The course deals with modelling and analysis of non-linear
structures and solids. The main emphasis is on the modelling
aspect, i.e. the justification and properties of the theory, and
the development of the theory in a form suitable for computational
analysis. The idea is to present the theory and the corresponding
numerical methods as a gradual development, from simple bar and
truss systems via finite rotations over beams to non-linear
kinematics and material behaviour of solids. Care is taken to
explain why as well as how.
Læringsmål:
En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:
Understand the basic form of non-linear problems in terms of a
residual which is reduced by a sequence of iterations
Recognize and use different non-linear strain formulations for
analysis of finite displacements
Formulate and use finite element models for trusses in terms of
finite strains
Understand and use matrix and pseudo-vector formulations to
describe finite rotations.
Formulate and use finite element models for beams with finite
displacements and rotations
Understand the relation between material and spatial continuum
mechanics formulations, including the role of objective strain
rates in spatial descriptions
Formulate plasticity models and algorithms for non-linear
material behavior and to use these in a numerical
implementation.
Formulate and use numerical techniques for solution of typical
non-linear equation systems associated with analysis of structures
and solids
Understand the role of dynamic effects and to use modern
integration techniques to analyze non-linear dynamic problems
Perform numerical analysis of small non-linear problems by use
of MATLAB based finite element routines
Present the methods, analysis and relevant conclusions for
non-linear problems of structures and solids in a written
report
Kursusindhold:
· Introduction to non-linearity, exact theory of truss structure
and numerical implementation.
· Theory of large rotations, and large displacement and co-rotating
beam theories.
· Finite deformation continuum mechanics and finite deformation
elements.
· Basic plasticity theory and numerical plasticity algorithms.
· Quasi-static and dynamic numerical solution methods.
The theory is supported by a set of MATLAB functions, by which the
student will familiarize himself with the numerical implementation
when providing his own illustrations of the theory.
Litteraturhenvisninger:
S. Krenk: Non-Linear Modelling and Analysis of Structures and
Solids, Cambridge University Press, Cambridge, 2009.
