No description available.

In this essay we present the Sobolev spaces and some basic properties of them. The Sobolev spaces serve as a theoretical framework for studying solutions to partial differential equations. The finite element method is presented which is a numerical method for solving partial differential equations.

No description available.

This thesis covers the master diploma work conducted at Hohai University, Nanjing, People's Republic of China. An overflow spillway section fitted for the Longtan Dam was designed and the loads acting on it was identified after an iterative flood routing calculation. The section was then evaluated, both theoretically and numerically using FEM with a linear-elastic isotropic constitutive model, with regards to the stability against compressive and tensile failure. Also, a numerical analysis of the seepage through and around the structure was conducted. The results show that, for a given design of the section, the structure can handle the compressive stresses that arises. However, the numerical analysis indicates a possible tensile failure at the dam heel, which is inconsistent with the theoretical stability analysis. The seepage analysis show that the maximum seepage occurs at the dam heel, the dam toe, and at grout curtains beneath the structure. A simple convergence analysis was done which showed stress singularities at the dam heel and dam toe. These were discussed and connected to the St Venant's principle, and these singularities shows the risk of blindly trusting numerical results.

The aim of this project was to design, construct and develop a space frame for a pneumatically driven vehicle for one driver through several simulations. The purpose of the vehicle was to compete in the ‘XI. International Aventics Pneumobile Competition’. This event is an opportunity for students to develop and improve their skills in different fields such as mechanical engineering, telemetry and electronics building and team working. However, this thesis topic will be focused mainly on the aspects of mechanical engineer based on the process of before and after the construction. This process was also examined through a number of races occurred during the competition. Specifically, the chassis that has been initially designed was developed through the whole process with purpose of lowering the mass while maintaining the strength. The study has produced two results - a real life model, which has participated in the competition and an improved model of the frame which was carried out in Autodesk Inventor and ADAMS software. Throughout the process the frame was remodeled and resulted with the weight loss from 48.3 kg to 31.9kg, while the strength was maintained. / XI. International Aventics Pneumobile Competition

On behalf of and in collaboration with Valmet AB this thesis has been fulfilled and executed at their development department in Sundsvall. Valmet AB design, develop and manufacture machines and equipment for the pulp, paper and energy industry. One of their key products is the TwinRoll press. The TwinRoll press consist, among others, of a part called mantle section which in terms of manufacturing is rather complex. This part itself consists of frame ribs, which during operation endure high loads in a high amount of cycles during its life-span. Due to this, fatigue failure sometimes occurs, which in consequence causes mantle section failure. Theoretical determination of the fatigue strength has been proven difficult, which has created needs for experimental fatigue testing. The goal with the thesis was to define a method for fatigue testing and to design and develop a rig which could perform the testing according to the defined method. The initial part of the project consisted of a literature study about fatigue testing and how it normally is performed. Then the work with the test method started and the loads during normal operation was specified, as well as parameters that might affect the test results. This part was important as the parameters could be transformed into requirements which the test rig needed to satisfy. When the method for testing and the measurable requirements were done, concepts were generated via individual sketching and brainstorming. A final concept was chosen for detailed design in SolidWorks after using methods like voting and Pugh’s concept selection matrix. The rig was modelled and drawings for manufacturing was produced, and then dimensioned through both simulations with FEM and calculations by hand. The final construction was then inspected with VR-technology. The conclusion of the thesis was that the frame ribs should, as a suggestion, be fatigue tested with constant stress amplitudes until failure, and then repeated for other stress values until the amount of generated data is enough for evaluation in a stress-number-diagram. A Wöhler-curve should then be generated for desired probability of failure and finally be evaluated in a Haigh-diagram. The developed test rig will perform testing on one frame rib at a time with a high frequency hydraulic cylinder, were the sample used is a piece of the mantle section. Furthermore, the sample is fixed in both directions to correspond to stress generated by shrinkage which an entire frame rib normally withstands.

