OpenMx: A Modular Research Environment for Item Response Theory Method Development:

The research activity described in this thesis is focused mainly on the study of finite-element techniques applied to thermo-fluid dynamic problems of plant components and on the study of dynamic simulation techniques applied to integrated building design in order to enhance the energy performance of the building. The first part of this doctorate thesis is a broad dissertation on second law analysis of thermodynamic processes with the purpose of including the issue of the energy efficiency of buildings within a wider cultural context which is usually not considered by professionals in the energy sector. In particular, the first chapter includes, a rigorous scheme for the deduction of the expressions for molar exergy and molar flow exergy of pure chemical fuels. The study shows that molar exergy and molar flow exergy coincide when the temperature and pressure of the fuel are equal to those of the environment in which the combustion reaction takes place. A simple method to determine the Gibbs free energy for non-standard values of the temperature and pressure of the environment is then clarified. For hydrogen, carbon dioxide, and several hydrocarbons, the dependence of the molar exergy on the temperature and relative humidity of the environment is reported, together with an evaluation of molar exergy and molar flow exergy when the temperature and pressure of the fuel are different from those of the environment. As an application of second law analysis, a comparison of the thermodynamic efficiency of a condensing boiler and of a heat pump is also reported. The second chapter presents a study of borehole heat exchangers, that is, a polyethylene piping network buried in the soil which allows a ground-coupled heat pump to exchange heat with the ground. After a brief overview of low-enthalpy geothermal plants, an apparatus designed and assembled by the author to carry out thermal response tests is presented. Data obtained by means of in situ thermal response tests are reported and evaluated by means of a finite-element simulation method, implemented through the software package COMSOL Multyphysics. The simulation method allows the determination of the precise value of the effective thermal properties of the ground and of the grout, which are essential for the design of borehole heat exchangers. In addition to the study of a single plant component, namely the borehole heat exchanger, in the third chapter is presented a thorough process for the plant design of a zero carbon building complex. The plant is composed of: 1) a ground-coupled heat pump system for space heating and cooling, with electricity supplied by photovoltaic solar collectors; 2) air dehumidifiers; 3) thermal solar collectors to match 70% of domestic hot water energy use, and a wood pellet boiler for the remaining domestic hot water energy use and for exceptional winter peaks. This chapter includes the design methodology adopted: 1) dynamic simulation of the building complex with the software package TRNSYS for evaluating the energy requirements of the building complex; 2) ground-coupled heat pumps modelled by means of TRNSYS; and 3) evaluation of the total length of the borehole heat exchanger by an iterative method developed by the author. An economic feasibility and an exergy analysis of the proposed plant, compared with two other plants, are reported. The exergy analysis was performed by considering the embodied energy of the components of each plant and the exergy loss during the functioning of the plants.

Real challenges to suppress undesirable fluid-excited acoustics are posed by a wide variety of engineering disciplines. Noise regulations, passenger comfort and component stability are motivators which are continuing to stimulate substantial efforts towards the understanding of aeroacoustic phenomena, and not least to quantify the usability (practicability and value) of traditional and advanced prediction methods. The latter is the primary focus of this thesis, particularly as applied to the transportation industries, aerospace, automotive and rail. Nowadays Computational Fluid Dynamics (CFD) is a tool well integrated into the industrial development and production life-cycles. This is possible now because of two main factors: the increase in the performance of relatively cheap personal computers and network facilities, and the progress made in general purpose CFD software between modeling complexity and practicability within the industrial environment. While CFD methodologies are well established for lots of applications such as aerodynamics, heat exchange, etc., aeroacoustic CFD simulations still represent a challenge, in particular their industrial practicability. In these years this has given rise to heavy investments by the automotive industry in international aeroacoustics consortia, whereby all the major car companies work together to study the limitations and advantages of aeroacoustics CFD. The general aim of these consortia is to develop methodologies which fit into, and improve upon, current design processes. The goal of the present work is to explore the multitude of different CFD modeling approaches for some typical industrial problems such as: cavity noise, vortex shedding noise, propeller and jet noise. Each of these problems has a particular mechanism for noise generation and different methods have been studied and tested, in order to develop and optimize a practical methodology for the analysis of each problem type. Furthermore each of the aeroacoustics problems considered are representative of a variety of industrial applications. Cavity noise is at the origin of phenomena such as sun-roof buffeting in convertibles or door-gap tonal noise. Vortex shedding noise is typical of any flows involving bluff bodies such as automobile antennas or aircraft landing gear. Propeller noise is typical to applications involving rotating machinery, such as fans, pumps and turbines. Different approaches ranging from steady and transient RANS simulations with the acoustic analogy (including porous and solid surface formulations), to Computational Aero Acoustics (CAA) and Large Eddy Simulation (LES) type computations have been studied and applied. Classic theories already exist to predict aerodynamically generated noise, which are both computationally and economically less expensive than CFD methods. However aeroacoustics CFD is the future, beginning as a promising present, for the following reasons:  Industries are interested in modeling complex geometries.  Many classic theories can be applied successfully but very often restrictions exist with respect to the configuration and flow conditions. For example, classic propeller theories cannot be used to model real-world configurations such as a propeller installed on a wing with some prescribed yaw or angle of attack.  The progress of all other Computer Aided Design and Engineering tools, such as linear or non-linear structural codes, are driving design towards a virtual multi-physics approach for the simulation of complex geometries. Due to previous experience and the wide availability of modeling options, it was decided to use the general purpose CFD software package ANSYS FLUENT for CFD investigations in this study.

