Variational method for solving problems of the plasticity of compressible media

Variational methods used in the theory of plastic flow are formulated on the assumption of the incompressibility of the deformable medium. In solving problems of the mechanics of soils and friable media and technological problems of the plastic shaping of uncompacted materials it is very important to take account of irreversible volumetric change. Extremum and variational theorems are proved in [1, 2] for rigid-plastic and viscoplastic expanding bodies. A variational equation equivalent to a complete system of differential equations is derived for a compressible plastic body.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 153–155, September–October, 1977.     

A finite-element approach in stream-tube method for solving fluid and solid mechanics problems

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity.     

Interpolation perturbation method for solving nonlinear problems

I.IntroductionInthispaper,onthebasisofRefll],usingtheinterPotationPerturbationmethod,theauthorseekstosolveseveralnon-Iinearproblems.Itsmainpointsare:Introducinganinterpolationfunction,wedeterminethisfunctionbyusingtheperturbationmethodandthenproceedtoseek…     

THE GENERAL METHOD FOR SOLVING DYNAMIC PROBLEMS

ＴＨＥＧＥＮＥＲＡＬＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＤＹＮＡＭＩＣＰＲＯＢＬＥＭＳ￥(孙右烈)ＳｕｎＹｏｕｌｉｅ（ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２０００７２，Ｐ．Ｒ．Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｔｈｅａｕ...     

求解弹性力学问题的有理单元法

传统的位移有限元法采用多项式形式的位移试函数,对于边数大于4的多边形单元,构造满足单元间协调性要求的多项式形式位移插值函数是一件困难的工作。本文利用逆距离权插值的思想并考虑到单元节点的分布,建立了边数大于4多边形单元上的有理函数形式的形函数。利用有理试函数,采用Galerkin法推导出求解平面弹性力学问题的有理单元法。采用有理单元法求解弹性力学问题,求解区域根据需要可以划分为任意多边形单元,极大地提高了网格划分的灵活性。有理单元法不依赖等参变换,不同单元的形函数表达形式统一,方便计算程序的编写。     

Precise integration method for solving singular perturbation problems

This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.     

三维接触问题的非光滑算法

给出了一种非光滑算法直接用于求解三维摩擦接触问题的不可微非线性互补模型,不再对模型进行光滑化处理,使算法更加简单。文中对非光滑算法的收敛性给出了严格的数学证明,数值实验表明该算法列式简单,但与光滑化算法同样有效。     

An efficient method for solving free-boundary diffusion problems

Summary A new method is introduced for solving free-boundary problems for the heat equation. The method is shown to be uniformly convergent both for first type and nonlinear second type boundary conditions. Approximate solutions are obtained by discretization of the time variable and recursive solution at each time step of classical heat conduction linear problems in slabs of known thickness. An error estimate is given. Numerical tests are presented in a few cases in which exact solutions are known.

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Sommario Si introduce un nuovo metodo per la soluzione di problemi a contorno libero per l'equazione del calore. Si dimostra la convergenza uniforme del metodo sia per condizioni al contorno del primo tipo che per condizioni al contorno del secondo tipo non lineari. Le soluzioni approssimate sono ottenute discretizzando la variabile temporale e risolvendo ricorsivamente ad ogni passo un classico problema lineare di conduzione in uno strato di spessore noto. E' data una stima dell'errore. Per alcuni casi nei quali è nota la soluzione esatta sono presentate prove numeriche.

     

Improved L-P method for solving strongly nonlinear problems

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｒｏｎｇｌｙｎｏｎｌｉｎｅａｒｏｓｃｉｌｌａｔｉｏｎｐｒｏｂｌｅｍ¨ｕ ω20 ｕ =εｆ(ｕ , ｕ ,¨ｕ) , (1 )ｗｈｅｒｅｔｈｅｓｙｍｂｏｌ“·”ｄｅｎｏｔｅｓｔｈｅｄｉｆｆｅｒｅｎｔｉａｔｉｏｎｗｉｔｈｒｅｓｐｅｃｔｔｏｔｈｅｉｎｄｅｐｅｎｄｅｎｔｖａｒｉａｂｌｅｔａｎｄω0ａｎｄεａｒｅａｌｌｔｈｅａｒｂｉｔｒａｒｙｃｏｎｓｔａｎｔｓ,ｈａｖｅｉｎｔｈｅｒｅｃｅｎｔｙｅａｒｓｓｅｖｅｒａｌｉｍｐｒｏｖｅｄＬ＿Ｐｍｅｔｈｏｄｓｗｈｅｎεｉｓｎｏｔｓｍａｌｌ (ｓｔｒｏ…     

