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Keywords: C⁰ finite element, higher order zig-zag shear, coupled magneto-electro-elasticity, mixed formulation, inf-sup test, bending.

Summary

A simple mixed variational formulation for the higher order zig-zag shear deformable coupled magneto-electro-elastic plates with a continuous interlaminar shear-stress is presented in this paper. In this formulation, the kinematics for the mechanical part are derived by superposing a piece-wise constant shearing strain field (i.e. different values in different lamina) on an overall quadratically varying field. The developed consistent kinematics associated to the mechanical displacements involve 5 unknowns, i.e. three displacements and two average shearing strains. However, for the electrical and magnetic potentials the cubic layer-wise kinematics is used. To achieve a suitable internal energy density like quantity we modify the Gibb's energy function via weakening the shear kinematic relation in the thickness direction through the projection of the assumed shear strain (obtained from the independent shearing stresses using the shear compliance coefficients) onto the space of the displacement driven shearing strains. For the development of C⁰ type finite elements, a modified Hellinger-Reissner like functional for the laminate is derived through 'partial' Legendre transformation [1]. The present paper focus on:

The development of a suitable mixed functional for the higher-order shear deformable magneto-electro-elastic plates featuring the continuous shearing stresses.
The formulation of a C⁰ finite element for the bending analysis of magneto-electro-elastic plates that satisfy the inf-sup conditions.

The finite elements based on the present mixed formulation do not require the C¹ continuity condition for the out-of-plane displacement and enjoy an equal order C⁰ interpolation for the nodal field variables. These elements are employed for the bending analysis of a laminated magneto-electro-elastic (MEE) composite plate. It has been observed that the finite element model developed in this paper does not show locking and is capable of producing satisfactory results even with a distorted mesh of linear elements. The fully coupled formulation developed is used for the analysis of MEE plates subject to electric and magnetic loadings. The advantage of the model developed is its applicability to both thin and thick smart sandwich or laminated plates. New results for the mechanical, electrical and magnetic loading are provided in this paper. The accuracy of the present elements are illustrated using numerical examples.

References

1: S.J. Hossain, B. Barman, S. Latifa, "On a variationally formulated higher order shear deformable C⁰ element for the analysis of laminated composite plates", Computers & Structures, 87(21-22), 1331-1348, 2009. doi:10.1016/j.compstruc.2009.06.012

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 93 PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: Paper 67 A Simple C0 Continuous Higher Order Hellinger-Reissner Type Element for the Analysis of Magneto-Electro-Elastic Plates featuring Continuous Interlaminar Stresses S.J. Hossain and S. Subhamoy Department of Civil Engineering, Indian Institute of Technology, Kharagpur, India doi:10.4203/ccp.93.67 purchase the full-text of this paper Full Bibliographic Reference for this paper S.J. Hossain, S. Subhamoy, "A Simple C0 Continuous Higher Order Hellinger-Reissner Type Element for the Analysis of Magneto-Electro-Elastic Plates featuring Continuous Interlaminar Stresses", in , (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 67, 2010. doi:10.4203/ccp.93.67 Keywords: C⁰ finite element, higher order zig-zag shear, coupled magneto-electro-elasticity, mixed formulation, inf-sup test, bending. Summary A simple mixed variational formulation for the higher order zig-zag shear deformable coupled magneto-electro-elastic plates with a continuous interlaminar shear-stress is presented in this paper. In this formulation, the kinematics for the mechanical part are derived by superposing a piece-wise constant shearing strain field (i.e. different values in different lamina) on an overall quadratically varying field. The developed consistent kinematics associated to the mechanical displacements involve 5 unknowns, i.e. three displacements and two average shearing strains. However, for the electrical and magnetic potentials the cubic layer-wise kinematics is used. To achieve a suitable internal energy density like quantity we modify the Gibb's energy function via weakening the shear kinematic relation in the thickness direction through the projection of the assumed shear strain (obtained from the independent shearing stresses using the shear compliance coefficients) onto the space of the displacement driven shearing strains. For the development of C⁰ type finite elements, a modified Hellinger-Reissner like functional for the laminate is derived through 'partial' Legendre transformation [1]. The present paper focus on: The development of a suitable mixed functional for the higher-order shear deformable magneto-electro-elastic plates featuring the continuous shearing stresses. The formulation of a C⁰ finite element for the bending analysis of magneto-electro-elastic plates that satisfy the inf-sup conditions. The finite elements based on the present mixed formulation do not require the C¹ continuity condition for the out-of-plane displacement and enjoy an equal order C⁰ interpolation for the nodal field variables. These elements are employed for the bending analysis of a laminated magneto-electro-elastic (MEE) composite plate. It has been observed that the finite element model developed in this paper does not show locking and is capable of producing satisfactory results even with a distorted mesh of linear elements. The fully coupled formulation developed is used for the analysis of MEE plates subject to electric and magnetic loadings. The advantage of the model developed is its applicability to both thin and thick smart sandwich or laminated plates. New results for the mechanical, electrical and magnetic loading are provided in this paper. The accuracy of the present elements are illustrated using numerical examples. References 1 S.J. Hossain, B. Barman, S. Latifa, "On a variationally formulated higher order shear deformable C⁰ element for the analysis of laminated composite plates", Computers & Structures, 87(21-22), 1331-1348, 2009. doi:10.1016/j.compstruc.2009.06.012 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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