This paper presents the results of finite element analysis of rubber structures based on novel strain energy functions stemming from the representation theorem of tensorial function. The stress tensor is represented b...This paper presents the results of finite element analysis of rubber structures based on novel strain energy functions stemming from the representation theorem of tensorial function. The stress tensor is represented by Taylor expansion, using the representation theorem of tensorial function of a single tensorial argument for all terms in each order of the expansion. The scalar-valued coefficient functions of the theorem are represented by the integrity bases of the strain tensor and material constants to be determined by experiment. The computer implementation of the new constitutive laws has been verified by comparing the FE results with analytical solutions. A complicated structure of rubber bearing was analyzed. The FE results show good correlation with experimental data.展开更多
Time-dependent behaviors due to various mismatch strains are very important to the reliability of micro-/nano-devices.This paper aims at presenting an analytical model to study the viscoelastic stress relaxation of th...Time-dependent behaviors due to various mismatch strains are very important to the reliability of micro-/nano-devices.This paper aims at presenting an analytical model to study the viscoelastic stress relaxation of the laminated microbeam caused by mismatch strain.Firstly,Zhang’s two-variable method is used to establish a mechanical model for predicting the quasi-static stress relaxation of the laminated microbeam.Secondly,the related analytical solutions are obtained by combining the differential method and the eigenvalue method in the temporal domain.Finally,the influence of the substrateto-film thickness/modulus ratio on the relaxation responses of the laminated microbeam subject to a step load of the mismatch strain is studied.The results show that the present predictions are consistent with the previous theoretical studies.Furthermore,the thickness dependence of stress relaxation time of the laminated microbeam is jointly determined by the intrinsic structural evolution factors and tension-bending coupling state;the stress relaxation time can be controlled by adjusting the substrate-to-film thickness/modulus ratio.展开更多
Based on[1],the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper.The characteristics of the stress structure in the smooth region have been found that the varia...Based on[1],the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper.The characteristics of the stress structure in the smooth region have been found that the variable z can separated out;the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality.The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction.The obtained expressions of the stresses are very simple and visualized.The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree.A new degree parameter of the plane strain state has been put forward and studied.The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level.The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.展开更多
The damping material optimal placement for the structure with damping layer is studied based on evolutionary structural optimization (ESO) to maximize modal loss factors. A mathematical model is constructed with the o...The damping material optimal placement for the structure with damping layer is studied based on evolutionary structural optimization (ESO) to maximize modal loss factors. A mathematical model is constructed with the objective function defined as the maximum of modal loss factors of the structure and design constraints function defined as volume fraction of damping material. The optimal placement is found. Several examples are presented for verification. The results demonstrate that the method based on ESO is effective in solving the topology optimization of the structure with unconstrained damping layer and constrained damping layer. This optimization method suits for free and constrained damping structures.展开更多
文摘This paper presents the results of finite element analysis of rubber structures based on novel strain energy functions stemming from the representation theorem of tensorial function. The stress tensor is represented by Taylor expansion, using the representation theorem of tensorial function of a single tensorial argument for all terms in each order of the expansion. The scalar-valued coefficient functions of the theorem are represented by the integrity bases of the strain tensor and material constants to be determined by experiment. The computer implementation of the new constitutive laws has been verified by comparing the FE results with analytical solutions. A complicated structure of rubber bearing was analyzed. The FE results show good correlation with experimental data.
基金Project supported by the National Natural Science Foundation of China(Nos.12172204,11772182,11272193,and 10872121)the Program of Shanghai Municipal Education Commission(No.2019-01-07-00-09-E00018)。
文摘Time-dependent behaviors due to various mismatch strains are very important to the reliability of micro-/nano-devices.This paper aims at presenting an analytical model to study the viscoelastic stress relaxation of the laminated microbeam caused by mismatch strain.Firstly,Zhang’s two-variable method is used to establish a mechanical model for predicting the quasi-static stress relaxation of the laminated microbeam.Secondly,the related analytical solutions are obtained by combining the differential method and the eigenvalue method in the temporal domain.Finally,the influence of the substrateto-film thickness/modulus ratio on the relaxation responses of the laminated microbeam subject to a step load of the mismatch strain is studied.The results show that the present predictions are consistent with the previous theoretical studies.Furthermore,the thickness dependence of stress relaxation time of the laminated microbeam is jointly determined by the intrinsic structural evolution factors and tension-bending coupling state;the stress relaxation time can be controlled by adjusting the substrate-to-film thickness/modulus ratio.
文摘Based on[1],the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper.The characteristics of the stress structure in the smooth region have been found that the variable z can separated out;the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality.The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction.The obtained expressions of the stresses are very simple and visualized.The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree.A new degree parameter of the plane strain state has been put forward and studied.The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level.The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.
基金Science and Technology Foundation of China Academy of Engineering Physics (20060321)
文摘The damping material optimal placement for the structure with damping layer is studied based on evolutionary structural optimization (ESO) to maximize modal loss factors. A mathematical model is constructed with the objective function defined as the maximum of modal loss factors of the structure and design constraints function defined as volume fraction of damping material. The optimal placement is found. Several examples are presented for verification. The results demonstrate that the method based on ESO is effective in solving the topology optimization of the structure with unconstrained damping layer and constrained damping layer. This optimization method suits for free and constrained damping structures.
