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.

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.

Assessment of Inverse Hyperbolic Zigzag Theory for Hygro-Thermomechanical Analysis of Laminated Composite and Sandwich Plates

2020 ◽  
Vol 33 (5) ◽  
pp. 04020060
Author(s):  
Nikhil Garg ◽  
Karkhanis Rahul Sanjay ◽  
Rosalin Sahoo ◽  
P. R. Maiti ◽  
B. N. Singh
Keyword(s):  
Laminated Composite ◽  
Thermomechanical Analysis ◽  
Sandwich Plates ◽  
Zigzag Theory

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.

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.

Sign in / Sign up

Export Citation Format

Share Document