Non-linear analysis of laminated metal matrix composites by an integrated micro/macro-mechanical model

The present paper describes an integrated micro/macro mechanical study of the elastic-viscoplastic behavior of unidirectional metal matrix composites (MMC). The micromechanical analysis of the elastic moduli is based on the Composites Cylinder Assemblage model (CCA) with comparisons also draw with a Representative Unit Cell (RUC) technique. These "homogenization" techniques are later incorporated into the Vanishing Fiber Diameter (VFD) model and a new formulation is proposed. The concept of a smeared element procedure is employed in conjunction with two different versions of the Bodner and Partom elastic-viscoplastic constitutive model for the associated macroscopic analysis. The formulations developed are also compared against experimental and analytical results available in the literature.

Numerical study of Petrov-Galerkin formulations for the shallow water wave equations

The behavior of Petrov-Galerkin formulations for shallow water wave equations is evaluated numerically considering typical one-dimensional propagation problems. The formulations considered here use stabilizing operators to improve classical Galerkin approaches. Their advantages and disadvantages are pointed out according to the intrinsic time scale (free parameter) which has a particular importance in this kind of problem. The influence of the Courant number and the performance of the formulation in dealing with spurious oscillations are adressed.

Heat Source Estimation with the Conjugate Gradient Method in Inverse Linear Diffusive Problems

In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms, with no prior information of the functional forms of timewise and spatial dependence of the source strength, using the conjugate gradient method with an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems: a one-dimensional cylindrical problem; a two-dimensional cylindrical problem; and a one-dimensional problem with two plates.

Non-Linear Unsteady Aerodynamic Response Approximation Using Multi-Layer Functionals

Non-linear functional representation of the aerodynamic response provides a convenient mathematical model for motion-induced unsteady transonic aerodynamic loads response, that accounts for both complex non-linearities and time-history effects. A recent development, based on functional approximation theory, has established a novel functional form; namely, the multi-layer functional. For a large class of non-linear dynamic systems, such multi-layer functional representations can be realised via finite impulse response (FIR) neural networks. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process in which a limited sample of system input-output data sets is presented to the temporal neural network. The present work describes a procedure for the systematic identification of parameterised neural network models of motion-induced unsteady transonic aerodynamic loads response. The training process is based on a conventional genetic algorithm to optimise the network architecture, combined with a simplified random search algorithm to update weight and bias values. Application of the scheme to representative transonic aerodynamic loads response data for a bidimensional airfoil executing finite-amplitude motion in transonic flow is used to demonstrate the feasibility of the approach. The approach is shown to furnish a satisfactory generalisation property to different motion histories over a range of Mach numbers in the transonic regime.

Control of Structures with Cubic and Quadratic Non-Linearities with Time Delay Consideration

This paper studies the effect of time delay on the active non-linear control of dynamically loaded flexible structures. The behavior of non-linear systems under state feedback control, considering a fixed time delay for the control force, is investigated. A control method based on non-linear optimal control, using a tensorial formulation and state feedback control is used. The state equations and the control forces are expressed in polynomial form and a performance index, quadratic in both state vector and control forces, is used. General polynomial representations of the non-linear control law are obtained and implemented for control algorithms up to the fifth order. This methodology is applied to systems with quadratic and cubic non-linearities. Strongly non-linear systems are tested and the effectiveness of the control system including a delay for the application of control forces is discussed. Numerical results indicate that the adopted control algorithm can be efficient for non-linear systems, chiefly in the presence of strong non-linearities but increasing time delay reduces the efficiency of the control system. Numerical results emphasize the importance of considering time delay in the project of active structural control systems.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

Substitution-Newton-Raphson method applied to the modeling of a vapour compression refrigeration system using different representations of the thermodynamic properties of R-134a

This paper gives a detailed presentation of the Substitution-Newton-Raphson method, suitable for large sparse non-linear systems. It combines the Successive Substitution method and the Newton-Raphson method in such way as to take the best advantages of both, keeping the convergence features of the Newton-Raphson with the low requirements of memory and time of the Successive Substitution schemes. The large system is solved employing few effective variables, using the greatest possible part of the model equations in substitution fashion to fix the remaining variables, but maintaining the convergence characteristics of the Newton-Raphson. The methodology is exemplified through a simple algebraic system, and applied to a simple thermodynamic, mechanical and heat transfer modeling of a single-stage vapor compression refrigeration system. Three distinct approaches for reproducing the thermodynamic properties of the refrigerant R-134a are compared: the linear interpolation from tabulated data, the use of polynomial fitted curves and the use of functions derived from the Helmholtz free energy.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Combinatorics on Words. New Aspects on Avoidability, Defect Effect, Equations and Palindromes

In this thesis we examine four well-known and traditional concepts of combinatorics on words. However the contexts in which these topics are treated are not the traditional ones. More precisely, the question of avoidability is asked, for example, in terms of k-abelian squares. Two words are said to be k-abelian equivalent if they have the same number of occurrences of each factor up to length k. Consequently, k-abelian equivalence can be seen as a sharpening of abelian equivalence. This fairly new concept is discussed broader than the other topics of this thesis. The second main subject concerns the defect property. The defect theorem is a well-known result for words. We will analyze the property, for example, among the sets of 2-dimensional words, i.e., polyominoes composed of labelled unit squares. From the defect effect we move to equations. We will use a special way to define a product operation for words and then solve a few basic equations over constructed partial semigroup. We will also consider the satisfiability question and the compactness property with respect to this kind of equations. The final topic of the thesis deals with palindromes. Some finite words, including all binary words, are uniquely determined up to word isomorphism by the position and length of some of its palindromic factors. The famous Thue-Morse word has the property that for each positive integer n, there exists a factor which cannot be generated by fewer than n palindromes. We prove that in general, every non ultimately periodic word contains a factor which cannot be generated by fewer than 3 palindromes, and we obtain a classification of those binary words each of whose factors are generated by at most 3 palindromes. Surprisingly these words are related to another much studied set of words, Sturmian words.

