Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…...Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.展开更多
In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.
By elastic-plastic finite deformation finite element analysis (FEA), the conservation of J-integral is investigated in detail for a welded joint with an overmatchingweld in plane stress case. It is indicated that J-in...By elastic-plastic finite deformation finite element analysis (FEA), the conservation of J-integral is investigated in detail for a welded joint with an overmatchingweld in plane stress case. It is indicated that J-integral is path dependent under various conditions at least in the cases studied in this paper. Meanwhile, the above conclusions are verified by the hybrid method results in which combined Moire interferometry with FEA.展开更多
The Fenghua River Bridge is a major structure on the highway between Hengzhang and Guojiachi, which is to be built with a four-span prestress concrete (PC) box girder and symmetrical cantilever castings. In this paper...The Fenghua River Bridge is a major structure on the highway between Hengzhang and Guojiachi, which is to be built with a four-span prestress concrete (PC) box girder and symmetrical cantilever castings. In this paper, a finite element method (FEM) model is set up to study the effects of concrete differential aging time on the construction phases of the Fenghua River Bridge by calculating the vertical displacement of the folding segment of the middle span and the longitudinal bending moment of Pier 12#. In the model, the girders are classified into 150 changing sections based on the desgn scheme, and their construction is to be carried in 16 phases respectively to build 12 blocks connected by a side folding segment and a middle folding segment, covered with a second dead load and in completion for 20 years. It is found that the internal forces and deformations of the concrete structures at the aging time of 60 d are quite different from those of 0 d aging time while the behaviors of the structures of 120 d aging time is nearly the same as those of 60 d aging time― the differences are so small that can be neglected, suggesting that the creep develops obviously about one month after the cement is hardened and the development fades later on.展开更多
The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is il-lustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and...The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is il-lustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and dis-placement fields under axisymmetrical and asymmetric stress conditions. For the same rock masses and under axisym-metrical stress conditions,the radius of the plastic zone in terms of Hoek-Brown criterion is generally an approximation of the radius in terms of the Mohr-Coulomb criterion. The radius in terms of the Hoek-Brown criterion is larger under low stress conditions. For poor quality rock masses (GSI<25),measures (such as grouting,setting rock bolts,etc.) that improve the GSI of rock masses are effective in improving the stability of tunnels. It is not advisable to improve the sta-bility of the tunnels by providing a small support resistance p through shotcrete,except for very poor quality jointed rock masses. Without reference to the quality of the rock mass,the disturbance factor D should not less than 0.5. Meas-ures which disturb rock masses during tunnel construction should be taken carefully when the tunnel depth increases.展开更多
In marine application,marine grade steel is generally used for haul and superstructures.However,aluminum has also become a good choice due to its lightweight qualities,while rusting of aluminum is minimal compared to ...In marine application,marine grade steel is generally used for haul and superstructures.However,aluminum has also become a good choice due to its lightweight qualities,while rusting of aluminum is minimal compared to steel.In this paper a study on friction stir welding of aluminum alloys was presented.The present investigation deals with the effects of different friction stir welding tool geometries on mechanical strength and the microstructure properties of aluminum alloy welds.Three distinct tool geometries with different types of shoulder and tool probe profiles were used in the investigation according to the design matrix.The effects of each tool shoulder and probe geometry on the weld was evaluated.It was also observed that the friction stir weld tool geometry has a significant effect on the weldment reinforcement,microhardness,and weld strength.展开更多
The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the...The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the n-dimensional simplex and the squared distance between its circumcenter and barycenter times the squared circumradius of its inscribed simplex is not less than the 2(n-1)th power of n times its squared inradius, and is equal to when the simplex is regular and its inscribed siplex is a tangent point one. Deduction from this inequality reaches a generalization of n-dimensional Euler inequality indicating that the circumradius of the simplex is not less than the n-fold inradius. Another inequality is derived to present the relationship between the circumradius of the n-dimensional simplex and the circumradius and inradius of its pedal simplex.展开更多
文摘Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.
文摘In this paper, we use a geometric identity in the n-dimensional Euclidean space En and give the further improveme nt of Klamkin inequality in the space En.
文摘By elastic-plastic finite deformation finite element analysis (FEA), the conservation of J-integral is investigated in detail for a welded joint with an overmatchingweld in plane stress case. It is indicated that J-integral is path dependent under various conditions at least in the cases studied in this paper. Meanwhile, the above conclusions are verified by the hybrid method results in which combined Moire interferometry with FEA.
文摘The Fenghua River Bridge is a major structure on the highway between Hengzhang and Guojiachi, which is to be built with a four-span prestress concrete (PC) box girder and symmetrical cantilever castings. In this paper, a finite element method (FEM) model is set up to study the effects of concrete differential aging time on the construction phases of the Fenghua River Bridge by calculating the vertical displacement of the folding segment of the middle span and the longitudinal bending moment of Pier 12#. In the model, the girders are classified into 150 changing sections based on the desgn scheme, and their construction is to be carried in 16 phases respectively to build 12 blocks connected by a side folding segment and a middle folding segment, covered with a second dead load and in completion for 20 years. It is found that the internal forces and deformations of the concrete structures at the aging time of 60 d are quite different from those of 0 d aging time while the behaviors of the structures of 120 d aging time is nearly the same as those of 60 d aging time― the differences are so small that can be neglected, suggesting that the creep develops obviously about one month after the cement is hardened and the development fades later on.
基金Project 50639100 supported by the National Natural Science Foundation of China
文摘The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is il-lustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and dis-placement fields under axisymmetrical and asymmetric stress conditions. For the same rock masses and under axisym-metrical stress conditions,the radius of the plastic zone in terms of Hoek-Brown criterion is generally an approximation of the radius in terms of the Mohr-Coulomb criterion. The radius in terms of the Hoek-Brown criterion is larger under low stress conditions. For poor quality rock masses (GSI<25),measures (such as grouting,setting rock bolts,etc.) that improve the GSI of rock masses are effective in improving the stability of tunnels. It is not advisable to improve the sta-bility of the tunnels by providing a small support resistance p through shotcrete,except for very poor quality jointed rock masses. Without reference to the quality of the rock mass,the disturbance factor D should not less than 0.5. Meas-ures which disturb rock masses during tunnel construction should be taken carefully when the tunnel depth increases.
文摘In marine application,marine grade steel is generally used for haul and superstructures.However,aluminum has also become a good choice due to its lightweight qualities,while rusting of aluminum is minimal compared to steel.In this paper a study on friction stir welding of aluminum alloys was presented.The present investigation deals with the effects of different friction stir welding tool geometries on mechanical strength and the microstructure properties of aluminum alloy welds.Three distinct tool geometries with different types of shoulder and tool probe profiles were used in the investigation according to the design matrix.The effects of each tool shoulder and probe geometry on the weld was evaluated.It was also observed that the friction stir weld tool geometry has a significant effect on the weldment reinforcement,microhardness,and weld strength.
文摘The problem on the geometrc inequalities involving an n-dimensional simplex and its inscribed simplex is studied. An inequality is established, which reveals that the difference between the squared circumradius of the n-dimensional simplex and the squared distance between its circumcenter and barycenter times the squared circumradius of its inscribed simplex is not less than the 2(n-1)th power of n times its squared inradius, and is equal to when the simplex is regular and its inscribed siplex is a tangent point one. Deduction from this inequality reaches a generalization of n-dimensional Euler inequality indicating that the circumradius of the simplex is not less than the n-fold inradius. Another inequality is derived to present the relationship between the circumradius of the n-dimensional simplex and the circumradius and inradius of its pedal simplex.
