It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or...It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.展开更多
n this paper with Von Karmanis basic assumptions a kinematically admissible continuous velocity field has been established to drawing through parabolic dies (or called trumpet dies). Then by. using the curvilinear an...n this paper with Von Karmanis basic assumptions a kinematically admissible continuous velocity field has been established to drawing through parabolic dies (or called trumpet dies). Then by. using the curvilinear and the integral as a function of the upper limit an upper bound analytical solution of the drawing stress is obtained.展开更多
The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip...The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip elements and other crack linear elements, the boundary element formulas of the torsion rigidity and stress intensity factors were given. Some typical torsion problems of a cylinder involving a straight, kinked or curvilinear crack were calculated. The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas, which demonstrates the validity and applicability of the present boundary element method.展开更多
The Salnt-Venant torsion problems of a composite cylinder with curvilinear cracks were investigated. By considering the bimaterial interface as a boundary of the outer bar or inner one, the problem was reduced to the ...The Salnt-Venant torsion problems of a composite cylinder with curvilinear cracks were investigated. By considering the bimaterial interface as a boundary of the outer bar or inner one, the problem was reduced to the solution of boundary integral equations on the crack, external boundary and interface. Using the new boundary element method, some typical torsion problems of a composite cylinder involving a straight or kinked crack were calculated. The obtained results were compared with data in the literature to show validity and applicability of the present method.展开更多
基金Funded by the Natural Science Foundation Project of CQCSTC(No.cstc2012jj A50018)the Basic Research of Chongqing Municipal Education Commission(No.KJ120631)the Science Research Foundation Project of CQNU(No.16XYY31)
文摘It is explored that the line integral is a path independent in two or three arbitrary dimensional orthogonal curvilinear coordinate systems, which is based on the integral condition with the path independent in two or three dimensional rectangular coordinate systems. Firstly, according to the coordinate transformation, the condition that the line integral is the path independent in the polar coordinate system is obtained easily from the Green's theorem in two-dimensional rectangular coordinate system and the condition is extended to arbitrary two-dimension orthogonal curvilinear coordinates. Secondly, through the coordinate transformation relationship and the area projection method, the Stokes formula in three-dimensional rectangular coordinate system is promoted to the spherical coordinate system and cylindrical coordinate system, and the condition that the line integral is a path independent is obtained. Furthermore, the condition is extended to arbitrary three-dimension orthogonal curvilinear coordinates. Lastly, the conclusions are made.
文摘n this paper with Von Karmanis basic assumptions a kinematically admissible continuous velocity field has been established to drawing through parabolic dies (or called trumpet dies). Then by. using the curvilinear and the integral as a function of the upper limit an upper bound analytical solution of the drawing stress is obtained.
文摘The Saint-Venant torsion problems of a cylinder with curvilinear cracks were considered and reduced to solving the boundary integral equations only on cracks. Using the interpolation models for both singular crack tip elements and other crack linear elements, the boundary element formulas of the torsion rigidity and stress intensity factors were given. Some typical torsion problems of a cylinder involving a straight, kinked or curvilinear crack were calculated. The obtained results for the case of straight crack agree well with those given by using the Gauss-Chebyshev integration formulas, which demonstrates the validity and applicability of the present boundary element method.
基金the National High-Tech Research and Development Program of China(863Program)(No.2007AA09Z317)
文摘The Salnt-Venant torsion problems of a composite cylinder with curvilinear cracks were investigated. By considering the bimaterial interface as a boundary of the outer bar or inner one, the problem was reduced to the solution of boundary integral equations on the crack, external boundary and interface. Using the new boundary element method, some typical torsion problems of a composite cylinder involving a straight or kinked crack were calculated. The obtained results were compared with data in the literature to show validity and applicability of the present method.
