This module will enable you to understand the theory and limitations of the finite element (F.E.) method for solving problems in solid mechanics, to gain the ability to develop a basic F.E. program and to be able to use an existing F.E. package to solve problems in elastic solid mechanics. 

• LO1: Implement the finite element method in the development of a linear elastic 2D Finite Element code 

• LO2: Apply and critically evaluate the finite element method in the analysis of solid mechanics problems 

• LO3: Evaluate the results from finite element analyses and reflect on the uses and limitations of the method 

• LO4: Demonstrate comprehensive understanding of the Finite Element theory 

The module will be delivered through a mix of face-to-face, on campus, teaching and learning activities (lectures, tutorials, computer lab sessions). The student will gradually develop a finite element program in a software package, e.g. MATLAB.  At the end of the course, there will also be an opportunity to use an existing finite element package in these laboratory sessions. 

Revision notes on linear algebra and basic Matlab coding will be provided at the beginning of the course. All Matlab commands required for the code implementation will be provided in a set of notes for self-study. Assistance on code implementation from the lecturer and teaching instructors will be provided in weekly computer laboratory sessions. 

Whilst studying this module, the students will develop and practice a range of formal and informal skills as follows: 

• Code implementation in Matlab (or a similar software package) 

• Application of a commercial Finite Element software package (e.g. LUSAS) in solving engineering problems 

• Presentation of FE analyses and results in a short report 

• Peer learning and collaboration (informally)  

The module is assessed by a combination of a formal 2-hour written examination (65% of module marks), held in the assessment period at the end of the Semester, and a portfolio submission consisting of mostly exercises completed in timetabled sessions (35% of the marks). 

The written examination will be graded and will aim to test the individual understanding of the underlying theory, application, and limitations of the Finite element method (LO 1-4). A basic understanding of the FE method, a good understanding of the fundamental assumptions and basic application of these in standard problems is required for a pass. A good performance will require a solid understanding and application of the theory and a good awareness of its limitations. An excellent performance will require a deep understanding of the theory, assumptions and limitations that translates in their application to non-standard problems. 

The portfolio will involve the completion of short programming tasks and a short report on a finite element analysis of a civil engineering problem (LO 1-3). For the programming tasks the students will be required to complete lines of code in pre-set templates, with assistance from the lecturer and teaching instructors. Thus, there will be opportunities for students to obtain feedback on their progress during the timetabled sessions. The report will include a comparison of solutions between those obtained with the MATLAB program developed by the student with those obtained from an existing finite element package and/or an analytical solution. 

THE OPPORTUNITY FOR REASSESSMENT IN THIS MODULE: 

The opportunity for reassessment in this module will be set at component level.  

Opportunities for re-assessment is only permitted provided you have not failed more credit than in the resit rule adopted by your programme.  If the amount of credit you have failed is more than permitted by the relevant resit rule, you may be permitted to repeat study if you are within the threshold set for the Repeat rule adopted by your programme.  You will be notified of your eligibility to resit/repeat any modules after the Examining Board in the Summer period. 

All resit assessments will be held in the Resit Examination period, prior to the start of the following academic session. 

Vector matrix algebra 
Essential elements of the theory of elasticity 
Mapping of 1, 2 and 3D domains and the role of the Jacobian 
Numerical Integration, in particular Gaussian Quadrature 
Interpolation and the isoparametric concept 
Derivation of element stiff matrices and force vectors using the principle of virtual work. 
Boundary conditions 
The assembly process 
Data input and results output 
The overall structure of a finite element program 
Pre and post processing with graphical programs 
Development of a finite element program in MATLAB (or similar package) 
Solution of a problem in solid mechanics with the developed program and with an existing finite element package 
A brief introduction to non-linear analysis