共查询到20条相似文献，搜索用时 15 毫秒
1.
黄择言 《应用数学和力学(英文版)》1985,6(11):1097-1102
Taking advantage of successive approximations the present boundary-value problemis solved.We find the first-order and second-order solutions,and there fore we obtain theformulae in the second approximatior for the displacement,strain,and stress fields. 相似文献
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ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｃｏｎｓｉｄｅｒｔｈｅｅｘｔｅｎｄｅｄｌｉｎｅａｒｃｏｍｐｌｅｍｅｎｔａｒｉｔｙｐｒｏｂｌｅｍ (ＸＬＣＰ)ｉｎｔｒｏｄｕｃｅｄｂｙＭａｎｇａｓａｒｉａｎａｎｄＰａｎｇ[1](ａｌｓｏｓｅｅＹｅ[2 ]) :Ｆｉｎｄａｖｅｃｔｏｒ(ｘ ,ｙ) ∈Ｒ2ｎｓｕｃｈｔｈａｔＭｘ-Ｎｙ∈Ｋ ,ｘＴｙ=0 , ｘ≥ 0 ,ｙ≥ 0 ,( 1 )ｗｈｅｒｅＭ ,Ｎ ∈Ｒｍ×ｎａｒｅｇｉｖｅｎ ,ａｎｄＫｉｓａｐｏｌｙｈｅｄｒａｌｓｅｔｉｎＲｍｄｅｆｉｎｅｄｂｙＫ :=ｕ∈Ｒｍ｜Ｇｕ≥ｇ , Ｇ∈Ｒｌ×ｍ,ｇ∈Ｒｌ.Ｔｈｉｓｐｒｏ… 相似文献
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A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics. 相似文献
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The recurrent neural network (RNN) model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN. 相似文献
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王慎行 《应用数学和力学(英文版)》1986,7(12):1143-1157
This paper is offered to introduce a new differential equation, bihypergeometric equation, and to give its solutions.First received July 24, 1982. 相似文献
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Inequality constraints occur in many different fields of application, e.g., in structural mechanics, flow processes in porous media or mathematical finance. In this paper, we make use of the mathematical structure of these conditions in order to obtain an abstract computational framework for problems with inequality conditions. The constraints are enforced locally by means of Lagrange multipliers which are defined with respect to dual basis functions. The reformulation of the inequality conditions in terms of nonlinear complementarity functions leads to a system of semismooth nonlinear equations that is solved by a generalized version of Newton's method for semismooth problems. By this, both nonlinearities in the pde model and inequality constraints are treated within a single Newton iteration which converges locally superlinear. The scheme can efficiently be implemented in terms of an active set strategy with local static condensation of the non‐essential variables. Numerical examples from different fields of application illustrate the generality and the robustness of the method (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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A kind of mathematical programs with equilibrium constraints(MPEC)is studied.By using the idea of successive approximation,a smoothing nonlinear program- ming,which is equivalent to the MPEC problem,is proposed.Thereby,it is ensured that some classical optimization methods can be applied for the MPEC problem.In the end, two algorithm models are proposed with the detail analysis of the global convergence. 相似文献
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Zhiyong Si Tong Zhang Kun Wang 《International Journal of Computational Fluid Dynamics》2013,27(3-4):135-141
In this article, a Newton iterative mixed finite element method is presented for solving the stationary conduction–convection problems in two dimensions. The stability and the errors generated by both partitioning the space and solving nonlinear equations are analysed, which show that our method is stable and has good precision. Finally, some numerical experiments are given to confirm its effect. 相似文献
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M. Hintermüller G. Stadler 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2003,83(4):219-237
Es wird ein verallgemeinertes Newton‐Verfahren für die numerische Lösung von linear‐quadratischen Optimalsteuerprozessen mit zweiseitigen Restriktionen an die Steuerung eingeführt und analysiert. Bedingungen werden hergeleitet, unter denen der Algorithmus global konvergiert. Unter Verwendung von Glättungseigenschaften des Lösungsoperators der Zustandsgleichung und einem verallgemeinerten Ableitungsbegriff lassen sich lokal superlineare Konvergenzeigenschaften nachweisen. Umfassende numerische Tests unterstützen die theoretischen Ergebnisse, beweisen die Effizienz des neuen Verfahrens und liefern einen numerischen Nachweis für die Gitterunabhängigkeit des Algorithmus. A semi‐smooth Newton method for the numerical solution of linear‐quadratic optimal control problems with bilateral control constraints is introduced and analyzed. Conditional global convergence results are proved. Based on the smoothing property of the control‐to‐state operator and on generalized derivatives locally superlinear convergence is established. A report on comprehensive numerical tests supports the theoretical results, proves the efficiency of the new algorithm, and allows to argue mesh‐independence. 相似文献
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Ulji 《应用数学和力学(英文版)》2005,26(8):1083-1092
IntroductionLetX Rn,F:X→Rnbe given, the variational inequality, denoted byVI(X,F),is tofind a vectorx∈ Xsuch thatF(x)T(y-x)≥0, y∈ X. (1)DenoteN∶={1,2,…,n},whenX =[a,b]∶={x∈Rn|ai≤xi≤bi,i∈N},theVI(X,F)is called the box constrained variational ine 相似文献
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在将接触条件表为具有惩罚因子的线性互补形式后,本文详细推导了适用于弹性接触问题的虚功方程,在此基础上,结合有限元离散技术,简捷地导出了一种求解有摩擦弹性接触问题的线性互补方法;这种方法不必迭代,在无卸载时,只要一个增量步即可求得解答,计算效率较高,文末通过实例,说明了方法的正确性及有效性。 相似文献
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Z. Wang 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2008,88(3):179-190
The Kantorovich theorem is extended to Newton‐Josephy method for solving nonlinear complementarity problem. All the convergence conditions established in this article can be tested in the digital computer. 相似文献
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Y. Fang N. Huang 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2004,84(8):564-567
The purpose of this paper is to give a sufficient and necessary condition for an acceptable solution of an extended nonlinear complementarity problem. As a consequence, a characterization of an acceptable solution of a vertical implicit nonlinear complementarity problem is also established. 相似文献
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在最优控制理论中根据模拟理论思想发展了塑性力学和接触力学中的参变量变分原理, 并建立了控制输入受限的线性二次(linear quadratic, LQ)最优控制问题的求解新方程---耦合的Hamilton正则方程与线性互补方程. 通过将连续时间离散成一系列等间距时间区段, 在离散时域内采用参数二次规划方法给出数值求解输入受限的LQ最优控制问题的新算法. 数值仿真验证了该算法在求解控制输入受限的LQ最优控制问题中的有效性, 并且该算法具有较快的收敛性, 在大步长下具有较高的计算精度. 相似文献
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In the current paper the boundary integral equations (BIE) for elastic contact problems with friction are derived from the incremental virtual work principle. After introducing contact conditions of adhesion and slip into BIE all variants on boundary are made to discretize by quadratic isoparametric boundary element. In the current paper not only an auto-increment loading law is presented but also the iterative calculation laws for open, slip and adhesion condition are given. The results of numerical examples are satisfactory. 相似文献
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In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analytical properties. The optimality conditions of the penalized minimization problems are proven. To implement the al- gorithm, the cross-entropy method and the importance sampling are used based on the Monte-Carlo technique. Numerical tests show the effectiveness of the proposed algorithm. 相似文献