Linear prediction in optical spectroscopy

A linear prediction procedure is one of the approved numerical methods of signal processing. In the field of optical spectroscopy it is used mainly for extrapolation known parts of an optical signal in order to obtain a longer one or deduce missing signal samples. The first is needed particularly when narrowing spectral lines for the purpose of spectral information extraction. In the present paper the coherent anti-Stokes Raman scattering (CARS) spectra were under investigation. The spectra were significantly distorted by the presence of nonlinear nonresonant background. In addition, line shapes were far from Gaussian/Lorentz profiles. To overcome these disadvantages the maximum entropy method (MEM) for phase spectrum retrieval was used. The obtained broad MEM spectra were further underwent the linear prediction analysis in order to be narrowed.

Biomass and mineralmass estimates in a "cerrado" ecosystem

This work aimed to develop allometric equations for tree biomass estimation, and to determine the site biomass in different "cerrado" ecosystems. Destructive sampling in a "campo cerrado" (open savanna) was carried out at the Biological Reserve of Moji-Guaçu, State of São Paulo, southeastern Brazil. This "campo cerrado" (open savanna) grows under a tropical climate and on acid, low nutrient soils. Sixty wood plants were cut to ground level and measurements of diameter, height and weight of leaves and stems were taken. We selected the best equations among the most commonly used mathematical relations according to R² values, significance, and standard error. Both diameter (D) and height (H) showed good relationship with plant biomass, but the use of these two parameters together (DH and D²H) provided the best predictor variables. The best equations were linear, but power and exponential equations also showed high R² and significance. The applicability of these equations is discussed and biomass estimates are compared with other types of tropical savannas. Mineralmass was also estimated. "Cerrados" proved to have very important carbon reservoirs due to their great extent. In addition, high land-use change that takes place nowadays in the "cerrado" biome may significantly affect the global carbon cycle.

Using the best linear predictor (BLP) in the selection between and among half-sib progenies of the CMS-39 maize population

Data of corn ear production (kg/ha) of 196 half-sib progenies (HSP) of the maize population CMS-39 obtained from experiments carried out in four environments were used to adapt and assess the BLP method (best linear predictor) in comparison with to the selection among and within half-sib progenies (SAWHSP). The 196 HSP of the CMS-39 population developed by the National Center for Maize and Sorghum Research (CNPMS-EMBRAPA) were related through their pedigree with the recombined progenies of the previous selection cycle. The two methodologies used for the selection of the twenty best half-sib progenies, BLP and SAWHSP, led to similar expected genetic gains. There was a tendency in the BLP methodology to select a greater number of related progenies because of the previous generation (pedigree) than the other method. This implies that greater care with the effective size of the population must be taken with this method. The SAWHSP methodology was efficient in isolating the additive genetic variance component from the phenotypic component. The pedigree system, although unnecessary for the routine use of the SAWHSP methodology, allowed the prediction of an increase in the inbreeding of the population in the long term SAWHSP selection when recombination is simultaneous to creation of new progenies.

Reference values for lung function tests: I. Static volumes

Static lung volume (LV) measurements have a number of clinical and research applications; however, no previous studies have provided reference values for such tests using a healthy sample of the adult Brazilian population. With this as our main purpose, we prospectively evaluated 100 non-smoking subjects (50 males and 50 females), 20 to 80 years old, randomly selected from more than 8,000 individuals. Gender-specific linear prediction equations were developed by multiple regression analysis with total lung capacity (TLC), functional residual capacity (FRC), residual volume (RV), RV/TLC ratio and inspiratory capacity (IC) as dependent variables, and with age, height, weight, lean body mass and indexes of physical fitness as independent ones. Simpler demographic and anthropometric variables were as useful as more complex measurements in predicting LV values, independent of gender and age (R2 values ranging from 0.49 to 0.78, P<0.001). Interestingly, prediction equations from North American and European studies overestimated the LV at low volumes and underestimated them at high volumes (P<0.05). Our results, therefore, provide a more appropriate frame of reference to evaluate the normalcy of static lung volume values in Brazilian males and females aged 20 to 80 years.

Reference values for lung function tests: II. Maximal respiratory pressures and voluntary ventilation

The strength of the respiratory muscles can be evaluated from static measurements (maximal inspiratory and expiratory pressures, MIP and MEP) or inferred from dynamic maneuvers (maximal voluntary ventilation, MVV). Although these data could be suitable for a number of clinical and research applications, no previous studies have provided reference values for such tests using a healthy, randomly selected sample of the adult Brazilian population. With this main purpose, we prospectively evaluated 100 non-smoking subjects (50 males and 50 females), 20 to 80 years old, selected from more than 8,000 individuals. Gender-specific linear prediction equations for MIP, MEP and MVV were developed by multiple regression analysis: age and, secondarily, anthropometric measurements explained up to 56% of the variability of the dependent variables. The most cited previous studies using either Caucasian or non-Caucasian samples systematically underestimated the observed values of MIP (P<0.05). Interestingly, the self-reported level of regular physical activity and maximum aerobic power correlates strongly with both respiratory and peripheral muscular strength (knee extensor peak torque) (P<0.01). Our results, therefore, provide a new frame of reference to evaluate the normalcy of some useful indexes of respiratory muscle strength in Brazilian males and females aged 20 to 80.