Application of a perturbation method to the solution of eddycurrent testing problems

This paper presents an analytical solution for the change of the impedance of a double conductor line due to eddy currents induced in presence of an infinitely long horizontal cylindrical flaw with vertically symmetric cross-section. The solution, found by a perturbation method, is applicable in the case the conductivities of the flaw and of the surrounding material do not differ by much. Numerical results for flaws of circular and elliptic cross-sections are presented     

A conforming solution to curved plate bending problems

A curved triangular element for plate bending is developed, using the displacement method of formulation. The element has one outwardly curved side and conforms on an arbitrary quadratic boundary. To the user, the element appears as a single curved triangle. Internally, however, the element is subdivided into a straight-sided triangle and a ‘curved segment’. The straight-sided triangle is extensively documented in the literature^2-5 and is referred to in the paper as the Cowper triangle. The curved segment is a two-noded element with 12 degrees-of-freedom. It has one straight side and one curved side. Independent expansions are assumed in each domain and explicit shape functions derived. The theoretical solution to a few practical problems is contained in each of the two expansions. In such cases, the curved triangle produces perfect results. Otherwise, the accuracy is of the same order as that obtained in similar problems with straight boundaries. The method is easily extended to elements of higher order.     

A general boundary element method approach to the solution of three-dimensional frictionless contact problems

A direct boundary element method is presented for three-dimensional stress analysis of frictionless contact problems. The isoparametric formulation of the boundary element method is implemented for the general case of contact in the absence of friction, which is limited to linear elastic homogeneous and isotropic materials. An iterative procedure is employed to determine the correct size of the contact zone by finding a boundary solution compatible with the contact condition. The applicability of the procedure is tested by application to three problems of advancing and conforming contact. The computed results are compared with numerical and analytical solutions where possible.     

Application of direct variational method to the solution of mixed boundary value problems

A direct variational method has been considered for solving mixed boundary value problems for linear elliptical equations. The main idea of the method consists in searching the unknown solution in a class of functions satisfying the differential equation and some of the boundary conditions. The functional to be minimized may be expressed in terms of the boundary values of the unknown solution, and thus the dimension of the variational problem is reduced. Reduction of the functional defined on the domain to a functional on its boundary corresponds to the common in the elsaticity theory of application of Clapeyron's theorem for the transformation of functionals of minimum elastic potential energy and complementary work. The reduced problem may be solved by the Ritz direct method. Some examples from the elasticity and seepage theories have been given to demonstrate the effectiveness of the method. Among the problems that have been solved by the method we may mention the plane elastic problem for a crack in a strip, three-dimensional elastic problems for a plane rectangular crack in an infinite elastic medium and the problem of a rectangular die in sliding contact with an elastic half-space (numerical solutions exhibit correct asymptotic behaviour in the neighbourhood of corners of cracks or die), and the plane and axisymmetric seepage problems.     

Multivariable approach to the finite difference solution of elasto-plastic problems

The solutions of plane elasto-plastic problems usually use one or two field variables—namely a stress functions or the displacements. The use of three, four or five field variables is investigated and it is concluded that the three stresses from the best basis for a multivariable approach. Attempts to solve the governing equations with an initial value technique were exhaustively tried and discarded in preference to a boundary value or elliptical technique. The problem solved to check the method is that of a hole in plane strain uniaxial tension. Effective plastic strain distributions are plotted, along with stress and strain concentration data and distributions of the mean to effective stress ratio. Comparison is made between solutions produced using incremental and deformation theories.     

Application of the parametric method to the solution of problems of the unsteady thermal boundary layer

A generalization of a parametric method developed earlier for the calculation of the dynamic boundary layers is presented for problems of the unsteady laminar thermal boundary layer.     

Approximate approach to solution of three-dimensional heat conduction problems

An approximate approach is presented for the solution of a three-dimensional heat conduction problem for one type of heat-protective coating frequently encountered in practice. The method proposed, based on the reduction of the initial three-dimensional problem to a set of two problems of less dimensionality, makes it possible, with satisfactory precision, to shorten substantially the computer time spent in determining thermal conditions of elements of a given design.Translated from Inzherneno-fizicheskii Zhurnal, Vol. 61, No. 2, pp. 319–322, August, 1991.     

用于多目标优化的蚁群算法的构建及其应用

从蚁群的生物学行为出发,将成群募集和海量募集两种机制融入蚁群算法,并针对多目标优化的特性,综合考虑解的被支配度和分散度,抽提出一种启发式规则,用以评价食物源的优劣,进而构建多目标连续蚁群优化算法(MO-CACO).通过两个多目标典型函数的优化测试,验证了MO-CACO具有较强的多目标全局寻优能力,且稳健性良好,所求得的最优解集的多目标值能均匀地逼近Pareto最优前沿的各部分.将MO-CACO用于二甲苯异构化装置的操作优化,取得了满意的结果,MO-CACO可为化工过程多目标决策提供支持.     

