Parametric method for the solution of an ill-posed inverse heat-conduction problem in application to the optimization of thermal regimes

A method is proposed for the stable approximate solution of an ill-posed inverse heat-conduction problem, to which the investigated problem of optimal control of the thermal regime of a rigid body is reduced.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 51, No. 4, pp. 668–673, October, 1986.     

On the solution of an inverse natural convection problem using various conjugate gradient methods

The inverse problem of determining the time‐varying strength of a heat source, which causes natural convection in a two‐dimensional cavity, is considered. The Boussinesq equation is used to model the natural convection induced by the heat source. The inverse natural convection problem is solved through the minimization of a performance function utilizing the conjugate gradient method. The gradient of the performance function needed in the minimization procedure of the conjugate gradient method is obtained by employing either the adjoint variable method or the direct differentiation method. The accuracy and efficiency of these two methods are compared, and a new method is suggested that exploits the advantageous aspects of both methods while avoiding the shortcomings of them. Copyright © 2000 John Wiley & Sons, Ltd.     

Engineering solution to the problem of ingot solidification in slab continuous-casting machines

An engineering solution to ingot solidification and the regularities of growth of an ingot envelope thickness and the coordinate of the end of slab solidification directly on slab continuous-casting machines (SCCM) are given, and ingot solidification conditions are determined. Examples of calculation of the envelope thickness and the coordinate of the end of solidification are provided for slab continuous-casting machines utilized at the Cherepovetsk integrated metallurgical complex (CherMC) and at the cast-and-iron works of the Aisenhüttenstadt Joint-Stock Company. A graphical algorithm for determining the cooling capacity of the secondary cooling zone is presented, and a nomogram for calibration of the cooling capacity of forced secondary cooling against the major and minor radii of an SCCM is developed.Vologda Polytechnic Institute, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 2, pp. 312–318, March–April, 1995.     

Finite element analysis of solidification using object-oriented and parallel techniques

This paper describes an implementation in C++ and in parallel of an explicit finite element formulation for the solution of transient heat conduction problems with phase change. The scheme requires a very small timestep because of its conditional stability, but, as no matrix inversion is required, the cost per timestep is an order of magnitude lower than for a conventional scheme. The principles of using object-oriented techniques for general finite element programming are briefly explained, while the advantages for parallel processing are described in detail, including the classes used to perform message passing. An example is given showing the performance of the scheme on two completely different parallel machines: a shared memory Silicon Graphics Power Challenge, and a distributed memory Cray T3D. The results indicate that the program scales efficiently for large meshes. © 1997 John Wiley & Sons, Ltd.     

On the finite element solution of an exterior boundary value problem

This paper compares three methods for dealing with an exterior boundary value problem by the Finite Element Method, one of which involves using an infinite element. The methods are illustrated by application to the problem of ground water flow round a tunnel with permeable invert. The use of a special trial function with a variable parameter in the infinite element gives a particularly efficient method of solution.     

Finite-difference solution of the conjugate heat transfer,natural convection,and solidification problem

A mathematical model of the solidification of a binary melt under convection conditions with a two-phase zone taken into account is formulated on the basis of average transfer equations. Results of a numerical solution are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 2, pp. 286–293, August, 1984.     

Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides

We analyse mathematically the problem of determining refractive index profiles from some desired/measured guided waves propagating in optical fibres. We establish the uniqueness of the solution of this inverse spectral problem assuming that only one guided mode is known. We then propose an iterative computational procedure for solving numerically the considered inverse spectral problem. Numerical results are presented to illustrate the potential of the proposed regularized Newton algorithm to efficiently and accurately retrieve the refractive index profiles even when the guided mode measurements are highly noisy.     

Approximate solution of the problem of solidification of curvilinear walls and hollow bodies under transient conditions

An approximate solution is obtained for the problem of solidification of curvilinear walls, hollow and continuous bodies in a transient process under conditions of operation of a set of thermal regime factors.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 5, pp. 828–833, May, 1982.     

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.     

Application of ELSP solution techniques to the deterministic robotic scheduling problem

This paper studies the flexible deterministic robotic scheduling problem (FDRSP) where one tool changer (robot) is in charge of several machining operations and overlapping tool changes are not allowed. The relationship between the FDRSP and the economic lot scheduling problem (ELSP) is explored. The most promising solution techniques for the ELSP guaranteeing feasibility in advance are modified and applied to the FDRSP. It is concluded that the basic period approach performs the best in small problems, while the rounding to powers of two approach is superior for medium to large problems.     