Stephen J. Hartley Oxford University Press, New York, 1998, 260 pp. ISBN 0-19-511315-2, $45.00 Concurrent Programming is a thorough treatment of Java multi-threaded programming for both a stand-alone and distributed environment. Designed mostly for students in concurrent or parallel programming classes, the text is also an excellent reference for the practicing professional developing multi-threaded programs or applets. Hartley first provides a complete explanation of the features of Java necessary to write concurrent programs, including topics such as exception handling, interfaces, and packages. He then gives the reader a solid background to write multi-threaded programs and also presents the problems introduced when writing concurrent programs—namely race conditions, mutual exclusion, and deadlock. Hartley also provides several software solutions that do not require the use of common process and thread mechanisms. Once the groundwork is laid for writing concurrent programs, Hartley then takes a different approach than most Java references. Rather than presenting how Java handles mutual exclusion with the synchronized keyword (although it is covered later), he first looks at semaphore-based solutions to classic concurrent problems such as bounded-buffer, readers-writers, and the dining philosophers. Hartley also uses the same approach to develop Java classes for monitors and message passing. This unique approach to introducing concurrency allows the readers to both understand how Java threads are synchronized and how the basic synchronization mechanism can be used to construct more abstract tools such as semaphores. If there is a shortcoming with the text it is with the lack of sufficient coverage of remote method invocation (RMI), although there is a section covering RMI. This is quite understandable as RMI is a fairly recent phenomenon with the Java community. Also, the classes that Hartley provides could easily implement RMI rather than sockets to handle communication. The strengths of the book include its ease in reading, several examples at the end of chapters, a package similar to Xtango that provides algorithm animation, and a supportive web site by the author (see www.mcs.drexel.edu/~shartley/ConcProgJava/index.html ) including compressed source code. As Java becomes more dominant on the server side of multi-tier applications, writing thread-safe concurrent applications becomes even more important. Concurrent Programming is a strong step towards teaching students and professionals such skills. Greg Gagne, Westminster College of Salt Lake City Salt Lake City, Utah

Hybrid Wafer-Level Packaging for RF-MEMS and Optoelectronic Applications

According to the recent development of the Computational Mechanics, the future development and competitive ability of finite element analysis software seems to be related with the implementation of complicated physical, mechanical and geometric models of solids and fluids. These are coupled models, problems that include physical and geometric nonlinearities, the models or boundary-value problems with small physical or geometric parameters. Thin-walled solids, deformation with large strains and shape distortions, problems coupling solids and fluids supply well- known examples. The modeling of composite materials is another and quite important example nowadays. It begins with solving so- called cell problems and leads to modeling deforming and damaging of composite structural elements as well as to technological problems simulation. The latter type of problems is the problem of a resin with short fibers flow into a mold of complex shape. Another example concerns the process of a resin with long fibers polymerization in a mold followed by the problem of laminate warping. Porous ground and fractured rock are not composites in the commonly used meaning of the term. However, Compositional Mechanics methods are used for their analysis. It is reasonable to mention rather complicated problem of fluid filtration in a porous media experiencing large strains. It seems that a multi scale approach is the most general technique of composite mechanics. It results in so-called local problems in the representative volume element. This paper shows finite-element implementations of local problems developed by the author. Mechanical models and computational algorithms were implemented as home-made computer code. The code has been thoroughly tested and can be used together with FIDESES finite element analysis software as third party package. I may be noted that the developed numerical simulations were elaborated during long term cooperation with the Technical University of Berlin, Dr. Mirtsch GmbH and famous French tire maker Michelin. Further development of the package can be associated with the use of a multi scale approach aiming composite structural elements deformation and progressive damaging modeling, resin with short fibers flow simulation as well as numerical simulation of laminate production process.