Development of a systems approach to the solution of physicochemical gasdynamics problems

An automated system for numerical solution of certain problems of physicochemical gasdynamics is developed. The system includes the following main elements: structured physicochemical databases, a generator of kinetic equations of vibrational relaxation and chemical reactions, programs for direct solution of equations of gasdynamics with kinetic equations, a program module for building a compact mechanism of leading processes, and a module for selecting an optimum solution from the set of permissible ones. A variational problem of physicochemical gasdynamics connected with finding the best profile of an ultrasonic nozzle is solved. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 6, pp. 952–957, November–December, 1997.     

Application of a variational method for the solution of nonstationary heat conduction problems

We present an application of a variational principle due to Ainola, compatible with Kantorovich's method, for the solution of the first and second boundary value problems.     

Green''s function method solution of the Reissner''s plate problem

Green's functions can play a significant role in the development of numerical procedures based on the BEM. For that reason the construction of Green's functions and matrices is of great practical importance. In this study, the extension of the Green's function formalism is introduced to Reissner's plate theory, which accounts for the effect of transverse normal stress and transverse shear deformation. The development of Green's matrix for the governing boundary value problem is described based on the separation of variables. The explicit expressions for the entries of Green's matrix are derived. The algorithm is developed for computation of the stress-strain for a rectangular plate. A validation example is presented, illustrating an equal level of accuracy attained for both displacement and stress.     

BEM solution of two dimensional unilateral contact problems with friction by a new approach

Recently, a new numerical resolution method has been introduced for frictionless unilateral contact problems which reduces the resolution of the unilateral problem to the resolution of a nonlinear equation. This reduction is based on a reformulation of the unilateral problem, which at the same time governs the usual unknowns and extra unknowns characterising the contact zone position. The supplementary equations needed by the introduction of these extra unknowns are given by writing the contact force and the gap between the body and its support vanish simultaneously on the contact zone boundary. The boundaries of the bodies in contact are supposed regular in the contact zone vicinity. The aim of the present paper is to extend this resolution method to unilateral contact problems with Coulomb friction.     

Trefftz method for Kirchhoff plate bending problems

Kirchhoff plate bending problems were studied by both the Trefftz direct and indirect approximations in which non-singular, complete Trefftz functions are used as the weighting and/or trial functions. The Trefftz direct method involved only the quantities of engineering interest. Numerical results are given to show the efficiency and the excellent accuracy of the present method.     

Application of a differential-difference method to the solution of one-dimensional nonstationary heat conduction problems with a moving boundary

A differential-difference method is applied to obtain an approximate solution of one-dimensional nonstationary heat conduction problems with a moving boundary in rectangular and cylindrical systems of coordinates. Recursion formulas are obtained for the determination of successive values of the unknown functions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 17, No. 4, pp. 719–724, October, 1969.     

Development of a genetic algorithm‐based lookup table approach for efficient numerical integration in the method of finite spheres with application to the solution of thin beam and plate problems

It is observed that for the solution of thin beam and plate problems using the meshfree method of finite spheres, Gaussian and adaptive quadrature schemes are computationally inefficient. In this paper, we develop a novel technique in which the integration points and weights are generated using genetic algorithms and stored in a lookup table using normalized coordinates as part of an offline computational step. During online computations, this lookup table is used much like a table of Gaussian integration points and weights in the finite element computations. This technique offers significant reduction of computational time without sacrificing accuracy. Example problems are solved which demonstrate the effectiveness of the procedure. Copyright © 2006 John Wiley & Sons, Ltd.     

The viscoplastic circular plate—A new solution

Summary In a previous paper a theory of viscoplasticity was developed in which the dynamic yield surface is defined as the surface which encloses the quasistatic yield surface and has a constant distance from it. In the present paper, by means of the above theory, the problem of a thin circular plate under uniformly distributed transverse pressure is solved. The material of the plate is assumed to be rigidviscoplastic. The solution is compared with previous solutions of the same problem.

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Die viskoplastische Kreisplatte-Eine neue Lösung

Zusammenfassung In einer vorangeganenen Arbeit wurde eine Theorie der Viskoplastizität entwickelt und die dynamische Fließfläche definiert, eine Fläche, die die quasistatische Fließfläche in konstantem Abstand umgibt. In vorliegender Arbeit wird mit Hilfe dieser Theorie das Problem einer dünnen Kreisplatte unter Gleichlast gelöst. Der Plattenwerkstoff wird als starr-viskoplastisch vorausgesetzt. Die Lösung wird mit anderen desselben Problems verglichen.

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With 10 Figures

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This research has been supported by the National Science Foundation under a grant with Yale University.     

Application of the boundary integral equation method to Reissner's plate model

Numerical solution of Reissner's model for the bending of elastic plates by an advanced boundary integral equation method is outlined. Construction of fundamental solutions and computational strategy is fully described. Implementation of the resulting one-dimensional model is illustrated by two test problems, including comparison to analytical solutions.