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.

Simulating maize phenology as a function of air temperature with a linear and a nonlinear model

The objective of this study was to adapt a nonlinear model (Wang and Engel - WE) for simulating the phenology of maize (Zea mays L.), and to evaluate this model and a linear one (thermal time), in order to predict developmental stages of a field-grown maize variety. A field experiment, during 2005/2006 and 2006/2007 was conducted in Santa Maria, RS, Brazil, in two growing seasons, with seven sowing dates each. Dates of emergence, silking, and physiological maturity of the maize variety BRS Missões were recorded in six replications in each sowing date. Data collected in 2005/2006 growing season were used to estimate the coefficients of the two models, and data collected in the 2006/2007 growing season were used as independent data set for model evaluations. The nonlinear WE model accurately predicted the date of silking and physiological maturity, and had a lower root mean square error (RMSE) than the linear (thermal time) model. The overall RMSE for silking and physiological maturity was 2.7 and 4.8 days with WE model, and 5.6 and 8.3 days with thermal time model, respectively.

Improving node number simulation in soybean

The objective of this study was to improve the simulation of node number in soybean cultivars with determinate stem habits. A nonlinear model considering two approaches to input daily air temperature data (daily mean temperature and daily minimum/maximum air temperatures) was used. The node number on the main stem data of ten soybean cultivars was collected in a three-year field experiment (from 2004/2005 to 2006/2007) at Santa Maria, RS, Brazil. Node number was simulated using the Soydev model, which has a nonlinear temperature response function [f(T)]. The f(T) was calculated using two methods: using daily mean air temperature calculated as the arithmetic average among daily minimum and maximum air temperatures (Soydev tmean); and calculating an f(T) using minimum air temperature and other using maximum air temperature and then averaging the two f(T)s (Soydev tmm). Root mean square error (RMSE) and deviations (simulated minus observed) were used as statistics to evaluate the performance of the two versions of Soydev. Simulations of node number in soybean were better with the Soydev tmm version, with a 0.5 to 1.4 node RMSE. Node number can be simulated for several soybean cultivars using only one set of model coefficients, with a 0.8 to 2.4 node RMSE.

Stability and adaptability of runner peanut genotypes based on nonlinear regression and AMMI analysis

The objective of this work was to estimate the stability and adaptability of pod and seed yield in runner peanut genotypes based on the nonlinear regression and AMMI analysis. Yield data from 11 trials, distributed in six environments and three harvests, carried out in the Northeast region of Brazil during the rainy season were used. Significant effects of genotypes (G), environments (E), and GE interactions were detected in the analysis, indicating different behaviors among genotypes in favorable and unfavorable environmental conditions. The genotypes BRS Pérola Branca and LViPE‑06 are more stable and adapted to the semiarid environment, whereas LGoPE‑06 is a promising material for pod production, despite being highly dependent on favorable environments.

Photomultiplier nonlinear response in time-domain laser-induced luminescence spectroscopy

A new procedure to find the limiting range of the photomultiplier linear response of a low-cost, digital oscilloscope-based time-resolved laser-induced luminescence spectrometer (TRLS), is presented. A systematic investigation on the instrument response function with different signal input terminations, and the relationship between the luminescence intensity reaching the photomultiplier and the measured decay time are described. These investigations establish that setting the maximum intensity of the luminescence signal below 0.3V guarantees, for signal input terminations equal or higher than 99.7 ohm, a linear photomultiplier response.

Simulação de espectros de ressonância paramagnética eletrônica (RPE) através do programa NLSL

EPR users often face the problem of extracting information from frequently low-resolution and complex EPR spectra. Simulation programs that provide a series of parameters, characteristic of the investigated system, have been used to achieve this goal. This work describes the general aspects of one of those programs, the NLSL program, used to fit EPR spectra applying a nonlinear least squares method. Several motion regimes of the probes are included in this computational tool, covering a broad range of spectral changes. The meanings of the different parameters and rotational diffusion models are discussed. The anisotropic case is also treated by including an orienting potential and order parameters. Some examples are presented in order to show its applicability in different systems.

Geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral finite elements with reduced integration

This work presents a geometric nonlinear dynamic analysis of plates and shells using eight-node hexahedral isoparametric elements. The main features of the present formulation are: (a) the element matrices are obtained using reduced integrations with hourglass control; (b) an explicit Taylor-Galerkin scheme is used to carry out the dynamic analysis, solving the corresponding equations of motion in terms of velocity components; (c) the Truesdell stress rate tensor is used; (d) the vector processor facilities existing in modern supercomputers were used. The results obtained are comparable with previous solutions in terms of accuracy and computational performance.

