Abstract
An important theorem proved by W. Z. Chien[1] states the equivalence of the functionals in general variational principles of potential energy and complementary energy. The stated theorem is applied now in formulation of general variational principle in finite elasticity with body couple (polar elasticity). Comoving coordinate system is being used in the derivation throughout (refer to[6], [8]).
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References
Chien, W. Z.,Variational Methods and Finite Elements, Vol. 1 (in Chinese), Science Press (1980), §7.4.
Nemat-Nasser, S., General variational principles in nonlinear and linear elasticity with applications,Mechanics Today, 1, (1972), 214–261.
Washizu, K.,Variational Methods in Elasticity and Plasticity, Pergamon Press. (1968).
Fraeijs de Veubeke, B. M., A new variational principle for finite elastic displacements,Int. J. Eng. Sci., 10, 9 (1972) 754–764
Guo Z. H., Unified theory of variaitonal principles in nonlinear theory of elasticity.Appl. Math. and Mech. (in Chinese), 1 (1980) 5–23.
Chen Z. D., Geometric field theory of finite deformation in continuum mechanics, (Enegry principle of finite elastic deformation), (in Chinese),J. Tsing Hua University, 19, 4 (1979), 44–57.
Nowacki, W., Theory of micropolar elasticity,CISM, Udine, (1972), §3.2.
Chen Z. D., Geometric field theory of finite deformation of continuum mechanics, (in Chinese),Acta Mechanica Sinica, 2 (1979), 107–117.J. China Institute of Mining Technology, 1(1978), 1–19. 2 (1979), 11–26.
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Zhi-da, C. Application of Chien's theorem to general variational principle in finite elasticity with body couple. Appl Math Mech 2, 209–214 (1981). https://doi.org/10.1007/BF01876779
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DOI: https://doi.org/10.1007/BF01876779