Simulation of Steady-State Nonlinear Heat Transfer Problems Through the Minimization of Quadratic Functionals

In this work it is presented a systematic procedure for constructing the solution of a large class of nonlinear conduction heat transfer problems through the minimization of quadratic functionals like the ones usually employed for linear descriptions. The proposed procedure gives rise to an efficient and easy way for carrying out numerical simulations of nonlinear heat transfer problems by means of finite elements. To illustrate the procedure a particular problem is simulated by means of a finite element approximation.

Estudo do estado fundamental de aglomerados de silício via redes neurais

We introduce a global optimization method based on the cooperation between an Artificial Neural Net (ANN) and Genetic Algorithm (GA). We have used ANN to select the initial population for the GA. We have tested the new method to predict the ground-state geometry of silicon clusters. We have described the clusters as a piling of plane structures. We have trained three ANN architectures and compared their results with those of pure GA. ANN strongly reduces the total computational time. For Si10, it gained a factor of 5 in search speed. This method can be easily extended to other optimization problems.

Methane combustion kinetic rate constants determination: an ill-posed inverse problem analysis

Methane combustion was studied by the Westbrook and Dryer model. This well-established simplified mechanism is very useful in combustion science, for computational effort can be notably reduced. In the inversion procedure to be studied, rate constants are obtained from [CO] concentration data. However, when inherent experimental errors in chemical concentrations are considered, an ill-conditioned inverse problem must be solved for which appropriate mathematical algorithms are needed. A recurrent neural network was chosen due to its numerical stability and robustness. The proposed methodology was compared against Simplex and Levenberg-Marquardt, the most used methods for optimization problems.

Optimization of the use of carbon paste electrodes (CPE) for electrochemical study of the chalcopyrite

The use of carbon paste electrodes (CPE) of mineral sulfides can be useful for electrochemical studies to overcome problems by using massive ones. Using CPE-chalcopyrite some variables were electrochemically evaluated. These variables were: (i) the atmosphere of preparation (air or argon) of CPE and elapsed time till its use; (ii) scan rate for voltammetric measurements and (iii) chalcopyrite concentration in the CPE. Based on cyclic voltammetry, open-circuit potential and electrochemical impedance results the recommendations are: oxygen-free atmosphere to prepare and kept the CPE until around two ours, scan rates from 10 to 40 mV s-1, and chalcopyrite concentrations > 20%.

Retrieval of kinetic rates in reactions with semi batch liquid phase using ill-posed inverse problem theory

A neural network procedure to solve inverse chemical kinetic problems is discussed in this work. Rate constants are calculated from the product concentration of an irreversible consecutive reaction: the hydrogenation of Citral molecule, a process with industrial interest. Simulated and experimental data are considered. Errors in the simulated data, up to 7% in the concentrations, were assumed to investigate the robustness of the inverse procedure. Also, the proposed method is compared with two common methods in nonlinear analysis; the Simplex and Levenberg-Marquardt approaches. In all situations investigated, the neural network approach was numerically stable and robust with respect to deviations in the initial conditions or experimental noises.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Nonlinear dynamics and control of multibody systems

The dynamics of flexible systems, such as robot manipulators , mechanical chains or multibody systems in general, is becoming increasingly important in engineering. This article deals with some nonlinearities that arise in the study of dynamics and control of multibody systems in connection to large rotations. Specifically, a numerical scheme that adresses the conservation of fundamental constants is presented in order to analyse the control-structure interaction problems.

Object-oriented Programming Applied to the Development of Structural Analysis and Optimization Software

This paper presents the development of a two-dimensional interactive software environment for structural analysis and optimization based on object-oriented programming using the C++ language. The main feature of the software is the effective integration of several computational tools into graphical user interfaces implemented in the Windows-98 and Windows-NT operating systems. The interfaces simplify data specification in the simulation and optimization of two-dimensional linear elastic problems. NURBS have been used in the software modules to represent geometric and graphical data. Extensions to the analysis of three-dimensional problems have been implemented and are also discussed in this paper.

Covalidation of Integral Transforms and Method of Lines in Nonlinear Convection-Diffusion with Mathematica

The Mathematica system (version 4.0) is employed in the solution of nonlinear difusion and convection-difusion problems, formulated as transient one-dimensional partial diferential equations with potential dependent equation coefficients. The Generalized Integral Transform Technique (GITT) is first implemented for the hybrid numerical-analytical solution of such classes of problems, through the symbolic integral transformation and elimination of the space variable, followed by the utilization of the built-in Mathematica function NDSolve for handling the resulting transformed ODE system. This approach ofers an error-controlled final numerical solution, through the simultaneous control of local errors in this reliable ODE's solver and of the proposed eigenfunction expansion truncation order. For covalidation purposes, the same built-in function NDSolve is employed in the direct solution of these partial diferential equations, as made possible by the algorithms implemented in Mathematica (versions 3.0 and up), based on application of the method of lines. Various numerical experiments are performed and relative merits of each approach are critically pointed out.