After the course, the student is able to:
- Apply constraint equations by the Lagrangian multiplier technique and the penalty method, analyze the choice between these methods and synthesize the best choice in a given mechanical problem based on the main characteristics of the method and the problem at hand;
- Explain the basics of direct and iterative solvers for linear systems and their applicability and synthesize the best solution method for a given problem in the mechanical domain;
- Explain the principles of modelling strategies for large and complex structures (e.g. sub-modelling and sub-structuring) and formulate a solution approach for a given problem in the mechanical domain;
- Analyze different types of dynamic analyses (natural frequency, harmonic and implicit or explicit transient), formulate a solution approach and evaluate the results of such a dynamic analysis;
- Analyze and evaluate the accuracy of a FEM solution of a given mechanical problem, using error estimators;
- Recognize numerical phenomena such as locking and formulate a strategy to resolve the negative effect of such phenomena for a given problem in the mechanical domain;
- Explain the differences between shell and continuum elements and formulate an effective modelling strategy for a mechanical problem in which the choice between these types of elements is relevant;
- Apply solution techniques for non-linear sets of equations including numerical stabilization methods.
- Analyze geometrical nonlinearities that occur in structural analysis, synthesize a modelling approach for a given nonlinear problem and evaluate results of such a problem.
- Apply a linear stability analysis to structures and evaluate the results of such an analysis.
After a short recapitulation of Introduction to Finite Element Modelling and the addressing the links with Fundamentals of Numerical Methods, various advanced topics are addressed, covering the application of constraint equations, as an extension of boundary conditions and the principles of solving a typical Finite Element problem.
Subsequently, the solution is analyzed in terms of its accuracy and common numerical issues such as locking. Methods to improve the quality or mitigate numerical issues, while marginally compromising the efficiency of the solution, are addressed.
The domain of problems will then be extended with dynamic problems, addressed based on comparatively basic structures, what the possibilities, yet also implications of dynamics are in a Finite Element setting.
Advancing to the different types of elements available in a Finite Element Model will provide insight when to choose for shell elements over continuum elements, in light of their characteristics and limitations.
Finally, the implications of geometrical nonlinearities will be addressed, shedding light on the solution processes required in cases related to large deformations and buckling of complex structures.
This course gives the student the ability to work in an advanced way with the Finite Element Method, which differs (but is essential for) working in an advanced way with a Finite Element Package. The students should realize that this course does include a significant amount of mathematics, required to analyze and evaluate results from a FEM solution. Working knowledge of Math B1, B2, C1, D1 and D2 is assumed, as well as knowledge of the basics of the Finite Element Method (IFEM).