Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics.The numerical error resulting from the stress determination is a m...Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics.The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization.To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM)is proposed.The derivatives of the shear stress on the calculation path are determined by using the differential matrix which converts the differential form of the equations of equilibrium into a series of algebraic equations.The advantage of the proposed method is that the auxiliary lines,grids,and error accumulation which are commonly used in traditional shear difference methods(SDMs)are not required.Simulation and experimental results indicate that the proposed meshless method is able to provide high computational accuracy in the full-field stress determination.展开更多
In this paper, we show that any complete Riemannian manifold of dimension great than 2 must be compact if it has positive complex sectional curvature and δ-pinched 2-positive curvature operator, namely, the sum of th...In this paper, we show that any complete Riemannian manifold of dimension great than 2 must be compact if it has positive complex sectional curvature and δ-pinched 2-positive curvature operator, namely, the sum of the two smallest eigenvalues of curvature operator are bounded below by δ.scal 〉 O. If we relax the restriction of positivity of complex sectional curvature to non- negativity, we can also show that the manifold is compact under the additional condition of positive asymptotic volume ratio.展开更多
基金Project supported by the National Key R&D Program of China(No.2018YFF01014200)the National Natural Science Foundation of China(Nos.11727804,11872240,12072184,12002197,and 51732008)the China Postdoctoral Science Foundation(Nos.2020M671070 and 2021M692025)。
文摘Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics.The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization.To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM)is proposed.The derivatives of the shear stress on the calculation path are determined by using the differential matrix which converts the differential form of the equations of equilibrium into a series of algebraic equations.The advantage of the proposed method is that the auxiliary lines,grids,and error accumulation which are commonly used in traditional shear difference methods(SDMs)are not required.Simulation and experimental results indicate that the proposed meshless method is able to provide high computational accuracy in the full-field stress determination.
文摘In this paper, we show that any complete Riemannian manifold of dimension great than 2 must be compact if it has positive complex sectional curvature and δ-pinched 2-positive curvature operator, namely, the sum of the two smallest eigenvalues of curvature operator are bounded below by δ.scal 〉 O. If we relax the restriction of positivity of complex sectional curvature to non- negativity, we can also show that the manifold is compact under the additional condition of positive asymptotic volume ratio.
