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41.
盛宝怀 《数学物理学报(A辑)》2005,25(1):11-20
建立了基于扰动超球Jacobi结点的Marcinkiewicz zygmund不等式并借助一种新的K泛函给出了基于扰动超球Jacobi结点的积分型Lagrange插值算子逼近的Steckin Marchaud型不等式. 相似文献
42.
The fundamental part of the contact stress problem solution using a finite element method is to locate possible contact areas reliably and efficiently. In this research, a remeshing technique is introduced to determine the contact region in a given accuracy. In the proposed iterative method, the meshes near the contact surface are modified so that the edge of the contact region is also an element’s edge. This approach overcomes the problem of surface representation at the transition point from contact to non-contact region. The remeshing technique is efficiently employed to adapt the mesh for more precise representation of the contact region. The method is applied to both finite element and boundary element methods. Overlapping of the meshes in the contact region is prevented by the inclusion of displacement and force constraints using the Lagrange multipliers technique. Since the method modifies the mesh only on the contacting and neighbouring region, the solution to the matrix system is very close to the previous one in each iteration. Both direct and iterative solver performances on BEM and FEM analyses are also investigated for the proposed incremental technique. The biconjugate gradient method and LU with Cholesky decomposition are used for solving the equation systems. Two numerical examples whose analytical solutions exist are used to illustrate the advantages of the proposed method. They show a significant improvement in accuracy compared to the solutions with fixed meshes. 相似文献
43.
In this paper we prove three conjectures of Revers on Lagrange interpolation for fλ(t)=|t|λ,λ>0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants LN( fλ,t) for 0<|t|<1, and discuss their convergence at t=0. We also establish an asymptotic relation for max|t|1| |t|λ−LN( fλ,t)|. The proofs are based on strong asymptotics for |t|λ−LN( fλ,t), 0|t|<1. 相似文献
44.
X. R. Ma 《Proceedings of the American Mathematical Society》2005,133(11):3179-3189
We present a necessary and sufficient condition for two matrices given by two bivariate functions to be inverse to each other with certainty in the cases of Krattenthaler formula and Warnaar's elliptic matrix inversion. Immediate consequences of our result are some known functions and a constructive approach to derive new matrix inversions from known ones.
45.
Jili Wang Linshan Wang 《Annals of Differential Equations》2014,(2):184-190
In this paper, the stability in Lagrange sense of a class of stochastic static neural networks with mixed time delays is studied. Based on the Lyapunov stability theory and with the help of stochastic analysis technique, the criteria for the stability in Lagrange sense of stochastic static neural networks with mixed time delays is obtained. One example is given to verify the advantage and applicability of the proposed results. 相似文献
46.
Jonathan M. Borwein Jay S. Treiman Qiji J. Zhu 《Transactions of the American Mathematical Society》1998,350(6):2409-2429
We consider nonsmooth constrained optimization problems with semicontinuous and continuous data in Banach space and derive necessary conditions without constraint qualification in terms of smooth subderivatives and normal cones. These results, in different versions, are set in reflexive and smooth Banach spaces.
47.
沈惠川 《数学物理学报(A辑)》1998,18(1):78-88
将弹性有限变形问题纳入Lagrange力学的理论体系中,并用经典力学中业已存在的Routh方法构建了有限变形平面应变问题和有限变形平面应力问题的基本微分方程,讨论了有限变形大挠度问题vonkarman方程中存在的矛盾进而提出了两种改进方案. 相似文献
48.
49.
By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the error estimate for local approximation. And we also point out that the numerical differentiation formula constructed by Li [J.P. Li, General explicit difference formulas for numerical differentiation, J. Comput. Appl. Math. 183 (2005) 29-52] is actually a special case of the Lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes. 相似文献
50.
A multibody frictional mortar contact formulation (Gitterle et al., 2010) is extended for the simulation of solids undergoing finite strains with inelastic material behavior. The framework includes the modeling of finite strain inelastic deformation, the numerical treatment of frictional contact conditions and specific finite element technology. Several well-established and recent models are employed for each of these building blocks to capture the distinct physical aspects of the deformation behavior. The approach is based on a mortar formulation and the enforcement of contact constraints is realized with dual Lagrange multipliers. The introduction of nonlinear complementarity functions into the frictional contact conditions combined with the global equilibrium leads to a system of nonlinear equations, which is solved in terms of the semi-smooth Newton method. The resulting method can be interpreted as a primal–dual active set strategy (PDASS) which deals with contact nonlinearities, material and geometrical nonlinearities in one iterative scheme. The consistent linearization of all building blocks of the framework yields a robust and highly efficient approach for the analysis of metal forming problems. The effect of finite inelastic strains on the solution behavior of the PDASS method is examined in detail based on the complementarity parameters. A comprehensive set of numerical examples is presented to demonstrate the accuracy and efficiency of the approach against the traditional node-to-segment penalty contact formulation. 相似文献