Course Details

1. Review the necessity of computational mechanics and applications in oil and gas and offshore engineering.
2. Explain the theory, fundamentals and application of the finite element method in performing structural, thermal and flow analysis. Demonstrate the solution of differential equations (1D, 2D and 3D) and their background.
3. Describe mechanical problems with the aid of the finite element method and apply appropriate approximation methods to determine nodal displacements and further mechanical parameter.
4. Apply of matrix algebra to describe mechanical problems with the finite element method and describe the relationship between external loads, displacement and structural stiffness.
5. Explain and apply the discretization method and resulting the degrees of freedom for describing structural, thermal and flow problems.
6. Demonstrate the mesh generation and the approximation of the global solution through the appropriate mesh. Perform division of the solution domain in finite elements and apply appropriate shape functions to describe the solution within the finite element (Galerkin-Ritz method).
7. Analyse total structural and heat problems with the use of appropriate shape functions.
8. Reproduce and compose complex engineering methods with the aid of the finite element method as to explain their behaviour and identify problematic regions with the use of commercial software.

·   Introduction: Overview of theapplications of Computational Mechanics in Oil & Gas and OffshoreEngineering. Necessity and outline of the selected course topics.

·    Problems ofComputational Mechanics: Problems ofstructural, thermal and fluid flow analysis. Differential equations in 1D, 2Dand 3D spaces.

·    Theory andfundamentals of the Finite Element Method: Decompose the computational mechanics problem in “small” (finite) 1D, 2Dor 3D elements. Use of low order Taylorapproximation for the solution in each element. Introduce nodal interpolationand the nodal values as unknowns. Satisfy the differential equation within thefinite element using the Galerkin-Ritz methodology, thus transforming the unknown functions in discrete unknown nodal values and the differentialequation in algebraic equations. The Finite Volume Method as a zero-orderfinite element method. Matrix formulation. Today’s available Software.

·    Finite Elements inComputational Mechanics Problems: Nodalvariables matrices, load vectors and displacements hypotheses for bars, beams,plane elements, plates and shells, nodal variables matrices and load vectorsfor Laplace and Poisson equations. Demonstration using commercial Software.

·    Mesh generation: Approximation of the global solution through an appropriate mesh offinite elements. Convergence aspects and self adaptive meshing with use ofcommercial mesh generating software. Structure and unstructured grids Delaunayor advancing-front methods, Constrained Delaunay Triangulation,Mixed-Element/Hybrid Grids. Demonstration using commercial Software.

·    Application ondifferent examples: Application of thefinite element analysis on specific structural, heat and flow problems.Demonstration using commercial Software.

·   Computer laboratory work: Individual orsmall group studies where students can apply their gained knowledge oncommercial FE-software (ANSYS/SAP) and evaluate practical problems for better comprehension.

• M. Saeed, Finite Elements Analysis - Theory And Application With Ansys, Pearson, 2nd Edition, 2003.
• C. Tirupathi, R. B. Ashok, Introduction to Finite Elements in Engineering, Pearson, 3rd Edition, 2002.
• A. Kanarachos, Chr. Provatides, Finite Elements in Mechanical Engineering Sciences, Papasotiriou, 4th Edition,2000 (in Greek).
• A. Kanarachos, Chr. Provatides, Finite Elements in Mechanical Engineering Sciences - Exercises, Papasotiriou, 4th Edition,2000 (in Greek).

• D. Hutton, Fundamentals of Finite Element Analysis, McGraw Hill, 2004.
• G. R. Buchanan, Finite Element Analysis, McGraw Hill, 1995.
• N.-H. Kim and B. V. Sankar, Introduction to Finite Element Analysis and Design, Wiley, 2009.
• E. Madenci, I. Guven, The finite element method and applications in engineering using ANSYS, Springer, 2006.

The taught part of course is delivered to the students by means oflectures, conducted with the help of computer presentations. Lecture notes andpresentations are available through the web for students to use in combinationwith the textbooks. Furthermore theoretical principles are explained by meansof specific examples and solution of specific problems.

Lectures are supplemented with computer laboratory work carried out withthe supervision of a lab assistant. Here a demonstration of actual problems andcomputational methods takes place. Additionally, during laboratory sessions,students apply their gained knowledge and identify the principles taught in thelecture sessions by means of working on different modelling tasks andevaluating simulation results.