Upper and lower bounds of the solution for an elliptic plate problem using a genetic algorithm

Summary This paper presents a new method of treating engineering problems, in which Mathematical Programming is combined with the Method of Weighted Residual (MWR), and is, therefore, referred to as Mathematical Programming MWR (MP-MWR). If a solutionZ(x) exists in the defining domainV of a problem, it is limited bound by any two functionsZ _u(x) andZ _l(x). These functions satisfy the definite condition that ifRZ _u(x)>0>RZ₁(x), thenZ _uZZ_l inV, whereR is the residual operator. By using the optimization method of genetic algorithms (GAs), it is also possible to obtain the values of minimumZ _u(x) and maximumZ _l(x) which satisfy the above inequality. One advantage of MP-MWR is that the demands on computer memory are less than those required when applying the finite element method. In this paper a boundary value problem is studied as an example. The efficiency, accuracy, and simplicity of the MP-MWR approach are fully illustrated, indicating that the proposed method may be readily extended to solve a wide range of physical engineering problems.     

On the solution of the two-dimensional problem of a plane crack of arbitrary shape in an anisotropic material

In the present report we investigate the formulae of the stress field in the neighbourhood of a plane crack of arbitrary shape in an anisotropic material for the two-dimensional case. Moreover we consider the expression of the stress field in the neighbourhood of a plane crack in a transversely isotropic solid for the two-dimensional case. The construction of the solution for the anisotropic problem is presented as is the derivation of the expression for the surface tractions necessary to maintain the fundamental solution in a bounded region.     

On the solution of the third boundary problem for axially-symmetric regions

We present a variational method for solving a problem concerning the temperature field distribution inside a two-dimensional axially-symmetric region assuming convective heat transfer on its boundary.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 3, pp. 531–533, March, 1970.     

Assessment of the co-elution problem in gas chromatography-mass spectrometry using non-linear optimization techniques

Multivariate curve resolution based on the minimization of an objective function (MCR-FMIN) defined directly from the non-fulfillment of constraints was applied for the first time as a deconvolution method to separate co-eluted gas chromatographic-mass spectrometric (GC-MS) signals. Simulated and real (standard real mixture and limon oil) GC-MS data were used to evaluate the feasibility of this method. The MCR-FMIN solutions have been obtained based on the rotation of principal component analysis (PCA) solutions using the non-linear optimization algorithms. Calculation of the initial values of R rotation matrix using model free analysis methods such as fixed-size moving window-evolving factor analysis (FSMW-EFA), evolving latent projective graphs (ELPGs), and heuristic evolving latent projection (HELP) was proposed for faster convergence and avoiding to be stuck in local minima in MCR-FMIN algorithm. The band boundaries of feasible solutions (MCR-BANDS) obtained using MCR-FMIN were calculated for simulated data to assess the reliability of the method. In addition, the results of this method were compared with those of two most common self-modeling curve resolution (SMCR) methods of multivariate curve resolution-alternating least square (MCR-ALS) and HELP. A reasonable result can be obtained by selecting proper constraints, such as non-negativity, unimodality, normalization, and selectivity. However, when the number of components or the level of noise in each peak cluster increase, the convergence of algorithm becomes difficult and the results are not reliable. For quick and accurate analysis of co-eluted multi-component problematic GC-MS data MCR-FMIN can be considered as an alternative method to the MCR-ALS and HELP methods.     

On a numerical solution of the plastic buckling problem of structures

An automated digital computer procedure is presented for the accurate and efficient solution of the plastic buckling problem of structures. This is achieved by a Sturm sequence method employing a bisection strategy, which eliminates the need for having to solve the buckling eigenvalue problem at each incremental (decremental) loading stage that is associated with the usual solution techniques. The plastic bucking mode shape is determined by a simple inverse iteration process, once the buckling load has been established. Numerical results are presented for plate problems with various edge conditions. The resulting computer program written in FORTRAN for the JPL UNIVAC 1108 machine proves to be most economical in comparison with other existing methods of such analysis.     

Cracks in anisotropic materials—an iterative solution of the eigenvalue problem

An iterative method based on finite element analysis is proposed for the evaluation of the asymptotic crack tip field of an anisotropic elastic material. The method uses several iterations of analyses rather than solving the eigenvalue problem.

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Résumé On propose une méthode itérative basée sur une analyse par éléments finis pour évaleur le champ asymptotique à l'extrémité d'une fissure dans un matériau élastique anisotrope.La méthode comporte plusieurs itérations dans l'analyse, plutôt que la solution d'une problème d'eigenvalues.

     

Numerical solution of the point contact problem using the finite element method

The elastohydrodynamic lubrication problem, in which the lubricant pressure and film thickness are sensitive to surface deformation, is solved by using a finite element procedure and the Newton method. The numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling. The present analysis shows that pressure spikes are formed near the outlet region, a result which has been found in the line contact problem and which has been conjectured in the present problem.