Os modelos existentes de propagação de ondas de ultra-som em meios líquidos e sólidos consideram a geração e recepção das ondas produzidas por transdutores simulados segundo o modelo do pistão plano ou com excitações cuja amplitude varia radialmente no pistão. Esses modelos são simplificados e não explicam completamente o comportamento real de transdutores de ultra-som interagindo com líquidos e sólidos. As verificações experimentais de propagação da onda de ultra-som em meios líquidos mostram que a onda de borda é diferente da onda plana. Observa-se também a existência de outras ondas não previstas nos modelos anteriores. Essas ondas são conhecidas como ondas head. A utilização do método dos elementos finitos (MEF) para a modelagem de propagação de ondas de ultra-som, incluindo o transdutor piezelétrico, permite a obtenção de resultados realísticos, conseguindo assim descrever com maior precisão o comportamento do transdutor e das ondas de ultra-som se propagando em diferentes meios e interagindo com defeitos que se comportam como refletores. Apesar disso, os resultados desses modelos dependem das características precisas dos materiais que compõem o transdutor. O transdutor de ultra-som é composto por uma cerâmica piezelétrica, por camadas de casamento e de retaguarda que geralmente são compósitos de epóxi com alumina e epóxi com tungstênio respectivamente, e pelo encapsulamento. Neste trabalho é analisada a resposta transiente de um transdutor circular de 2 MHz, com diâmetro de 12,7 mm, banda larga. O modelo do transdutor foi implementado com o método de elementos finitos. A análise transiente pelo MEF é implementada com o software ANSYS. Na primeira parte do trabalho o transdutor é analisado no modo de transmissão em água. Os resultados do modelo com MEF foram comparados com os resultados do modelo do pistão plano e com verificações experimentais obtidas em tanque de imersão com um hidrofone tipo agulha. Na segunda parte é realizada a análise do transdutor operando em modo pulso-eco radiando em peças de teste com e sem defeito, utilizando acoplamento direto e acoplamento por buffer de água. Os resultados do MEF apresentam boa concordância com os resultados obtidos experimentalmente. / Simple models for ultrasonic wave propagation in liquid and solid media consider the wave generation and reception by transducers that behave as plane pistons. These models are simplified and they do not explain completely the behavior of an ultrasonic transducer when interacting with other media. Experimental verifications of ultrasonic wave propagation in liquid show that the pressure amplitude of the edge wave is different from the plane wave. Also it is observed the existence of other types of waves not foreseen in these previous models. These waves are known as head waves. More realistic models for ultrasonic wave propagation are obtained using the finite element method (FEM). These models include the piezoelectric transducer, thus, describing with higher precision the behavior of the transducer and the ultrasonic waves propagating in different mediums and interacting with defects. The precision of the models depends on the accurate determination of the mechanical and electrical properties of the involved materials. The ultrasonic transducer is composed by a piezoelectric ceramic, a matching layer and a backing layer that are generally made by epoxy/alumina and epoxy/tungsten composites respectively. In this work it is analyzed the transient response of a circular transducer of 12.7 mm diameter and 2 MHz center frequency. The transducer model was implemented with the finite element method. The FEM transient analysis was executed in the ANSYS software. In the first part of the work the transducer is analyzed in transmission mode in water and the MEF results are compared with the plane piston model and with experimental verifications using a hydrophone. In the second part it is carried at the transducer analysis operating in pulse-echo mode radiating into test pieces with and without defects, using direct and water buffer coupling. The MEF results show good agreement with the results obtained experimentally in the laboratory.

O estudo das forças de corte em usinagem tem várias aplicações, tais como definir a melhor geometria da ferramenta e sua interação com a peça. Este trabalho apresenta os resultados de simulações do processo de torneamento utilizando o método dos elementos finitos no corte ortogonal em aço AISI 4340 usando insertos de metal duro, comparando-os com resultados experimentais. As simulações foram realizadas no programa comercial Abaqus/Explicit TM considerando os efeitos térmicos do processo oriundos tanto da deformação do material quanto dos atritos nas interface peça-ferramenta-cavaco. As variáveis do processo estudadas foram a velocidade de corte e o avanço. Os resultados da força de corte simulada mostraram-se bem próximos daqueles obtidos experimentalmente, com erro médio em torno de 5%, enquanto que os da força de avanço apresentaram erro médio de cerca de 27%. / Cutting force is a very important parameter, which can be used to determine tool geometry and its interaction with the workpiece. This work presents some orthogonal cutting simulations using Abaqus/Explicit TM finite element methods code with carbide tool on an AISI 4340 hardened steel workpiece. Comparison with experimental results are also carried out. The simulation considers the thermal effect caused by material deforming and friction between tool, workpiece and chips. The main parameters changed during the simulations are the cutting speed and the feed rate. As results, the simulated cutting forces showed an error around 5% and the simulated feed forces about 27% when compared to the experimental values.

Der Standard des Message Passing Interfaces (MPI) stellt dem Entwickler paralleler Anwendungen ein mächtiges Werkzeug zur Verfügung, seine Softwa- re effizient und weitgehend unabhängig von Details des parallelen Systems zu entwerfen. Im Rahmen einer Projektarbeit erfolgte die Umstellung der Kommunikationsbibliothek eines bestehenden FEM-Programmes auf den MPI-Mechanismus. Die Ergebnisse werden in der hier gegebenen Beschreibung der Cubecom-Implementierung zusammengefasst. In einem zweiten Teil dieser Arbeit wird untersucht, auf welchem Wege mit der in MPI verfügbaren Funktionalität auch die Koppelrandkommunikation mit einem einheitlichen und effizienten Verfahren durchgeführt werden kann. Sowohl fuer die Basisimplementierung als auch die MPI-basierte Koppelrandkommunikation wird die Effizienz untersucht und ein Ausblick auf weitere Anwendungsmoeglichkeiten gegeben.

In der vorliegenden Arbeit wird die Anwendung eines bereits im 2D-Fall benutzten Mechanismus zur MPI-basierten Koppelrandkommunikation auf das 3D-FEM-System SPC PMPo-3D beschrieben. Insbesondere soll der Einfluss der Partitionierung auf die Laufzeit im Vergleich mit den Resultaten für das Originalsystem, fuer das entsprechende Untersuchungen bereits in durchgefuehrt wurden, betrachtet werden. Weiterhin wird ein Ausblick auf weitere Optimierungsmöglichkeiten des Verfahrens gegeben.