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A Coupled Analysis of Smart Plate Under Electro-Mechanical Loading Using Enhanced Lower-Order Shear Deformation Theory

개선된 저차 전단 변형 이론을 이용한 전기, 기계 하중을 받는 스마트 복합재 구조물의 연성 해석

  • Published : 2007.01.01

Abstract

Enhanced lower order shear deformation theory is developed in this study. Generally, lower order theories are not adequate to predict accurate deformation and stress distribution through the thickness of laminated plate. For the accurate prediction of detailed stress and deformation distributions through the thickness, higher order zigzag theories have been proposed. However, in most cases, simplified zigzag higher order theory requires $C_1$, shape functions in finite element implementation. In commercial FE softwares, $C_1$, shape functions are not so common in plate and shell analysis. Thus zigzag theories are useful for the highly accurate prediction of thick composite behaviors but they are not practical in the sense that they cannot be used conveniently in the commercial package. In practice, iso-parametric $C_0$ plate model is the standard model for the analysis and design of composite laminated plates and shells. Thus in the present study, an enhanced lower order shear deformation theory is developed. The proposed theory requires only $C_0$ shape function in FE implementation. The least-squared energy error between the lower order theory and higher order theory is minimized. An enhanced lower order shear deformation theory(ELSDT) in this paper is proposed for smart structure under complex loadings. The ELSDT is constructed by the strain energy transformation and fully coupled mechanical, electric loading cases are studied. In order to obtain accurate prediction, zigzag in-plane displacement and transverse normal deformation are considered in the deformation Held. In the electric behavior, open-circuit condition as well as closed-circuit condition is considered. Through the numerous examples, the accuracy and robustness of present theory are demonstrated.

Keywords

Shear Deformable Plate Theory;Coupled Electro-Mechanical Loading;Smart Composite Plate Model

References

  1. Lo, K. H., Christensen, R. M., and Wu, F. M., 1977, 'A Higher-Order Theory of Plate Deformation Part 2: Laminated Plates,' Transaction of the ASME J. App. Mech., Vol. 44, pp. 669-676 https://doi.org/10.1115/1.3424155
  2. Levinson, M., 1980, 'An Accurate Simple Theory of the Statics and Dynamics of Elastic Plates,' Mech. Research Communications, Vol. 7, pp. 343-350 https://doi.org/10.1016/0093-6413(80)90049-X
  3. Reddy, J. N., 1987, 'A Generalization of Two-Dimensional Theories of Laminated Plates,' Comm. in Num. Meth. In Eng., Vol. 3, pp. 173-180 https://doi.org/10.1002/cnm.1630030303
  4. Cho, M. and Parmerter, R. R., 1992, 'An Efficient Higher-Order Plate Theory for Laminated Composites,' Composite Structures, Vol. 20, pp. 113-123 https://doi.org/10.1016/0263-8223(92)90067-M
  5. Cho, Y. B. and Averill, R. C., 2000, 'First-Order Zig-Zag Sublaminate Plate Theory and Finite Element Model for Laminated Composite and Sandwich Panels,' Composite Structures, Vol. 50, No. 1, pp. 1-15 https://doi.org/10.1016/S0263-8223(99)00063-X
  6. Oh, J. and Cho, M., 2004, 'A Finite Element Based on Cubic Zig-Zag Plate Theory for the Prediction of Thermo-Electric-Mechanical Behaviors,' Int. J. of Solids & Structures, Vol. 41, No. 5-6, pp. 1357-1375 https://doi.org/10.1016/j.ijsolstr.2003.10.019
  7. Whitney, J. M., 1972, 'Stress Analysis of Thick Laminated Composites and Sandwich Plates,' J. of Comp. Mat., Vol. 6, pp. 426-440 https://doi.org/10.1177/002199837200600401
  8. Ray, M. C., Bhattacharya, R. and Samanta, B., 1993, 'Exact Solution for Static Analysis of Intelligent Structures,' AIAA J., Vol. 31, No. 9, pp. 1684-1691 https://doi.org/10.2514/3.11831
  9. Carrera, E., 2003, 'Historical Review of Zig-Zag Theories for Multilayered Plates and Shells,' Applied Mechanics Review, Vol. 56, pp. 287-308 https://doi.org/10.1115/1.1557614
  10. Cho, M. and Oh, J., 2004, 'Higher Order Zig-Zag Theory for Fully Coupled Thermo-Electric–- Mechanical Smart Composite Plates,' Int. J. of Solids & Structures, Vol. 41, No. 5-6, pp. 1331-1356 https://doi.org/10.1016/j.ijsolstr.2003.10.020
  11. Sheikh, A. H., Topdar, P. and Halder, S., 2001, 'An Appropriate FE Model for Through-Thickness Variation of Displacement and Potential in Thin/Moderately Thick Smart Laminates,' Composite Structures, Vol. 51, pp. 401-409 https://doi.org/10.1016/S0263-8223(00)00156-2