Graphene has remarkable strength,such as yield strength and elastic constant.The dynamic behaviour of graphene sheet is affected by geometrical variation in atomic arrangement.This paper introduced graphene with armch...Graphene has remarkable strength,such as yield strength and elastic constant.The dynamic behaviour of graphene sheet is affected by geometrical variation in atomic arrangement.This paper introduced graphene with armchair atomic structure for estimating fundamental natural frequencies.The presented analysis can be useful for the possible high frequency nanomechanical resonator systems.The analytical formulation,based on classical plate theory and continuum solid modelling based finite element method have been performed for estimation of fundamental natural frequencies of single layer graphene sheet(SGLS)with different boundary conditions.The free edge and clamped edge boundary conditions have been considered.For simplifying analytical formulations,Blevins approach for dynamic solution has been adopted and for validating analytical results.The finite element analysis of SLGS has been performed using ANSYS software.The effect of variation in geometrical parameters in terms of width and length of SLGS has been analysed for realization of ultra-high frequency based nanomechanical resonator systems.展开更多
A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problem...A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional finite element method （FEM） and boundary element method （BEM）, and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.展开更多
In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respec...In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respect to initial state for the NHD system. To this end, we construct corresponding linear variational system （LVS） for the solution of the NHD system, also prove the boundedness of fundamental matrix solutions for the LVS. On this basis, the strong stability is proved by such boundedness.展开更多
文摘Graphene has remarkable strength,such as yield strength and elastic constant.The dynamic behaviour of graphene sheet is affected by geometrical variation in atomic arrangement.This paper introduced graphene with armchair atomic structure for estimating fundamental natural frequencies.The presented analysis can be useful for the possible high frequency nanomechanical resonator systems.The analytical formulation,based on classical plate theory and continuum solid modelling based finite element method have been performed for estimation of fundamental natural frequencies of single layer graphene sheet(SGLS)with different boundary conditions.The free edge and clamped edge boundary conditions have been considered.For simplifying analytical formulations,Blevins approach for dynamic solution has been adopted and for validating analytical results.The finite element analysis of SLGS has been performed using ANSYS software.The effect of variation in geometrical parameters in terms of width and length of SLGS has been analysed for realization of ultra-high frequency based nanomechanical resonator systems.
文摘A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional finite element method （FEM） and boundary element method （BEM）, and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.
基金This work was supported by the National Science Foundation for the Youth of China （Grant Nos. 11501574, 11401073 and 11701063）, the National Natural Science Foundation of China （Grant Nos. 11771008, 61673083 and 61773086）, the National Science Foundation for the Tianyuan of China （Grant No. 11626053）, the Natural Science Foundation of Shandong Province in China （Grant No.： ZR2015FM014, ZR2015AL010 and ZR2017MA005）, the Fundamental Research Funds for the Cen- tral Universities in China （Grant No. DUT16LK07） and the Project funded by China Postdoctoral Science Foundation （Grant No. 2016M601296）.
文摘In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respect to initial state for the NHD system. To this end, we construct corresponding linear variational system （LVS） for the solution of the NHD system, also prove the boundedness of fundamental matrix solutions for the LVS. On this basis, the strong stability is proved by such boundedness.