On the development of an unstructured grid solver for inert and reactive high speed flow simulations

An unstructured grid Euler solver for reactive compressible flow applications is presented. The method is implemented in a cell centered, finite volume context for unstructured triangular grids. Three different schemes for spatial discretization are implemented and analyzed. Time march is implemented in a time-split fashion with independent integrators for the flow and chemistry equations. The capability implemented is tested for inert flows in a hypersonic inlet and for inert and reactive supersonic flows over a 2-D wedge. The results of the different schemes are compared with each other and with independent calculations using a structured grid code. The strengths and the possible weaknesses of the proposed methods are discussed.

Multiple scales analysis of nonlinear oscillations of a portal frame foundation for several machines

An analytical study of the nonlinear vibrations of a multiple machines portal frame foundation is presented. Two unbalanced rotating machines are considered, none of them resonant with the lower natural frequencies of the supporting structure. Their combined frequencies is set in such a way as to excite, due to nonlinear behavior of the frame, either the first anti-symmetrical mode (sway) or the first symmetrical mode. The physical and geometrical characteristics of the frame are chosen to tune the natural frequencies of these two modes into a 1:2 internal resonance. The problem is reduced to a two degrees of freedom model and its nonlinear equations of motions are derived via a Lagrangian approach. Asymptotic perturbation solutions of these equations are obtained via the Multiple Scales Method.

Dynamics of coherent vortices in mixing layers using direct numerical and large-eddy simulations

Coherent vortices in turbulent mixing layers are investigated by means of Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). Subgrid-scale models defined in spectral and physical spaces are reviewed. The new "spectral-dynamic viscosity model", that allows to account for non-developed turbulence in the subgrid-scales, is discussed. Pseudo-spectral methods, combined with sixth-order compact finite differences schemes (when periodic boundary conditions cannot be established), are used to solve the Navier- Stokes equations. Simulations in temporal and spatial mixing layers show two types of pairing of primary Kelvin-Helmholtz (KH) vortices depending on initial conditions (or upstream conditions): quasi-2D and helical pairings. In both cases, secondary streamwise vortices are stretched in between the KH vortices at an angle of 45° with the horizontal plane. These streamwise vortices are not only identified in the early transitional stage of the mixing layer but also in self-similar turbulence conditions. The Re dependence of the "diameter" of these vortices is analyzed. Results obtained in spatial growing mixing layers show some evidences of pairing of secondary vortices; after a pairing of the primary Kelvin-Helmholtz (KH) vortices, the streamwise vortices are less numerous and their diameter has increased than before the pairing of KH vortices.

Effect of wave frequency on the nonlinear interaction between Görtler vortices and three-dimensional Tollmien-Schlichting waves

The nonlinear interaction between Görtler vortices (GV) and three-dimensional Tollmien-Schlichting (TS) waves nonlinear interaction is studied with a spatial, nonparallel model based on the Parabolized Stability Equations (PSE). In this investigation the effect of TS wave frequency on the nonlinear interaction is studied. As verified in previous investigations using the same numerical model, the relative amplitudes and growth rates are the dominant parameters in GV/TS wave interaction. In this sense, the wave frequency influence is important in defining the streamwise distance traveled by the disturbances in the unstable region of the stability diagram and in defining the amplification rates that they go through.

Development of a three-dimensional nonlinear viscoelastic constitutive model of solid propellant

A three dimensional nonlinear viscoelastic constitutive model for the solid propellant is developed. In their earlier work, the authors have developed an isotropic constitutive model and verified it for one dimensional case. In the present work, the validity of the model is extended to three-dimensional cases. Large deformation, dewetting and cyclic loading effects are treated as the main sources of nonlinear behavior of the solid propellant. Viscoelastic dewetting criteria is used and the softening of the solid propellant due to dewetting is treated by the modulus decrease. The nonlinearities during cyclic loading are accounted for by the functions of the octahedral shear strain measure. The constitutive equation is implemented into a finite element code for the analysis of propellant grains. A commercial finite element package ‘ABAQUS’ is used for the analysis and the model is introduced into the code through a user subroutine. The model is evaluated with different loading conditions and the predicted values are in good agreement with the measured ones. The resulting model applied to analyze a solid propellant grain for the thermal cycling load.

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.

A frequency-domain pseudo-force method for dynamic structural analysis nonlinear systems and nonproportional damping

A frequency-domain method for nonlinear analysis of structural systems with viscous, hysteretic, nonproportional and frequency-dependent damping is presented. The nonlinear effects and nonproportional damping are considered through pseudo-force terms. The modal coordinates uncoupled equations are iteratively solved. The treatment of initial conditions in the frequency domain which is necessary for the treatment of the uncoupled equations is initially adressed.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.