We have developed a new derivative-free algorithm based on Radial Basis Functions (RBFs). Derivative-free optimization is an active field of research and several algorithms have been proposed recently. Problems of this nature in the industrial setting are quite frequent. The reason is that in a number of applications the optimization process contains simulation packages which are treated as black boxes. The development of our own algorithm was originally motivated by an application in biomedical imaging: the medical image registration problem. The particular characteristics of this problem have incited us to develop a new optimization algorithm based on trust-region methods. However it has been designed to be generic and to be applied to a wide range of problems. The main originality of our approach is the use of RBFs to build the models. In particular we have adapted the existing theory based on quadratic models to our own models and developed new procedures especially designed for models based on RBFs. We have tested our algorithm called BOOSTERS against state-of-the-art methods (UOBYQA, NEWUOA, DFO). On the medical image registration problem, BOOSTERS appears to be the method of choice. The tests on problems from the CUTEr collection show that BOOSTERS is comparable to, but not better than other methods on small problems (size 2-20). It is performing very well for medium size problems (20-80). Moreover, it is able to solve problems of dimension 200, which is considered very large in derivative-free optimization. We have also developed a new class of algorithms combining the robustness of derivative-free algorithms with the faster rate of convergence characterizing Newtonlike-methods. In fact, they define a new class of algorithms lying between derivative-free optimization and quasi-Newton methods. These algorithms are built on the skeleton of our derivative-free algorithm but they can incorporate the gradient when it is available. They can be interpreted as a way of doping derivative-free algorithms with derivatives. If the derivatives are available at each iteration, then our method can be seen as an alternative to quasi-Newton methods. At the opposite, if the derivatives are never evaluated, then the algorithm is totally similar to BOOSTERS. It is a very interesting alternative to existing methods for problems whose objective function is expensive to evaluate and when the derivatives are not available. In this situation, the gradient can be approximated by finite differences and its costs corresponds to n additional function evaluations assuming that Rn is the domain of definition of the objective function. We have compared our method with CFSQP and BTRA, two gradient-based algorithms, and the results show that our doped method performs best. We have also a theoretical analysis of the medical image registration problem based on maximization of mutual information. Most of the current research in this field is concentrated on registration based on nonlinear image transformation. However, little attention has been paid to the theoretical properties of the optimization problem. In our analysis, we focus on the continuity and the differentiability of the objective function. We show in particular that performing a registration without extension of the reference image may lead to discontinuities in the objective function. But we demonstrate that, under some mild assumptions, the function is differentiable almost everywhere. Our analysis is important from an optimization point of view and conditions the choice of a solver. The usual practice is to use generic optimization packages without worrying about the differentiability of the objective function. But the use of gradient-based methods when the objective function is not differentiable may result in poor performance or even in absence of convergence. One of our objectives with this analysis is also that practitioners become aware of these problems and to propose them new algorithms having a potential interest for their applications.

