On completion of this course, the student will be able to:
- calculate stresses (force equilibrium, etc) and use tensors
- explain occurring deformations based on material theory
- apply 3D elasticity theory on components of a construction
- evaluate and understand the results of a calculation
- recognize the problem at hand and simplify it based on the correct interpretation of elasticity theory
- describe and explain the mathematical and mechanical backgrounds of the Finite Element Method
- derive 1-, 2- and 3-dimensional element formulations
- 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
This is a part of Semester 4 of the Bachelor Mechanical Engineering (UT-VU) See here for the compete description of this semester.|
ELASTICITY + FEM is the fifth course of the SOLID MECHANICS learning line.
In this course, the linear elastic theory (Hook’s Law) is discussed and extended towards more complex 3D situations (principle stresses, etc.). This includes the use of tensors, tensor analyses and linear algebra. The student learns to apply these theories to simple constructions. During the lectures, multiple real-life examples and materials (polymers, glasses or powders) will be discussed for the student to see the applicability and importance of this course. In this course also an introduction to the Finite Element Method is given which currently is the most widely used tool to analyze mechanical behaviour 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 behaviour. 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.
Please note: This course takes place in Amsterdam and is only accessible for BSc UT-VU ME students.