At the end of the course the student can …
- Compute stresses and deflections of frames and beam structures with the help of the Finite Element Method and be able to analyze and evaluate the results;
- Describe and explain the mathematical and mechanical backgrounds of the Finite Element Method;
- Be able to derive 1-, 2- and 3-dimensional element formulations;
- Write a simple Finite Element program in MATLAB;
- Make an efficient Finite Element model of a real problem and analyze using a Finite Element program;
- Interpret results of a Finite Element calculation and evaluate the accuracy of the calculation.
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This is a part of module 11, ME 11 Production Systems Engineering of the Bachelor Mechanical Engineering.. See here for the compete description of the module.
In this course an introduction to the Finite Element Method is given which currently is the most widely used tool to analyze mechanical behavior of structures. With this method the stiffness and strength of any structure can be computed efficiently and accurately starting from simple structures that can be calculated using different methods by hand such as trusses and beams to more complicated structures to which analytical solutions are too hard to determine or may even not exist. Within the course the background of the method will be given including the mechanics and the mathematics. Firstly in the course truss and beam Finite Element formulations will be derived. These will be followed by introducing a more general approach that is applicable to any structure using the Virtual Work theorem. Complete derivation of Finite Element equations for 1-, 2- and 3-dimensional structures will be given based on linear static material behavior. Linear and higher-order elements will be introduced and derived and an introduction to numerical integration methods will be given. Since the Finite Element method is an approximation a theoretical background will be given in order to validate and interpret the results of a simulation. The course also progresses in the direction of direct application of the given knowledge using commercial Finite Element programs such as ANSYS. In the practical exercises realistic problems will be solved using this software and the validity and the accuracy of the simulations will be discussed.
Non-ME students can take this course if they meet the entry requirements.
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