Integration of Pasturing Systems for Cattle Finishing Programs

A 3-year study, using 84 fall-born and 28 spring-born calves of similar genotypes, was conducted to integrate pasturing systems with drylot feeding systems. Calves were started on test following weaning in May and October. Seven treatments were imposed: 1) fall-born calves directly into feedlot; 2 and 3) fall-born calves put on pasture with or without ionophore and moved to the feedlot at the end of July; 4 and 5) fall-born calves put on pasture with or without ionophore and moved to the feedlot at the end of October; 6 and 7) spring-born calves put on pasture with or without ionophore and moved to the feedlot at the end of October. A bromegrass pasture consisting of 16 paddocks, each 1.7 acre in size, was available. Each treatment group had access to 1 paddock at a time and was rotated at approximately 3-day intervals. In the feedlot, steers were provided an 82% concentrate diet containing whole-shelled corn, ground alfalfa hay, and a protein, vitamin and mineral supplement containing ionophore and molasses. As pens of cattle reached about 1150 lb. average live weight, they were processed and carcass traits were evaluated. Pasture daily gains were highest for cattle on pasture for the longest duration (P < .03), and overall daily gains were highest for drylot cattle (P < .01) and decreased with increased time spent on pasture. Although differences among treatments existed in numerical scores for yield and quality grades (P < .05 and P < .03, respectively), all treatments provided average yield grade scores of 2 and quality grades of low Choice or higher. Use of four production costs and pricing scenarios revealed that fall-born calves placed on pasture for varying lengths of time were the most profitable (P < .04) among the treatments. Furthermore, employing a 5% price sensitivity analysis, indicated that fed-cattle selling price had great impact on profit potential and was followed in importance by feeder purchase price and corn grain price. Overall, these findings should provide significant production alternatives for some segments of the cattle feeding industry and also lend substantial credence to the concept of sustainable agriculture.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.

Energy-Entropy-Momentum integration of discrete thermo-visco-elastic dynamics.

A novel time integration scheme is presented for the numerical solution of the dynamics of discrete systems consisting of point masses and thermo-visco-elastic springs. Even considering fully coupled constitutive laws for the elements, the obtained solutions strictly preserve the two laws of thermo dynamics and the symmetries of the continuum evolution equations. Moreover, the unconditional control over the energy and the entropy growth have the effect of stabilizing the numerical solution, allowing the use of larger time steps than those suitable for comparable implicit algorithms. Proofs for these claims are provided in the article as well as numerical examples that illustrate the performance of the method.

A robust numerical framework for the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

Mixing Snapshots and Fast Time Integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

Experimental and numerical analysis of reinforced concrete elements subjected to blast loading

