According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In thi...According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In this paper, an important integral relation in terms of convolutions is given,which can be con- sidered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not on- ly 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 in- trinsic relationship among various principles can be explained clearly.展开更多
According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author, various energy principles in theory of elastic materials with voids can be established systematically, In this p...According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author, various energy principles in theory of elastic materials with voids can be established systematically, In this paper, an important integral relation is given, which can be considered essentially as the generalized pr- inciple of virtual work. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem of work in 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 generalized variational principles, and the principle of minimum potential and complementary energies. Furthermore, with this appro ach, the intrinsic relationship among various principles can be explained clearly.展开更多
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 wit...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.展开更多
This study investigates the forced vibration of functionally graded hexagonal nano-size plates for the first time.A quasi-three-dimensional(3D)plate theory including stretching effect is used to model the anisotropic ...This study investigates the forced vibration of functionally graded hexagonal nano-size plates for the first time.A quasi-three-dimensional(3D)plate theory including stretching effect is used to model the anisotropic plate as a continuum one where small-scale effects are considered based on nonlocal strain gradient theory.Also,the plate is assumed on a Pasternak foundation in which normal and transverse shear loads are taken into account.The governing equations of motion are obtained via the Hamiltonian principles which are solved using analytical based methods by means of Navier’s approximation.The influences of the exponential factor,nonlocal parameter,strain gradient parameter,Pasternak foundation coefficients,length-to-thickness,and length-to-width ratios on the dynamic response of the nanoplates are examined.In addition,the accuracy of an isotropic approximate instead of the anisotropic model is studied.The dynamic behavior of the system shows that mechanical mathematics-based models may get better results considering the anisotropic model because the dynamic response can cause prominent differences(up to 17%)between isotropic approximation and anisotropic model.展开更多
The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elastici...The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elasticity.Moore-Gibson-Thompson(MGT)heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity.By employing the normal mode technique,the non-dimensional coupled governing equations of motion are solved to determine the an-alytical expressions of the displacements,temperature,void volume fractions,microrotation vector,force stress tensors,and equilibrated stress vectors.Several two-dimensional graphs are presented to demon-strate the influence of various parameters,such as kernel functions,thermal conductivity,and nonlocality.Furthermore,different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables.Some particu-lar cases are also discussed in the presence and absence of different parameters.展开更多
基金The project supported by the Foundation of Zhongshan University Advanced Research Center
文摘According to the basic idea of dual-complementarity,in a simple and unified way proposed by the author,some basic principles in dynamic theory of elastic materials with voids can be established sys- tematically.In this paper, an important integral relation in terms of convolutions is given,which can be con- sidered as the generalized principle of virtual work in mechanics.Based on this relation,it is possible not on- ly 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 in- trinsic relationship among various principles can be explained clearly.
基金The project supported by the National Natural Science Foundation of China
文摘According to the basic idea of dual-complementarity, in a simple and unified way proposed by the author, various energy principles in theory of elastic materials with voids can be established systematically, In this paper, an important integral relation is given, which can be considered essentially as the generalized pr- inciple of virtual work. Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem of work in 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 generalized variational principles, and the principle of minimum potential and complementary energies. Furthermore, with this appro ach, the intrinsic relationship among various principles can be explained clearly.
基金Supported by the National Natural Science Foundation of China (Grant No. 10172097)the Scientific Foundation of the Ministry of Education of China for Doctoral Program (Grant No. 20030558025)
文摘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.
文摘This study investigates the forced vibration of functionally graded hexagonal nano-size plates for the first time.A quasi-three-dimensional(3D)plate theory including stretching effect is used to model the anisotropic plate as a continuum one where small-scale effects are considered based on nonlocal strain gradient theory.Also,the plate is assumed on a Pasternak foundation in which normal and transverse shear loads are taken into account.The governing equations of motion are obtained via the Hamiltonian principles which are solved using analytical based methods by means of Navier’s approximation.The influences of the exponential factor,nonlocal parameter,strain gradient parameter,Pasternak foundation coefficients,length-to-thickness,and length-to-width ratios on the dynamic response of the nanoplates are examined.In addition,the accuracy of an isotropic approximate instead of the anisotropic model is studied.The dynamic behavior of the system shows that mechanical mathematics-based models may get better results considering the anisotropic model because the dynamic response can cause prominent differences(up to 17%)between isotropic approximation and anisotropic model.
文摘The present study enlightens the two-dimensional analysis of the thermo-mechanical response for a mi-cropolar double porous thermoelastic material with voids(MDPTMWV)by virtue of Eringen’s theory of nonlocal elasticity.Moore-Gibson-Thompson(MGT)heat equation is introduced to the considered model in the context of memory-dependent derivative and variable conductivity.By employing the normal mode technique,the non-dimensional coupled governing equations of motion are solved to determine the an-alytical expressions of the displacements,temperature,void volume fractions,microrotation vector,force stress tensors,and equilibrated stress vectors.Several two-dimensional graphs are presented to demon-strate the influence of various parameters,such as kernel functions,thermal conductivity,and nonlocality.Furthermore,different generalized thermoelasticity theories with variable conductivity are compared to visualize the variations in the distributions associated with the prior mentioned variables.Some particu-lar cases are also discussed in the presence and absence of different parameters.
