Abstract
According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author[1], some basic principles in dynamic theory of elastic materials with voids can be established systematically. In this paper, an important integral relation in terms of convolutions is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem in dynamic theory of elastic materials with voids, but also to derive systematically the complementary functionals for the eight-field, six-field, four-field and two-field simplified Gurtin-type variational principles. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.
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Luo En, Cheung YK. On the variational principles in linear elastodynamics.Acta Mechanica Sinica, 1988. 4 (4): 337
Cowin Sc, Nunziato JW. Linear elastic materials with voids.J Elasticityl 1983, 13: 125
Cowin SC, Puri P. The classical pressure vessel problems for linear elastic materials with voids.J Elasticity, 1983, 13: 157
Passmen SL. Stress relaxation, creep, failure and hysteresis in a linear elastic material with voids.J Elasticity, 1984, 14: 201
Cowin SC. The stress around a hole in a linear elastic material with voids.Quart J Mech Appl Math, 1984, 37: 441
Iesan D. Some theorems in the theory of elastic materials with voids.J Elasticity, 1985, 15: 215
Chandrasekharaiah DS. Complete solutions in the theory of elastic materials with voids.Quart J Mech Appl Math, 1989, 42: 41
Ciarletta M, Scalia A. On some theorems in the linear theory of viscoelastic materials with voids.J Elasticity, 1991, 25: 149
Oden JT, Reddy JN. Variational methods in theoretical mechanics. 2nd ed. Berlin: Springer verlag, 1983, 309
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The project supported by the Foundation of Zhongshan University Advanced Research Center
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En, L. On some basic principles in dynamic theory of elastic materials with voids. Acta Mech Sinica 9, 142–148 (1993). https://doi.org/10.1007/BF02487493
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DOI: https://doi.org/10.1007/BF02487493