El hormigón es uno de los materiales de construcción más empleados en la actualidad debido a sus buenas prestaciones mecánicas, moldeabilidad y economía de obtención, entre otras ventajas. Es bien sabido que tiene una buena resistencia a compresión y una baja resistencia a tracción, por lo que se arma con barras de acero para formar el hormigón armado, material que se ha convertido por méritos propios en la solución constructiva más importante de nuestra época. A pesar de ser un material profusamente utilizado, hay aspectos del comportamiento del hormigón que todavía no son completamente conocidos, como es el caso de su respuesta ante los efectos de una explosión. Este es un campo de especial relevancia, debido a que los eventos, tanto intencionados como accidentales, en los que una estructura se ve sometida a una explosión son, por desgracia, relativamente frecuentes. La solicitación de una estructura ante una explosión se produce por el impacto sobre la misma de la onda de presión generada en la detonación. La aplicación de esta carga sobre la estructura es muy rápida y de muy corta duración. Este tipo de acciones se denominan cargas impulsivas, y pueden ser hasta cuatro órdenes de magnitud más rápidas que las cargas dinámicas impuestas por un terremoto. En consecuencia, no es de extrañar que sus efectos sobre las estructuras y sus materiales sean muy distintos que las que producen las cargas habitualmente consideradas en ingeniería. En la presente tesis doctoral se profundiza en el conocimiento del comportamiento material del hormigón sometido a explosiones. Para ello, es crucial contar con resultados experimentales de estructuras de hormigón sometidas a explosiones. Este tipo de resultados es difícil de encontrar en la literatura científica, ya que estos ensayos han sido tradicionalmente llevados a cabo en el ámbito militar y los resultados obtenidos no son de dominio público. Por otra parte, en las campañas experimentales con explosiones llevadas a cabo por instituciones civiles el elevado coste de acceso a explosivos y a campos de prueba adecuados no permite la realización de ensayos con un elevado número de muestras. Por este motivo, la dispersión experimental no es habitualmente controlada. Sin embargo, en elementos de hormigón armado sometidos a explosiones, la dispersión experimental es muy acusada, en primer lugar, por la propia heterogeneidad del hormigón, y en segundo, por la dificultad inherente a la realización de ensayos con explosiones, por motivos tales como dificultades en las condiciones de contorno, variabilidad del explosivo, o incluso cambios en las condiciones atmosféricas. Para paliar estos inconvenientes, en esta tesis doctoral se ha diseñado un novedoso dispositivo que permite ensayar hasta cuatro losas de hormigón bajo la misma detonación, lo que además de proporcionar un número de muestras estadísticamente representativo, supone un importante ahorro de costes. Con este dispositivo se han ensayado 28 losas de hormigón, tanto armadas como en masa, de dos dosificaciones distintas. Pero además de contar con datos experimentales, también es importante disponer de herramientas de cálculo para el análisis y diseño de estructuras sometidas a explosiones. Aunque existen diversos métodos analíticos, hoy por hoy las técnicas de simulación numérica suponen la alternativa más avanzada y versátil para el cálculo de elementos estructurales sometidos a cargas impulsivas. Sin embargo, para obtener resultados fiables es crucial contar con modelos constitutivos de material que tengan en cuenta los parámetros que gobiernan el comportamiento para el caso de carga en estudio. En este sentido, cabe destacar que la mayoría de los modelos constitutivos desarrollados para el hormigón a altas velocidades de deformación proceden del ámbito balístico, donde dominan las grandes tensiones de compresión en el entorno local de la zona afectada por el impacto. En el caso de los elementos de hormigón sometidos a explosiones, las tensiones de compresión son mucho más moderadas, siendo las tensiones de tracción generalmente las causantes de la rotura del material. En esta tesis doctoral se analiza la validez de algunos de los modelos disponibles, confirmando que los parámetros que gobiernan el fallo de las losas de hormigón armado ante explosiones son la resistencia a tracción y su ablandamiento tras rotura. En base a los resultados anteriores se ha desarrollado un modelo constitutivo para el hormigón ante altas velocidades de deformación, que sólo tiene en cuenta la rotura por tracción. Este modelo parte del de fisura cohesiva embebida con discontinuidad fuerte, desarrollado por Planas y Sancho, que ha demostrado su capacidad en la predicción de la rotura a tracción de elementos de hormigón en masa. El modelo ha sido modificado para su implementación en el programa comercial de integración explícita LS-DYNA, utilizando elementos finitos hexaédricos e incorporando la dependencia de la velocidad de deformación para permitir su utilización en el ámbito dinámico. El modelo es estrictamente local y no requiere de remallado ni conocer previamente la trayectoria de la fisura. Este modelo constitutivo ha sido utilizado para simular dos campañas experimentales, probando la hipótesis de que el fallo de elementos de hormigón ante explosiones está gobernado por el comportamiento a tracción, siendo de especial relevancia el ablandamiento del hormigón. Concrete is nowadays one of the most widely used building materials because of its good mechanical properties, moldability and production economy, among other advantages. As it is known, it has high compressive and low tensile strengths and for this reason it is reinforced with steel bars to form reinforced concrete, a material that has become the most important constructive solution of our time. Despite being such a widely used material, there are some aspects of concrete performance that are not yet fully understood, as it is the case of its response to the effects of an explosion. This is a topic of particular relevance because the events, both intentional and accidental, in which a structure is subjected to an explosion are, unfortunately, relatively common. The loading of a structure due to an explosive event occurs due to the impact of the pressure shock wave generated in the detonation. The application of this load on the structure is very fast and of very short duration. Such actions are called impulsive loads, and can be up to four orders of magnitude faster than the dynamic loads imposed by an earthquake. Consequently, it is not surprising that their effects on structures and materials are very different than those that cause the loads usually considered in engineering. This thesis broadens the knowledge about the material behavior of concrete subjected to explosions. To that end, it is crucial to have experimental results of concrete structures subjected to explosions. These types of results are difficult to find in the scientific literature, as these tests have traditionally been carried out by armies of different countries and the results obtained are classified. Moreover, in experimental campaigns with explosives conducted by civil institutions the high cost of accessing explosives and the lack of proper test fields does not allow for the testing of a large number of samples. For this reason, the experimental scatter is usually not controlled. However, in reinforced concrete elements subjected to explosions the experimental dispersion is very pronounced. First, due to the heterogeneity of concrete, and secondly, because of the difficulty inherent to testing with explosions, for reasons such as difficulties in the boundary conditions, variability of the explosive, or even atmospheric changes. To overcome these drawbacks, in this thesis we have designed a novel device that allows for testing up to four concrete slabs under the same detonation, which apart from providing a statistically representative number of samples, represents a significant saving in costs. A number of 28 slabs were tested using this device. The slabs were both reinforced and plain concrete, and two different concrete mixes were used. Besides having experimental data, it is also important to have computational tools for the analysis and design of structures subjected to explosions. Despite the existence of several analytical methods, numerical simulation techniques nowadays represent the most advanced and versatile alternative for the assessment of structural elements subjected to impulsive loading. However, to obtain reliable results it is crucial to have material constitutive models that take into account the parameters that govern the behavior for the load case under study. In this regard it is noteworthy that most of the developed constitutive models for concrete at high strain rates arise from the ballistic field, dominated by large compressive stresses in the local environment of the area affected by the impact. In the case of concrete elements subjected to an explosion, the compressive stresses are much more moderate, while tensile stresses usually cause material failure. This thesis discusses the validity of some of the available models, confirming that the parameters governing the failure of reinforced concrete slabs subjected to blast are the tensile strength and softening behaviour after failure. Based on these results we have developed a constitutive model for concrete at high strain rates, which only takes into account the ultimate tensile strength. This model is based on the embedded Cohesive Crack Model with Strong Discontinuity Approach developed by Planas and Sancho, which has proved its ability in predicting the tensile fracture of plain concrete elements. The model has been modified for its implementation in the commercial explicit integration program LS-DYNA, using hexahedral finite elements and incorporating the dependence of the strain rate, to allow for its use in dynamic domain. The model is strictly local and does not require remeshing nor prior knowledge of the crack path. This constitutive model has been used to simulate two experimental campaigns, confirming the hypothesis that the failure of concrete elements subjected to explosions is governed by their tensile response, being of particular relevance the softening behavior of concrete.