Products bear a lot of risks of getting damaged because of falling, getting compressed, etc. during transportation of logistics. In order to preserve products shape and quality, we can reduce the impact force during the logistics using packaging system. In general, we consider that packaging materials would not exhibit the strain rate effect while we predict free drop test results. In other words, the quasi-static compression stress-strain curve is used to simulate the results. But some packaging materials probably have the strain rate effect. Therefore, the foam packaging system of free drop test in this research considers the strain rate effect, that is the packaging materials are strain rate dependent. The energy loss is also considered into account when using numerical simulation methods to predict the maximum acceleration. The aim of this research is to understand the behavior of foam packaging materials during free drop by numerical simulation methods. Most of the literature on relevant research of foam packaging system neglects the strain rate effect to simplify the numerical simulation. But in this research it is shown that the strain rate effect would influence the maximum strain captured by high speed camera, even if there is no difference between free drop test and numerical simulation on maximum acceleration if the strain rate effect is not considered. So this research generalizes some experimental results to coordinate the relationship between the strain rate effect and the energy loss. Later, both energy method and single degree-of-freedom of nonlinear spring system are used to predict the results from free drop test. The constitutive law of foam packaging materials used in this research, for example expanded polypropylene (EPP), is constructed by series of quasi-static compression test and high-rate dynamic impact test. A numerical material constitutive law model considering the strain rate effect is also published to simulate the strain rate dependent property about EPP. We can accomplish the aim, considering the strain rate effect is used in this model when we are simulating the results, and to develop the numerical simulation which can predict maximum strain more accurately. In addition, for verifying that EPP has the strain rate effect, the high speed camera cooperated with the accelerometer through free drop test is used to derive the actual stress-strain curve of EPP packaging system. Finally, the fact that EPP is strain rate depenedent material has been proved. The microstructure photos of EPP by both optical electron microscope (OEM) and scanning electron microscope (SEM) were captured. This research also attempts to understand the relationship between strain rate effect and the microstructure of EPP. Furthermore, for designing EPP packaging system of real products, the appropriate range of strain energy density of EPP was chosen. The maximum acceleration, maximum strain and actual stress-strain curve of free drop test are predicted by numerical simulation methods considering the strain rate effect or not. To conclude, the results by several numerical simulation methods and free drop test are compared to explain that these methods which considers strain rate effect are feasible and accurate.

Excimontec is an open-source lattice KMC simulation software package for modeling organic semiconductor materials and devices, such as OPVs, OLEDs, and more. The software is being developed in C++11 and optimized for efficient execution on high performance computing clusters using MPI. This software package uses object-oriented design and extends the KMC_Lattice framework. This alpha release is built with KMC_Lattice v2.0-alpha.5 and allows the user to perform several simulation tests relevant for OPV and OLED devices. See the README for more information. Major New Updates in v0.3-alpha: Excitons now have a spin parameter to designate them as in either a singlet or triplet state. Singlet and triplet excitons have separate lifetimes and hopping rate constants. Singlets hop via a FRET mechanism and triplets hop via a Dexter electron exchange mechanism. Exciton intersystem and reverse intersystem crossing events dictated by a designated singlet-triplet splitting energy. Exciton-exciton and exciton-polaron annihilations events that depend on the spin state of the excitons Ability to create a correlated Gaussian density of states with 3 options for correlation functions and a specified characteristic correlation length. Improved input parameter file checking. Improved performance of exciton and polaron event calculations. NOTE: This software is still in the alpha phase of development, and as such, there may still be bugs that need to be squashed. Please report any bugs or submit feature requests in the Issues section. This release was developed under the financial assistance award 70NANB14H012 from U.S. Department of Commerce, National Institute of Standards and Technology as part of the Center for Hierarchical Materials Design (CHiMaD).

