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## Syllabus for

MHA165 - Finite element method, advanced course

Owner: TMASA
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: A
Department: 42 - APPLIED MECHANICS

Teaching language: English

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 No Sp 0198 Examination 5,0 c Grading: TH 5,0 c Contact examiner, Contact examiner

#### In programs

TMASA MECHANICAL ENGINEERING - Applied Mechanics, Year 4 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)

#### Examiner:

Professor  Peter Hansbo

#### Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

#### Course specific prerequisites

MHA 160 Strength of Materials - Advanced course, MHA021 Finite Element Method (or equivalent courses from other universities).

#### Aim

To give theoretical and practical knowledge about the finite element method as applied to advanced problems containing side conditions, nonlinearities, and time-dependency. An important part of the course deals with the principles of generating self-adaptive grids based on error estimates. MATLAB is used to build finite element codes from scratch.

#### Content

Repetition: isoparametric mappings, quadrature, mathematical prerequisites. Time dependent problems: vibration problems; heat conduction; implict and explict time-stepping; damping and dispersion; space-time finite elements. Non-linear problems: Newton's method; secant methods and BFGS, application to small strain plasticity. Mixed FEM: Lagrange multipliers;
penalty methods; stabilized methods, application to plate bending and incompressible elasticity. Error estimation and adaptivity: linear and non-linear problems, stationary and time-dependent.
Convective problems: stabilization by use of the streamline diffusion method; application to convection-diffusion problems. Non-conforming finite element methods: application to incompressibility and plate bending.

#### Organisation

Lectures, computer assignments.

Lecture notes.