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.
Litteratur:
S. Krenk: Non-Linear Modelling and Analysis of Structures and Solids, Cambridge University Press (in preparation).
