scholarly journals Reduction of Free Edge Peeling Stress of Laminated Composites Using Active Piezoelectric Layers

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Bin Huang ◽  
Heung Soo Kim
Keyword(s):  
Boundary Conditions ◽  
Virtual Work ◽  
Laminated Composites ◽  
Free Edge ◽  
Governing Equations ◽  
Kantorovich Method ◽  
Free Boundary Conditions ◽  
Extended Kantorovich Method ◽  
Piezoelectric Layers ◽  
Iteration Processes

An analytical approach is proposed in the reduction of free edge peeling stresses of laminated composites using active piezoelectric layers. The approach is the extended Kantorovich method which is an iterative method. Multiterms of trial function are employed and governing equations are derived by taking the principle of complementary virtual work. The solutions are obtained by solving a generalized eigenvalue problem. By this approach, the stresses automatically satisfy not only the traction-free boundary conditions, but also the free edge boundary conditions. Through the iteration processes, the free edge stresses converge very quickly. It is found that the peeling stresses generated by mechanical loadings are significantly reduced by applying a proper electric field to the piezoelectric actuators.

Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method

2021 ◽  
pp. 095440622199068
Author(s):  
Ahmad Mamandi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Functionally Graded ◽  
Kantorovich Method ◽  
Different Boundary Conditions ◽  
Extended Kantorovich Method ◽  
Skew Plate ◽  
Pasternak Elastic Foundation ◽  
Graded Material

In this study, bending deflection and stress analyses have been conducted for a thin skew plate made of functionally graded material (FGM) with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined loads including uniform transverse load, normal and shear in-plane forces, and planar body forces. The Cartesian partial differential equation governing the bending deflection of the skew plate has been converted into a partial differential equation in oblique coordinates using the conversion relations. Then, by employing the variational principle and residual weighted Galerkin method and using the Extended Kantorovich Method (EKM), the equation has been converted to a set of linear differential equations in terms of two functions in the longitudinal and transverse directions of the oblique plate, and afterward, the equation has been solved using the iterative solution method. Different boundary conditions in a combined form of simply and clamped supports have been investigated and their effects on bending deflection and generated in-plane normal and shear stresses are discussed.

Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Composite Structures in Cylindrical Bending

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
Santosh Kapuria ◽  
Poonam Kumari
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Thickness Direction ◽  
Kantorovich Method ◽  
Cylindrical Bending ◽  
Extended Kantorovich Method ◽  
Elasticity Problems ◽  
Plane Direction ◽  
3D Elasticity ◽  
2D Elasticity

The extended Kantorovich method originally proposed by Kerr in the year 1968 for two-dimensional (2D) elasticity problems is further extended to the three-dimensional (3D) elasticity problem of a transversely loaded laminated angle-ply flat panel in cylindrical bending. The significant extensions made to the method in this study are (1) the application to the 3D elasticity problem involving an in-plane direction and a thickness direction instead of both in-plane directions in 2D elasticity problems, (2) the treatment of the nonhomogeneous boundary conditions encountered in the thickness direction, and (3) the use of a mixed variational principle to obtain the governing differential equations in both directions in terms of displacements as well as stresses. This approach not only ensures exact satisfaction of all boundary conditions and continuity conditions at the layer interfaces, but also guarantees the same order of accuracy for all displacement and stress components. The method eventually leads to a set of eight algebraic-ordinary differential equations in the in-plane direction and a similar set of equations in the thickness direction for each layer of the laminate. Exact closed form solutions are obtained for each system of equations. It is demonstrated that the iterative procedure converges very fast irrespective of whether or not the initial guess functions satisfy the boundary conditions. Comparisons of the present predictions with the available 3D exact solutions and 3D finite element solutions for laminated cross-ply and angle-ply composite panels under different boundary conditions show a close agreement between them.

scholarly journals Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects

2013 ◽  
Vol 469 (2151) ◽  
pp. 20120565 ◽  
Author(s):  
Santosh Kapuria ◽  
Poonam Kumari
Keyword(s):  
Edge Effects ◽  
Electric Potential ◽  
Three Dimensional ◽  
Single Layer ◽  
Free Edge ◽  
Laminated Plates ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Hybrid Laminates ◽  
Laminated Panels

The powerful extended Kantorovich method (EKM) originally proposed by Kerr in 1968 is generalized to obtain a three-dimensional coupled piezoelasticity solution of smart piezoelectric laminated plates in cylindrical bending. Such solutions are needed to accurately predict the edge effects in these laminates under electromechanical loading. The Reissner-type mixed variational principle extended to piezoelasticity is used to develop the governing equations in terms of displacements, electric potential as well as stresses and electric displacements. It allows for exact satisfaction of the boundary conditions, including the non-homogeneous ones at all points. An n -term solution generates a set of 11 n algebraic ordinary differential equations in the inplane direction and a similar set in the thickness direction for each lamina, which are solved in closed form. The multi-term EKM is shown to predict the coupled electromechanical response, including the edge effects, of single-layer piezoelectric sensors as well as hybrid laminated panels accurately, for both pressure and electric potential loadings. This work will facilitate development of accurate semi-analytical solutions of many other unresolved problems in three-dimensional piezoelasticity, such as the free-edge stresses in hybrid laminates under bending, tension and twisting.

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