Improved Integration Methods for P-Adaptive Boundary Element Techniques

Non linear transformations are a good alternative for the numerical evaluation of singular and quasisingular integrals appearing in Boundary Element Method specially in the p-adaptive version. Some aspects of its numerical implementation in 2-D Potential codes is discussed and some examples are shown.

A robust numerical framework to the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

The effect of boundary conditions in the numerical solution of 3-D thermoelastic problems

After the extensive research on the capabilities of the Boundary Integral Equation Method produced during the past years the versatility of its applications has been well founded. Maybe the years to come will see the in-depth analysis of several conflictive points, for example, adaptive integration, solution of the system of equations, etc. This line is clear in academic research. In this paper we comment on the incidence of the manner of imposing the boundary conditions in 3-D coupled problems. Here the effects are particularly magnified: in the first place by the simple model used (constant elements) and secondly by the process of solution, i.e. first a potential problem is solved and then the results are used as data for an elasticity problem. The errors add to both processes and small disturbances, unimportant in separated problems, can produce serious errors in the final results. The specific problem we have chosen is especially interesting. Although more general cases (i.e. transient)can be treated, here the domain integrals can be converted into boundary ones and the influence of the manner in which boundary conditions are applied will reflect the whole importance of the problem.

Energy-consistent time integration for nonlinear viscoelasticity

This work is concerned with the numerical solution of the evolution equations of thermomechanical systems, in such a way that the scheme itself satisfies the laws of thermodynamics. Within this framework, we present a novel integration scheme for the dynamics of viscoelastic continuum bodies in isothermal conditions. This method intrinsically satisfies the laws of thermodynamics arising from the continuum, as well as the possible additional symmetries. The resulting solutions are physically accurate since they preserve the fundamental physical properties of the model. Furthermore, the method gives an excellent performance with respect to robustness and stability. Proof for these claims as well as numerical examples that illustrate the performance of the novel scheme are provided

A temperature-based thermodynamically consistent integration scheme for discrete thermo-elastodynamics

The formulation of thermodynamically consistent (TC) time integration methods was introduced by a general procedure based on the GENERIC form of the evolution equations for thermo-mechanical problems. The use of the entropy was reported to be the best choice for the thermodynamical variable to easily provide TC integrators. Also the employment of the internal energy was proved to not involve excessive complications. However, attempts towards the use of the temperature in the design of GENERIC-based TC schemes have so far been unfruitful. This paper complements the said procedure to attain TC integrators by presenting a TC scheme based on the temperature as thermodynamical state variable. As a result, the problems which arise due to the use of the entropy are overcome, mainly the definition of boundary conditions. What is more, the newly proposed method exhibits the general enhanced numerical stability and robustness properties of the entropy formulation.

