Coupled three-dimensional piezoelasticity solution for edge effects in Levy-type rectangular piezolaminated plates using mixed field extended Kantorovich method

2016 ◽  
Vol 140 ◽  
pp. 491-505 ◽  
Author(s):  
Poonam Kumari ◽  
Susanta Behera ◽  
Santosh Kapuria
Keyword(s):  
Edge Effects ◽  
Three Dimensional ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Mixed Field

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.

Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
Santosh Kapuria ◽  
Poonam Kumari
Keyword(s):  
Stress Field ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Laminated Plates ◽  
Elasticity Solution ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Single Term ◽  
3D Elasticity ◽  
Laminated Structures

In an article recently published in this journal, the powerful single-term extended Kantorovich method (EKM) originally proposed by Kerr in 1968 for two-dimensional (2D) elasticity problems was further extended by the authors to the three-dimensional (3D) elasticity solution for laminated plates. The single-term solution, however, failed to predict accurately the stress field near the boundaries; thus limiting its applicability. In this work, the method is generalized to the multiterm solution. The solution is developed using the Reissner-type mixed variational principle that ensures the same order of accuracy for displacements and stresses. An n-term solution generates a set of 8n algebraic-ordinary differential equations in the in-plane direction and a similar set in the thickness direction for each lamina, which are solved in close form. The problem of large eigenvalues associated with higher order terms is addressed. In addition to the composite laminates considered in the previous article, results are also presented for sandwich laminates, for which the inaccuracy in the single-term solution is even more prominent. It is shown that considering just one or two additional terms in the solution (n = 2 or 3) leads to a very accurate prediction and drastic improvement over the single-term solution (n = 1) for all entities including the stress field near the boundaries. This work will facilitate development of near-exact solutions of many important unresolved problems involving 3D elasticity, such as the free edge stresses in laminated structures under bending, tension and torsion.

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.

Analytical Piezoelasticity Solution for Natural Frequencies of Levy-Type Piezolaminated Plates

2019 ◽  
Vol 11 (03) ◽  
pp. 1950023 ◽  
Author(s):  
Susanta Behera ◽  
Poonam Kumari
Keyword(s):  
Natural Frequencies ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Single Layer ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Aspect Ratios ◽  
Support Conditions

First time, an analytical solution based on three-dimensional (3D) piezoelasticity is developed for the free vibration analysis of Levy-type piezolaminated plates using 3D extended Kantorovich method (EKM). Extended Hamilton principle (which is extended from elastic to piezoelectric case) is further extended to the dynamic version of mixed form containing contributions from the electrical terms. Multi-term multi-field extended Kantorovich method in conjunction with Fourier series (along [Formula: see text]-direction) is employed to obtain two sets of first-order homogeneous ordinary differential equations (8[Formula: see text] along [Formula: see text]- and [Formula: see text]-axes). A robust algorithm is designed (Fortran Code) to extract the natural frequencies and mode shapes of Levy-type piezolaminated plates. The accuracy and efficacy of this technique are verified thoroughly by comparing it with the existing results in the literature and with the 3D finite element (FE) solutions. Numerical results are presented for single-layer piezoelectric and smart sandwich plates considering five different boundary support conditions, three aspect ratios (length to thickness ratio) and electric open and close circuit conditions. The present results shall be used as a benchmark to assess various two-dimensional (2D) and 3D numerical solutions (e.g., FEM, DQM, etc.).

Extended Kantorovich method for static analysis of moderately thick functionally graded sector plates

2012 ◽  
Vol 86 ◽  
pp. 118-130 ◽  
Author(s):  
M.M. Aghdam ◽  
N. Shahmansouri ◽  
M. Mohammadi
Keyword(s):  
Static Analysis ◽  
Functionally Graded ◽  
Kantorovich Method ◽  
Extended Kantorovich Method
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