Jeff Magee and Jeff Kramer John Wiley and Sons, New York, NY, 1999, 374 pp. ISBN 0471987107, $64.99 The book is an introductory text to the ideas, concepts, and topics of concurrency. The text focuses on understanding concepts and techniques, and problems of concurrency, not on the implementation or language. The author's overall goal is that by a combination of learning and doing using Java should make the process of acquiring the skills relating to concurrency interesting, enjoyable, and challenging. The Java language is thus used only for illustration and programming experience of the reader. The book is intended for a computer science student or software developer. A background in programming is expected, as well as some familiarity with the essential concepts of object-oriented programming. Knowledge of the Java programming language and operating systems concepts is beneficial but not required. After reading the text, a reader can expect to have a broad understanding of the concepts of concurrency, the problems that arise, methods to emphasis desirable properties in a concurrent system, and ways to avoid the undesirable ones. The text provides a systematic treatment of concepts, as means to rigorously specify and model concurrent systems, with Java examples to animate and illustrate the concepts discussed. The book is organized into twelve chapters, with three appendices. The first eight chapters provide a concise and comprehensive foundation of concurrency, with the remaining four chapters focusing on more advanced concepts. The latter four chapters are somewhat supplemental and can be read at the discretion of the reader. The content of the text is self-contained, with no reliance upon external references. The authors provide a concluding set of notes and further topics which reference external works, but these are not used in the chapter contents. The introduction provides the foundation for the book, and an idea of what will follow in the rest of the text. The basics of modeling and Java are covered. Authors follow with the concepts of processes, threads and with the idea of concurrency. The emphasis is on using Java, and on the notation used to define a concurrent process or thread. The discussion continues covering interleaving and asynchronous concurrency. Various details about composition of parallel processes and finite state processing modeling are presented. The programming of concurrent execution using Java is then examined via the concept of multiple threads. Here, sharing objects among Java threads is also discussed. The concept of conditional synchronization is covered next, and is used to construct a monitor. The methods of the base object in Java is used, and a waiting queue associated with a Java object is discussed and implemented. This discussion is followed by introduction of deadlock. Authors show the conditions necessary for a deadlock to occur and present an analysis of a concurrent system establishing that such a system is deadlock-free. The classic Dining Philosopher's problem is used to illustrate the distinction between finding deadlocks in models and in programs. The presentation continues with the safety property (that asserts that nothing bad happens), and the liveliness property (that asserts that nothing good happens). Here, authors use the material on model-based design to consolidate many of the concepts previously discussed. No one modeling method or design methodology is emphasized. Then creation and elimination of threads in a running program is covered next. The dynamic starting and stopping of Java threads is presented. The discussion moves then to messaging passing. Asynchronous and synchronous messaging is presented with Java programming examples. The concept of a rendezvous, allowing for interaction in a messaging system, is also presented. Based on the concepts developed so far filter-pipeline, supervisor-worker, and announcer-listener concurrent architectures are examined. Java programs demonstrating how the elements of each model interact at runtime are developed. The presentation completes with modeling and implementing of timed systems. Time is signaled by the passage of successive time ticks. The authors then elaborate on a system that is event-based rather than thread-based. Java programs are used to illustrate in implementation the concepts discussed. The three appendices provide a reference, specification, and listing of semantics for the finite-state modeling algebra used by the authors throughout the book. The text is ideal for teaching in a classroom environment, or for a motivated reader to use for self-paced learning. Its organization follows a logical train of discussion and thought, with each chapter building successively on the other, with the more difficult concepts and topics withheld until later. This gradual approach makes the material flow smoothly and cohesively from the beginning to the end. The book is intended as a textbook, so does organize the material and discussion as one, but does not become too dry or bland to stifle the reader's interest in the material. The examples are inter-mixed with the discussion to highlight and emphasize essential points the authors make in each chapter. The text illustrates concepts well under discussion, and does not become a long-winded recital of theory. The topics examined are fundamental to concurrency, and are well illustrated and discussed, but no one topic is examined extensively. The code examples are well written concerning the programming style, indentation and comments. A CD is provided, containing the codes from the book. In addition supplementary material consisting of presentation slides and an errata is provided on the author's WWW site, as well as on the CD. The book is up to date both on the topics of concurrency, and with the Java applets, code, and programs used to illustrate them. Later, as the Java language evolves, the examples may need to be updated, but for the time being the text well represents that state of the Java language. William F. Gilreath, Micron Technology, Inc., Boise Idaho

In mathematics and statistics, the desire to eliminate mathematical tedium and facilitate exploration has lead to computer algebra systems. These computer algebra systems allow students and researchers to perform more of their work at a conceptual level. The design of generic algorithms for tedious computations allows modelers to push current modeling boundaries outward more quickly. Probability theory, with its many theorems and symbolic manipulations of random variables is a discipline in which automation of certain processes is highly practical, functional, and efficient. There are many existing statistical software packages, such as SPSS, SAS, and S-Plus, that have numeric tools for statistical applications. There is a potential for a probability package analogous to these statistical packages for manipulation of random variables. The software package being developed as part of this dissertation, referred to as “A Probability Programming Language” (APPL) is a random variable manipulator and is proposed to fill a technology gap that exists in probability theory. My research involves developing algorithms for the manipulation of discrete random variables. By defining data structures for random variables and writing algorithms for implementing common operations, more interesting and mathematically intractable probability problems can be solved, including those not attempted in undergraduate statistics courses because they were deemed too mechanically arduous. Algorithms for calculating the probability density function of order statistics, transformations, convolutions, products, and minimums/maximums of independent discrete random variables are included in this dissertation.

