PENG9520 Finite Element Modelling and Simulation of Structures Course description

The course teaches advanced topics in finite element modelling and simulation of structures such as reinforced concrete, steel and timber structures. The course will also expose students to some of the recent trends and research areas in FEM.

All physical structures exhibit nonlinear behaviour to some extent, and the assumptions of linearity are often simplistic and inadequate for real-life structures. In such cases, linear analysis is only an approximation that makes the analysis of structures more tractable. The analysis of a structure undergoing some form of nonlinear behaviour will be much more accurate if a nonlinear finite element analysis is carried out. Nonlinearities can be caused by changes in geometry or by nonlinear material behaviour. This is an advanced course which follows up on linear FEM and is based on the extension of formulation of the FE equilibrium equations to the nonlinear domain, covering both types of nonlinearities.

The course will be offered once a year, provided 3 or more students sign up for the course. If less than 3 students sign up for a course, the course will be cancelled for that year.

The following required coursework must be approved before the student can take the exam:

• Completion of an extensive individual project in the specialised module.

No formal requirements over and above the admission requirements. The course is based on knowledge and skills within solid mechanics, statics, design of reinforced concrete and steel structures as well knowledge in finite element method (FEM) in structural analysis and design.

Students who complete the course are expected to have the following learning outcomes, defined in terms of knowledge, skills and general competence:

Knowledge:

On successful completion of the course, the student:

• can interpret the philosophy behind principles, design and modelling considerations in using finite element methods (FEM) in analysis and design of structures.
• can describe the general steps used in FEM to model and solve complex nonlinear problems in structural analysis and design.
• has detailed knowledge of solution methods for nonlinear static problems, and some knowledge on solution methods for nonlinear dynamic problems.
• has detailed knowledge of nonlinear geometry and nonlinear material models (elastoplastic and others) and the applications of these models in structural analysis.
• can explore the complex issues in convergence of solutions using nonlinear FEM.

Skills:

On successful completion of the course, the student can:

• demonstrate the ability to use FEM to produce a reliable prediction of displacements and stresses in nonlinear structural problems of relevance to engineering practice.
• create and design complex engineering structures using finite element methods.
• develop expertise in the usage of commercial finite element software for both linear and nonlinear analysis of complex structures.

General competence:

On successful completion of the course, the student can:

• use advanced commercial FEM software.
• understand the importance of verification and validation in research and demonstrate the ability to make critical assessments
• communicate effectively through written reports.

An individual, oral examination. The examination will address both general topics from within the course and the specific project developed by the student.

The oral examination cannot be appealed.

Seminars, exercises, project assignment (scholarly work), scientific report and oral presentation.

The following required coursework must be approved before the student can take the exam:

Compulsory assignments. Obligatory attendance at practical training.

Students taking the course must have a thorough knowledge of advanced calculus, including ordinary and partial differential equations. The student should also be familiar with linear algebra and Fourier and Laplace transform theory. In terms of programming, the candidate should have some experience in implementing numerical methods, including schemes for solving partial differential equations.

The candidate should also have a certain knowledge of mathematical analysis, modern physics or physiology – depending on specialization.

The course will be offered once a year, provided 3 or more students sign up for the course. If less than 3 students sign up for a course, the course will be cancelled for that year.

None.

Students who complete the course are expected to have the following learning outcomes, defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of the course, the student:

• knows how mathematical models can be derived from facts and first principles.
• has a repertoire of methods to solve and/or analyse both ordinary differential equation (ODE) systems and certain partial differential equations (PDEs).
• is able to apply analytical and/or numerical solution methods for PDEs to models of heat transfer, wave propagation and diffusion-convection and discuss the relevance of these models to real-world phenomena.
• is able to construct and develop relevant models and discuss the validity of the models.

Skills

On successful completion of the course, the student can:

• can determine steady states of ODE systems and use linear approximation to elucidate the stability properties of these states.
• can solve and/or analyse selected PDE models.
• is able to implement and use some numerical methods for solving relevant PDEs.
• can devise the solution of certain composite quantitative problems.
• can disseminate results and findings in an accessible manner – both orally and in writing.

General competence

• is aware of the usefulness and limitations of mathematical modelling as well as of pitfalls frequently encountered in modelling and simulation.
• is able to discuss properties of a system using the equations of the mathematical model that describes the system.
• can explain and use numerical methods, know their strengths and weaknesses and interpret results of numerical simulations.

The teaching is organised as sessions where the subject material is presented, and as sessions where the students solve problems using analytical and/or numerical methods. Between these sessions, the students should work individually with literature studies and problem solving.

In the last, specialised part, the students are required to complete and present a rather extensive individual project involving theoretical and practical/implementational aspects.