Using the logarithmic strain measure for solving torsion problems

The problems of free and constrained torsion of a rod of solid circular cross-section are solved numerically using a tensor linear constitutive relation written in terms of the energy compatible Cauchy stress and Hencky logarithmic strain tensors. The only function used to determine the properties of the isotropic incompressible material of the rod is a power-law function that approximates the shear diagram and corresponds to an elastoplastic material with power-law hardening. The solution obtained shows that, despite the tensorial linearity of the state law, the use of the logarithmic strain measure allows one to describe qualitatively the effect of significant elongation of the rod in free torsion (the Poynting effect) as well as the arising normal longitudinal, radial, and circumferential stresses, whose values are commensurable, at large deformations, with the maximum tangential stresses in the cross-section. Computational dependences of the torsional moment on the angle of twist in free and constrained torsion are obtained. These dependences are found to be significantly different from each other; the limitmoment and the correspondingmaximum angle of twist for free torsion are found to be considerably lower than those for constrained torsion. It follows that the shear strength, which is traditionally calculated from the maximum torsional moment, becomes indeterminate. For constrained torsion, the dependence of the longitudinal compressive force on the angle of twist is obtained.     

Interpolation perturbation method for solving nonlinear problems

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

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。     

THE GENERAL METHOD FOR SOLVING DYNAMIC PROBLEMS

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

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.     

Improved L-P method for solving strongly nonlinear problems

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

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.

     

INTERPOLATION PERTURBATION METHOD FOR SOLVING THE BOUNDARY LAYER TYPE PROBLEMS

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

Modified asymptotic Adomian decomposition method for solving Boussinesq equation of groundwater flow

The Adomian decomposition method （ADM） is an approximate analytic method for solving nonlinear equations. Generally, an approximate solution can be ob- tained by using only a few terms. However, in applications, we need to use it flexibly according to the real problem. In this paper, based on the ADM, we give a modified asymptotic Adomian decomposition method and use it to solve the nonlinear Boussinesq equation describing groundwater flows. The example shows effectiveness of the modified asymptotic Adomian decomposition method.     

The asymptotic solving equations of thick ring shell and its solution under moment Mo

In this paper, from the fundamental equations of three dimensional elastic mechanics, we have found a sequence of asymptotic solving equations of thick ring shell (or body) applied arbitrary loads by the perturbation method based upon a geometric small parameter a=r_o/R_o, which may be divided into two independent equation groups which are similar to the equation groups for plane strain and torsional problems. Using these equations, we have also found first order and second order approximate solutions of thick ring shell applied moment M_o.     

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.     

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.