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Some basic principles in dynamic theory of viscoelastic materials with voids

Science China(Physics,Mechanics & Astronomy) 2007年第3期50卷 370-378页

作者： LUO En LI WeiHua Department of Applied Mechanics and Engineering Sun Yat-sen UniversityGuangzhou 510275China

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo, some basic principles in the dynamic theory of viscoelastic materials with voids can be estab- lished systematically. In this paper, an important integral relation in terms of con- volutions 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, but also to derive systemati- cally the complementary functionals for the eight-field, six-field, four-field simpli- fied gurtin-type variational principles and the potential energy-functional for the two-field one in the dynamic theory of viscoelastic materials with voids by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.

关键词： dynamic theory of viscoelastic materials with voids principle of virtual work reciprocal theorem simplified gurtin-type variational principle complementary relation

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Some basic principles for linear coupled dynamic thermopiezoelectricity

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Science China Mathematics 1999年第12期42卷 1292-1300页

作者：罗恩邝君尚 Department of Applied Mechanics and Engineering Zhongshan University Guangzhou China Department of Civil and Structural Engineering Hong Kong University of Science and Technology Hong Kong China

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way some basic principles for linear coupled dynamic thermopiezoelectricity can be established systematically. 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 linear coupled dynamic thermopiezoelectricity, but also to derive systematically the complementary functionals for eleven-field, nine-field, six-field and three-field simplified gurtin-type variational principles. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.

关键词： linear coupled dynamic thermopiezoelectricity principle of virtual work reciprocal theorem simplified gurtin-type variational principle complementary relation.

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Some basic principles for the linear theory of piezoelectric micropolar elastodynamics

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中国科学：物理学、力学、天文学英文版 2010年第6期53卷 1094-1100页

作者： LUO En & LI WeiHua Department of Applied Mechanics and Engineering,Sun Yat-sen University,Guangzhou 510275,China Department of Applied Mechanics and Engineering Sun Yat-sen University Guangzhou China

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,in a simple and unified way proposed by Luo,some basic principles in the linear theory of piezoelectric micropolar elastodynamics 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 not only possible to obtain the principle of virtual work and the reciprocal theorem,but also to systematically derive the complementary functionals for the eleven-field,nine-field and six-field simplified gurtin-type variational principles and the potential energy-functional for the three-field one in the linear theory of piezoelectric micropolar elastodynamics by the generalized Legendre transformations given in this paper. Furthermore,with this approach,the intrinsic relationships among various principles can be explained clearly.

关键词： piezoelectric micropolar elastodynamics principle of virtual work reciprocal theorem simplified gurtin-type variational principle complementary relation

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