution for static analysis of laminated composite plate integrated with piezoelectric fiber reinforced composite actuator is obtained using a recently developed Trigonometric Zigzag theory. The kinematic field consists of five independent field variables accommodating non-linear variation of transverse shear strains through the thickness of the laminated composite plate. The principle of minimum potential energy is adopted to derive the governing equations of equilibrium. Navier’s solution technique is employed to convert the system of coupled partial differential equations into a system of algebraic equations. The electric potential is assumed to vary linearly through the thickness of the piezoelectric layer. The analytical formulation also does not include voltage as an additional primary variable. The response in the form of deflection and stresses are obtained for smart composite plates subjected to electro-mechanical loads and compared with the elasticity solutions and available results reported by other researchers in the existing literature. The transverse shear stresses are accurately determined by an efficient post-processing technique of integrating the equilibrium equations of elasticity. Parametric studies on actuation in the response of the smart composite plate are also presented graphically in order to have a clear understanding of the static behavior.

scholarly journals A Family of C0 Quadrilateral Plate Elements Based on the Refined Zigzag Theory for the Analysis of Thin and Thick Laminated Composite and Sandwich Plates

2019 ◽  
Vol 3 (4) ◽  
pp. 100 ◽  
Author(s):  
Di Sciuva ◽  
Sorrenti
Keyword(s):  
Transverse Shear ◽  
Laminated Composite ◽  
Thin Plates ◽  
Sandwich Plates ◽  
Shear Locking ◽  
Reduced Integration ◽  
Quadrilateral Plate ◽  
Plate Elements ◽  
Transverse Shear Locking ◽  
Zigzag Theory

The present work focuses on the formulation and numerical assessment of a family of C0 quadrilateral plate elements based on the refined zigzag theory (RZT). Specifically, four quadrilateral plate elements are developed and numerically tested: The classical bi-linear 4-node element (RZT4), the serendipity 8-node element (RZT8), the virgin 8-node element (RZT8v), and the 4-node anisoparametric constrained element (RZT4c). To assess the relative merits and drawbacks, numerical tests on bending (maximum deflection and stresses) and free vibration analysis of laminated composite and sandwich plates under different boundary conditions and transverse load distributions are performed. Convergences studies with regular and distorted meshes, transverse shear-locking effect for thin and very thin plates are carried out. It is concluded that the bi-linear 4-node element (RZT4) has performances comparable to the other elements in the range of thin plates when reduced integration is adopted but presents extra zero strain energy modes. The serendipity 8-node element (RZT8), the virgin 8-node element (RZT8v), and the 4-node anisoparametric constrained element (RZT4c) show remarkable performance and predictive capabilities for various problems, and transverse shear-locking is greatly relieved, at least for aspect ratio equal to 5 × 102, without using any reduced integration scheme. Moreover, RZT4c has well-conditioned element stiffness matrix, contrary to RZT4 using reduced integration strategy, and has the same computational cost of the RZT4 element.

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.

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.

Effect of Stress Concentration on Laminated Plates

2012 ◽  
Vol 29 (2) ◽  
pp. 241-252 ◽  
Author(s):  
A. S. Sayyad ◽  
Y. M. Ghugal
Keyword(s):  
Stress Concentration ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Shear Stresses ◽  
Normal Strain ◽  
Concentrated Load ◽  
Transverse Shear Stresses

AbstractThis 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 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.

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.

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