Let M be a(2 k + 2 l + 2)-dimensional smooth manifold. For such M, Bande and Hadjar introduce a new geometric structure called contact pair which roughly is a couple of 1-forms of constant classes with complementary k...Let M be a(2 k + 2 l + 2)-dimensional smooth manifold. For such M, Bande and Hadjar introduce a new geometric structure called contact pair which roughly is a couple of 1-forms of constant classes with complementary kernels and foliations. We show the relationship between a pair of vector fields for a contact pair and a quadruple of functions on M. This is a generalization of the classical result for contact manifolds.展开更多
The stuctures of contact ion pairs of magnesium sulfate were studied. The geometries of contact ion pairs of MgSO 4(H 2O) n (n =1-6) were optimized by using Hartree Fock (HF/6 31+G *, HF/6 311+G ** ) and...The stuctures of contact ion pairs of magnesium sulfate were studied. The geometries of contact ion pairs of MgSO 4(H 2O) n (n =1-6) were optimized by using Hartree Fock (HF/6 31+G *, HF/6 311+G ** ) and density functional theory (DFT) (B3LYP/6 31+G *, B3LYP/6 311+G ** ) methods. The stable structures of monodentate, bidentate and tridentate contact ion pairs were obtained. The bidentate structure of contact ion pairs are the most stable compaired with the monodentate and tridentate ones for the same composition. The hydration enthalpies of contact ion pairs of MgSO 4 (H 2O) n (n =1-4) increase with their hydration numbers.展开更多
A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem （e.g., resistant coating and thermal barrier coatings） subjected to c...A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem （e.g., resistant coating and thermal barrier coatings） subjected to complicated load conditions. To decrease the calculation scale and calculation errors, the local Lagrange multipliers are solved only on a pair of contact nodes using the Jacobi iteration method, and the constraint modification of the tangential multipliers are required. After the calculation of the present node-pairs Lagrange multiplier, it is turned to next contact node-pairs until all node-pairs have finished. Compared with an ordinary contact algorithm, the new local node-pairs contact algorithm is allowed a more precise element on the contact face without the stiffness matrix singularity. The stress intensity factors （SIFs） and the contact region of an infinite plate central crack are calculated and show good agreement with those in the literature. The contact zone near the crack tip as well as its influence on singularity of stress fields are studied. Furthermore, the frictional contacts are also considered and found to have a significant influence on the SIFs. The normalized mode-II stress intensity factors KII for the friction coefficient decrease by 16% when f changes from 1 to 0.展开更多
基金supported by the National Natural Science Foundation of China(11671209,11871278)by the Starting Foundation for Research of Jinan University
文摘Let M be a(2 k + 2 l + 2)-dimensional smooth manifold. For such M, Bande and Hadjar introduce a new geometric structure called contact pair which roughly is a couple of 1-forms of constant classes with complementary kernels and foliations. We show the relationship between a pair of vector fields for a contact pair and a quadruple of functions on M. This is a generalization of the classical result for contact manifolds.
文摘The stuctures of contact ion pairs of magnesium sulfate were studied. The geometries of contact ion pairs of MgSO 4(H 2O) n (n =1-6) were optimized by using Hartree Fock (HF/6 31+G *, HF/6 311+G ** ) and density functional theory (DFT) (B3LYP/6 31+G *, B3LYP/6 311+G ** ) methods. The stable structures of monodentate, bidentate and tridentate contact ion pairs were obtained. The bidentate structure of contact ion pairs are the most stable compaired with the monodentate and tridentate ones for the same composition. The hydration enthalpies of contact ion pairs of MgSO 4 (H 2O) n (n =1-4) increase with their hydration numbers.
基金supported by the National Basic Research Program of China(Grant No.2012CB026200)the National Natural Science Foundation of China(Grant No.50878048)
文摘A new node-pairs contact algorithm is proposed to deal with a composite material or bi-material interface crack face contact and friction problem （e.g., resistant coating and thermal barrier coatings） subjected to complicated load conditions. To decrease the calculation scale and calculation errors, the local Lagrange multipliers are solved only on a pair of contact nodes using the Jacobi iteration method, and the constraint modification of the tangential multipliers are required. After the calculation of the present node-pairs Lagrange multiplier, it is turned to next contact node-pairs until all node-pairs have finished. Compared with an ordinary contact algorithm, the new local node-pairs contact algorithm is allowed a more precise element on the contact face without the stiffness matrix singularity. The stress intensity factors （SIFs） and the contact region of an infinite plate central crack are calculated and show good agreement with those in the literature. The contact zone near the crack tip as well as its influence on singularity of stress fields are studied. Furthermore, the frictional contacts are also considered and found to have a significant influence on the SIFs. The normalized mode-II stress intensity factors KII for the friction coefficient decrease by 16% when f changes from 1 to 0.
