Corrigendum to “Deflection and stress analysis of thin FGM skew plates on Winkler foundation with various boundary conditions using extended Kantorovich method” [Composites: Part B 51 (2013) 191–196]

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.

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Analytical solution for bending of moderately thick radially functionally graded sector plates with general boundary conditions using multi-term extended Kantorovich method

Composites Part B Engineering ◽

10.1016/j.compositesb.2011.11.068 ◽

2012 ◽

Vol 43 (3) ◽

pp. 1405-1416 ◽

Cited By ~ 32

Author(s):

S.M. Mousavi ◽

M. Tahani

Keyword(s):

Analytical Solution ◽

Boundary Conditions ◽

Functionally Graded ◽

General Boundary ◽

General Boundary Conditions ◽

Kantorovich Method ◽

Extended Kantorovich Method

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

The Scientific World JOURNAL ◽

10.1155/2014/439492 ◽

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.

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

Journal of Applied Mechanics ◽

10.1115/1.4003779 ◽

2011 ◽

Vol 78 (6) ◽

Cited By ~ 16

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.

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