Indicative contents

• Finite element theory: An overview of finite element methods and its applications. Revision of essential topics in mechanics of solids. Development of stiffness matrices for simple structural elements such as spar and beam elements. Discussion of further continuum elements such as higher order elements, plate bending, shell, axi-symmetric three-dimensional and isoparametric elements. Assembly of element stiffness matrices to form the system stiffness matrix, application of boundary conditions and discussion of numerical solution procedures to solve system equations. Numerical Integration. Equivalent nodal loading.
• Non-linear finite element theory; Finite element procedures for nonlinear analysis. Lagrangian and Eulerian formulations of 1D continua, Nonlinear continuum mechanics, constitutive equations. Material models, finite elements for nonlinear analysis of continua. Practical use of nonlinear finite element analysis, mesh descriptions, classification of partial differential equations, NLFEA: Step-by-step procedure, Explicit time integration method, Implicit time integration methods and solution of equilibrium equations, Stability of solutions, Numerical stability, Material stability. Finite Elements for Nonlinear Analysis of Structures, Solution Methods and Stability Analysis, Commercial FEM systems: Capabilities.
• Finite Element Modelling: Use of commercial finite element codes. Model definition within a preprocessor. Results interpretation and model validation within a postprocessor. Model definition via node and element patterns. Model definition via solid modeling and meshing techniques. Mesh quality and adaptive meshing. Sub-modeling.
• Heat Transfer Finite Element Analysis: Review of heat transfer theory. Finite element formulation of steady-state and transient heat transfer problems. Solution of practical problems. Dynamic Finite Element Analysis: Review of vibration theory. Finite element determination of natural frequencies and mode shapes. Modal analysis. Solution of practical problems.

Module Resources

• Essential reading
  1. Course notes
• Recommended Reading
  1. Tirupathi R. Chandrupatla, (2002), “Introduction to Finite Elements in Engineering”, Prentice Hall International Publications – New Delhi, ISBN: 8178086441
  2. Reddy J. N., (1993), “An Introduction to the Finite Element Method”, McGraw-Hill, ISBN: 0072466855
  3. Bathe K. J., (1997) Finite Element Procedures, Prentice - Hall, Englewood Cliffs, ISBN: 8112034075
  4. Cristfield M. A., (1991) Non-linear Finite Element Analysis of Solids and Structures, Vol. 1, Wiley, New York. ISBN: 047195649X
  5. Reddy J. N., (2005), “An Introduction to Non-linear Finite Element Analysis”, Oxford University Press, ISBN: 019852529X
  6. Ted Belytichko, Wing Kam Liu, Brian Moran, (2000), “Non-linear Finite Elements for Continua and Structures”, Wiley, ISBN: 0471987735
  7. Kleiber M., (1989), “Incremental Finite Element Modeling in Non-Linear Solid Mechanics”, John Wiley and Sons, ISBN: 0470-20832-5
  8. Fagan M. J., (1992), “Finite Element Analysis, Theory and Practice”, Longman Scientific and Technical, ISBN: 0470218177
  9. John O. Dow, (1999), “Finite Element Methods and Error Analysis Procedures: A Unified Approach”, Academic Press, ISBN 0122214404