INTERPOLATION PERTURBATION METHOD FOR SOLVING THE BOUNDARY LAYER TYPE PROBLEMS

ＹｕａｎＹｉｗｕ（袁镒吾）（ＲｅｃｅｉｖｅｄＯｃｔ．２，１９９４；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅｎＷｅｉｚａｎｇ）ＩＮＴＥＲＰＯＬＡＴＩＯＮＰＥＲＴＵＲＢＡＴＩＯＮＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＴＨＥＢＯＵＮＤＡＲＹＬＡＹＥＲＴＹＰＥＰＲＯＢ...     

A total linearization method for solving viscous free boundary flow problems by the finite element method

In this paper a total linearization method is derived for solving steady viscous free boundary flow problems (including capillary effects) by the finite element method. It is shown that the influence of the geometrical unknown in the totally linearized weak formulation can be expressed in terms of boundary integrals. This means that the implementation of the method is simple. Numerical experiments show that the iterative method gives accurate results and converges very fast.     

Method of successive approximations for solving boundary-value problems of plasticity with allowance for the stress mode

A method for solving boundary-value problems of plasticity with allowance for the stress mode is developed. To describe the elastoplastic deformation of an isotropic material, use is made of constitutive equations that include two nonlinear functions dependent on the stress mode and determined experimentally. The elastoplastic state of a thin cylindrical shell under axisymmetric loading is calculated as a numerical example. The numerical results demonstrate good convergence of the method. The effect of the stress mode on the strain distribution in a cylindrical shell is assessed     

Efficient solving method for unsteady incompressible interfacial flow problems

Unsteady interfacial problems, considered in an Eulerian form, are studied. The phenomena are modeled using the incompressible viscous Navier–Stokes equations to get the velocity field and an advection equation to predict interface evolutions. The momentum equation is solved by means of an implicit hybrid augmented Lagrangian–Projection method, whereas an explicit characteristic method coupled with a TVD SUPERBEE scheme is applied to the advection equation. The velocity components and the pressure are discretized on staggered grids with finite volumes. Emphasis is on the accuracy and robustness of the techniques described before. A precise explanation on the validation phase will be given, which uses such tests as the advection of a step function or Zalesak's problem to improve the calculation of the interface. The global approach is used on a physically hard interfacial test with strong disparities between viscosities and densities. Copyright © 1999 John Wiley & Sons, Ltd.     

The finite-element-force method for solving plane problems of elasticity

Using elements in the form of arbitrary sectors, the author has devised a plan for solving plane problems of elasticity by the force method. The method is characterized by a smaller number of nodes, a more convenient computation and a perfect adaptability to the particular shape of the region in question.     

A semi-numerical method for solving inverse heat conduction problems

A semi-numerical method is presented for solving the inverse heat conduction problems in homogeneous and composite bodies. The presented solution does not require both the initial temperature distribution in the body and the whole temperature-time history at the temperature sensor locations. Sample calculations confirm that this approach produces stable and accurate results for both exact and noisy data. The extension of the method presented to two or three dimensions is straightforward.     

Singular boundary method for solving plane strain elastostatic problems

This study documents the first attempt to apply the singular boundary method (SBM), a novel boundary only collocation method, to two-dimensional (2D) elasticity problems. Unlike the method of fundamental solutions (MFS), the source points coincide with the collocation points on the physical boundary by using an inverse interpolation technique to regularize the singularity of the fundamental solution of the equation governing the problems of interest. Three benchmark elasticity problems are tested to demonstrate the feasibility and accuracy of the proposed method through detailed comparisons with the MFS, boundary element method (BEM), and finite element method (FEM).     

A Newton's method scheme for solving free-surface flow problems

A Newton's method scheme is described for solving the system of non-linear algebraic equations arising when finite difference approximations are applied to the Navier–Stokes equations and their associated boundary conditions. The problem studied here is the steady, buoyancy-driven motion of a deformable bubble, assumed to consist of an inviscid, incompressible gas. The linear Newton system is solved using both direct and iterative equation solvers. The numerical results are in excellent agreement with previous work, and the method achieves quadratic convergence.     

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.