(Created 2008-07-17.)

SCIENTIFIC AND TECHNICAL COMPUTING | VSM045 |

**Aim**

The aim of the course is to give methods within modern structural dynamics and application of those withim various fields of structural design, i.e. building and vehicle design.

*Knowledge and understanding*

For a passing grade the student must

- Be able to solve conceptual construction assignments based on some real structural problems.
- Be able to measure and discuss physical properties on these structures.
- Be able to verify obtained computational results against experimentally measured values.
- Be able to identify and handle the physical concepts and their mathematical syntax.

*Skills and abilities*

For a passing grade the student must

- Be able to analyse general single-dof-problems.
- Be able to define, calculate and analyse structural dynamics multi-dof-problems, based on a finite element formulation.
- Be able to use and assess different solution strategies for structural dynamics problems.
- Be able to use advanced computational methods in structural dynamics to solve problems where there are several alternative solution possibilities, and be able to assess differencies in method and result.
- Present and argue for the chosen solution method at a final seminar.
- Be able to use advanced computational codes for high performance computing.

*Judgement and approach*

For a passing grade the student must

- Be able to assess different solutions and their accuracy.
- Be able to critically examine both own and others proposed solutions in an open discussion.
- Be able to propose solution based on incomplete data, recognise their scope and propose changes in basic conditions.
- Be able to summarise results in a computational report and assess colleagues' reports in relation to one's own.

**Contents**

Single-dof models. Generalized Single-dof models; rigid body models, models for deformable bodies. Time integration; Newmarks method, implicit method, explicit method. Multi-dof models; finite elements, direct integration, modal superposition, eigenvalue analysis, response diagram. Earthquake analysis.

The lectures describe the theoretical concepts in relation to the application, with conceptual construction assignments which show how the realistic questions enhance the mathematical and numerical descriptions. The construction assignments in a first phase relate to applied mechanics. They can be developed into other transient problems i.e. whithin thermal conduction, still with the finite element method as basis for the work.

Beyond this moments dealing with general computer code systems for finite element analysis, i.e. Abaqus, Nastran or LS-Dyna are planned. This kind of computer code systems can be used in a wide range of physical/engineering problems. Construction assignment 2 is designed so that it is natural to use one of these systems. Further, computer systems and computational strategies for high performance computing are discussed. These latter moments are carried out in cooperation with Lunarc, Center for Scientific Computing at Lund University. The computer systems that Lunarc have at their disposal will also be used in the course. For further information, see www.lunarc.lu.se.

**Literature**

Chopra, A. K.: Dynamics of Structures, Prentice Hall, 1995 or alt. litt. CALFEM ver 3.3 - A finite element toolbox to MATLAB. Structural Mechanics and Solid Mechanics. Lund University, Lund 1999.