Courses:

The analysis of complex static and dynamic problems involves, in essence, three steps:
     
     1. Selection of a mathematical model.
     2. Solution of the model.
     3. Interpretation of the predicted response.

Nowadays, finite element methods are used successfully for the analysis of very complex problems in various areas of engineering. A finite element analysis is now frequently imperative to reach a safe and cost-effective design. However, the appropriate and efficient use of finite element procedures is only possible if:

• the basic assumptions employed in the mathematical model and the finite element model are known, 
• the basic solution steps used in the finite element analysis have been studied, and finally, 
• the methods can be exercised confidently on the computer.

The objective of this course is to teach the student the theory and practical use of modern finite element methods for the solution of static and dynamic problems. The content of the course is as follows:

• Formulation of effective finite element methods for analysis of static and dynamic problems.
• Finite element modeling of static and dynamic problems.
• Computer numerical solution of equilibrium equations in static and dynamic analysis.
• Study of mode superposition analysis and effective direct integration methods for solution of structural vibration and wave propagation problems.
• Study of efficient eigensolution techniques for calculation of frequencies, mode shapes and buckling loads.
• Use of an existing general purpose finite element program for the solution of a structural engineering, heat transfer, field or fluid mechanics problem, or
• Development of a simple finite element analysis program and a study with that program.

The methods studied in this course are modern computational procedures applicable to the solution of problems in static (steady-state) analysis, forced vibration analysis, and wave propagation. Application areas are problems in stress analysis, heat transfer analysis, earthquake engineering, building structures, geomechanical engineering, ship structures, control theory, and so on.

Bathe, K. J., Finite Element Procedures. Englewood Cliffs, NJ: Prentice Hall Inc., 1996.

• Clough, R. W., and J. Penzien. Dynamics of Structures. 2nd ed. NY: McGraw-Hill Book Co., 1993.
• Tedesco, J. W., W. G. McDougal, and C. A. Ross. Structural Dynamics: Theory and Applications. CA: Addison Wesley Longman Inc., 1999.

The student's course grade is based on the performance in:

• the weekly homeworks
• the course project
• two 1½ hour exams

The reading requirements will be given in the lectures and will refer to the textbook Finite Element Procedures. We will primarily discuss the material in Chapters 1, 4, 5, 7, 8, 9, 10, and 11.