Abstract
Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations. To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates, the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle. Finally, it is pointed out that the modified H-R mixed variational principle for pure elastic, single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.
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Communicated by Zhong Wan-xie
Project supported by the National Natural Science Foundation of China (No. 10072038) and the Special Fund for PhD Program of Education Ministry of China (No. 2000005616)
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Guang-hui, Q., Jia-jun, Q. & Yan-hong, L. Modified H-R mixed variational principle for magnetoelectroelastic bodies and state-vector equation. Appl Math Mech 26, 722–728 (2005). https://doi.org/10.1007/BF02465422
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DOI: https://doi.org/10.1007/BF02465422
Key words
- magnetoelectroelastic body
- variational principle
- laminated plates
- state-vector equation
- semi-analytical solution