BYG701 Non-linear finite element method

University of Agder

Contents

The course is designed to give a PhD-candidate essential theoretical background to understand the challenges when modelling behaviours of solids / structures as involved in large non-linear deformation.

The course consists of two parts.

Part one covers basics of frame independent formulation

Part two covers solution techniques for FE methods

Completion of each part is followed by a compulsory exercise.

Learning outcomes

Upon completion of course, the PhD-candidate shall

-understand the basics of frame independent formulation with either Eulerian or Lagrangian approach

-understand the difference between small and large deformations, and the related strain and stress tensors

-know the concept of energy conjugate stress and strain tensors

-be familiar with theory and its main constitutive equations, and Lagrangian or Eulerian formulation of such equations in nonlinear FEM

-understand both the most often used explicit and implicit solution methods and theirs differences in FEM

-understand modeling instabilities caused by material, structural and the numerical singularity

-be familiar with sources of non-linearity, for example, the non-linearity in structural geometry, material property and boundary conditions

-be able to use some advanced FE software to solve both theoretical and practical problems

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