Nonlinear Finite Element

Institution:
IUSS Pavia
Specialization:
EE - Earthquake Engineering
Term:
Spring 2003
Teacher(s):
FERDINANDO AURICCHIO, THOMAS J.R. HUGHES
Credits:
6
Date (from - to):
02/05/2003 – 31/05/2003

Fundamental techniques used in the nonlinear finite element analysis of solids. Linear static and dynamic finite element analysis. Simple static nonlinear problems (partial differential equations and boundary conditions, through weak/variational formulations, discretisation by the Galerkin finite element method, and development of the matrix equations). Elementary techniques of nonlinear equation solving (consistent linearization, Newton and modified Newton strategies, line search, and secant methods). Problems accounting for large deformations, focusing on nonlinear elastostatics. The static large deformation formulation generalized to dynamics; basic methods of time integration, such as Newmark's and "alpha" methods. Additional topics: inelasticity (see, e.g., Simo and Hughes [1998]), and/or energy-momentum and space-time methods in dynamics, and/or the discontinuous Galerkin method.

Suggested readings:

  • Hughes, T.J.R. (2000): The Finite Element Method-Linear Static and Dynamic Finite Element Analysis, Dover Publications, Mineola, New York.
  • Zienkiewicz, O.C. and Taylor, R.L. (2002) “The Finite Element Method”, Vol. 1 and Vol. 2, Butterworth-Heinemann.
  • Marsden, J.E. and Hughes, T.J.R. (1994): The Mathematical Foundations of Elasticity, Dover Publications, Mineola, New York.
  • Simo, J.C. and Hughes, T.J.R. (1998): Computational Inelasticity, Springer, New York, New York.