Energy-entropy-momentum time integration methods for coupled smooth dissipative problems

Esta tesis aborda la formulación, análisis e implementación de métodos numéricos de integración temporal para la solución de sistemas disipativos suaves de dimensión finita o infinita de manera que su estructura continua sea conservada. Se entiende por dichos sistemas aquellos que involucran acoplamiento termo-mecánico y/o efectos disipativos internos modelados por variables internas que siguen leyes continuas, de modo que su evolución es considerada suave. La dinámica de estos sistemas está gobernada por las leyes de la termodinámica y simetrías, las cuales constituyen la estructura que se pretende conservar de forma discreta. Para ello, los sistemas disipativos se describen geométricamente mediante estructuras metriplécticas que identifican claramente las partes reversible e irreversible de la evolución del sistema. Así, usando una de estas estructuras conocida por las siglas (en inglés) de GENERIC, la estructura disipativa de los sistemas es identificada del mismo modo que lo es la Hamiltoniana para sistemas conservativos. Con esto, métodos (EEM) con precisión de segundo orden que conservan la energía, producen entropía y conservan los impulsos lineal y angular son formulados mediante el uso del operador derivada discreta introducido para asegurar la conservación de la Hamiltoniana y las simetrías de sistemas conservativos. Siguiendo estas directrices, se formulan dos tipos de métodos EEM basados en el uso de la temperatura o de la entropía como variable de estado termodinámica, lo que presenta importantes implicaciones que se discuten a lo largo de esta tesis. Entre las cuales cabe destacar que las condiciones de contorno de Dirichlet son naturalmente impuestas con la formulación basada en la temperatura. Por último, se validan dichos métodos y se comprueban sus mejores prestaciones en términos de la estabilidad y robustez en comparación con métodos estándar. This dissertation is concerned with the formulation, analysis and implementation of structure-preserving time integration methods for the solution of the initial(-boundary) value problems describing the dynamics of smooth dissipative systems, either finite- or infinite-dimensional ones. Such systems are understood as those involving thermo-mechanical coupling and/or internal dissipative effects modeled by internal state variables considered to be smooth in the sense that their evolutions follow continuos laws. The dynamics of such systems are ruled by the laws of thermodynamics and symmetries which constitutes the structure meant to be preserved in the numerical setting. For that, dissipative systems are geometrically described by metriplectic structures which clearly identify the reversible and irreversible parts of their dynamical evolution. In particular, the framework known by the acronym GENERIC is used to reveal the systems' dissipative structure in the same way as the Hamiltonian is for conserving systems. Given that, energy-preserving, entropy-producing and momentum-preserving (EEM) second-order accurate methods are formulated using the discrete derivative operator that enabled the formulation of Energy-Momentum methods ensuring the preservation of the Hamiltonian and symmetries for conservative systems. Following these guidelines, two kind of EEM methods are formulated in terms of entropy and temperature as a thermodynamical state variable, involving important implications discussed throughout the dissertation. Remarkably, the formulation in temperature becomes central to accommodate Dirichlet boundary conditions. EEM methods are finally validated and proved to exhibit enhanced numerical stability and robustness properties compared to standard ones.

Integration of modular process simulators under the Generalized Disjunctive Programming framework for the structural flowsheet optimization

The optimization of chemical processes where the flowsheet topology is not kept fixed is a challenging discrete-continuous optimization problem. Usually, this task has been performed through equation based models. This approach presents several problems, as tedious and complicated component properties estimation or the handling of huge problems (with thousands of equations and variables). We propose a GDP approach as an alternative to the MINLP models coupled with a flowsheet program. The novelty of this approach relies on using a commercial modular process simulator where the superstructure is drawn directly on the graphical use interface of the simulator. This methodology takes advantage of modular process simulators (specially tailored numerical methods, reliability, and robustness) and the flexibility of the GDP formulation for the modeling and solution. The optimization tool proposed is successfully applied to the synthesis of a methanol plant where different alternatives are available for the streams, equipment and process conditions.

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.

Accurate integration of forced and damped oscillators

The new methods accurately integrate forced and damped oscillators. A family of analytical functions is introduced known as T-functions which are dependent on three parameters. The solution is expressed as a series of T-functions calculating their coefficients by means of recurrences which involve the perturbation function. In the T-functions series method the perturbation parameter is the factor in the local truncation error. Furthermore, this method is zero-stable and convergent. An application of this method is exposed to resolve a physic IVP, modeled by means of forced and damped oscillators. The good behavior and precision of the methods, is evidenced by contrasting the results with other-reputed algorithms implemented in MAPLE.