Metric-based Evaluation of Implemented Software Architectures

In the context of global urbanization, the waterlogging occurs more frequently. The cause of waterlogging is that the traditional planning of urban rainwater network was backward, which led the rainwater on the ground cannot be collected and drained timely. This study aims to build an intelligent rainwater pipe network planning system based on the SWMM and GIS components. Firstly, the SWMM model was packaged into a .NET managed dynamic library through a software interoperability model to implement the seamless integration with GIS software components. Secondly, on basis of the vertical design elevation and the planning road network data of the city, a grid DEM that in view of road network was built. And the hydrological parameters were automatically extracted by using GIS spatial analysis based on the planned land type and the torrential rain model of the study area. Finally, with the geometric network analysis function of GIS and the rain-flood simulation function of SWMM, the intelligent layout and optimization of rainwater drainage network were realized. And based on the weight model, the urban rainwater pipe network was optimized. The experimental results demonstrated that our method is more efficient than the traditional method. Specifically: (1) the prediction accuracy of rainwater pipe network is improved; (2) the nodes that may overflow are adjusted to the best state, which reduces the risk of urban waterlogging. These findings indicate the optimized pipelines are more scientific and economical in the layout scheme, the selection of outlets and the calculation of pipe force.

This study was centered on the Development, Standardization and Application of Chemistry Achievement Test using the One-Parameter Logistic Model of Item Response Theory. Eight research questions and one hypothesis guided the study. The hypothesis was tested at 0.05 level of significance. The research design was instrumentation research. The Researcher developed an instrument titled “OKUKINS Chemistry Achievement Test (OKUKINS CAT) consisting of 80 items. A proportional stratified random sampling technique was used to obtain a sample of 200 students from a population of 19,082 Senior Secondary School Two (SS II) students from Delta Central Senatorial District of Delta State. The sample was further divided into two equal parts (set A and set B) representing sample A and B respectively while the original sample represent sample O. The OKUKINS CAT yielded favourable statistics under the One-Parameter Logistic Model (1-PLM) with regards to the difficulty (b) parameters and ability estimates. Analyses done using the Xcalibre 4.2 software confirmed suitable indices of b parameters as prescribed by the Xcalibre manual. Using sample O, b parameters ranged from -2.417 to +2.834. Using sample A, b parameters ranged from -2.115 to +2.293. Using sample B, the b parameters ranged from -2.138 to +2.960. The validity of the instrument was estimated using the fit statistics. The results indicated perfect fit of One-Parameter Logistic Model ( 1-PLM). Using sample O, 74 items out of the 80 items of the OKUKINS CAT fitted the 1-PLM. Using sample A, 79 items out of the 80 items of the OKUKINS CAT fitted the 1-PLM. Using sample B, all the 80 items which constitute the OKUKINS CAT fitted the 1-PLM. The study also revealed that gender has no significant influence on academic achievement in chemistry. Based on the findings, it was recommended among others that, all examination bodies such as JAMB, WAEC, NECO and NABTEB should re-visit and review their test items using IRT models since this has been recommended by the International Testing Commission.

We describe custom designed software oriented for teaching design and analysis of analog and digital filters. The tools described are used as teaching aids and are not intended as substitutes for lectures on the topics covered. The analog filter design covers approximation of the filter functions as well as the design of the active-RC filters stages. The digital filter design part is able to design IIR using transformations from the s-plane. FIR filters are designed using the Remez exchange algorithm. Another part of the software package is in charge of simulating an arbitrary digital filter topology for different wordlengths allowing students to observe the limitations inherent to each topology.

The disc brakes are exposed to large thermal stresses and heat during routine braking. The extraordinary thermal stresses, tremendous heat occurred in the disc during hard braking. The aim of the project or research work is to design and analysis of disc. The modelling or design of the disc is done using solid works software. The Thermal analysis is to be done on the Non-vented disc brakes using ANSYS software with different materials. The thermal analysis is done to analyze the thermal properties e.g. Thermal deformation. Comparison can be done for temperature distribution between different materials. In this analysis, different materials to check which material are best. Solid works is a 3d modelling software widely used in the design process. The ANSYS software is general-purpose finite element analysis (FEA) software package. Finite Element Analysis is a numerical solution method of deconstructing the complex system into very small pieces called elements. Keywords – Rotor brake, solid works, structure and thermal analysis, ANSYS.