To equip the student with the basic competence of using a typical finite element solver to tackle practical engineering problems from mechanical, civil, biomedical, aeronautical, or automobile industries.

On successful completion of this module a student will be able to:

LO1 Apply a systematic understanding of knowledge and specialist theoretical and methodological approaches in the analysis of continuum mechanics of engineering systems subjected to loading.
LO2 Systemically synthesise complex problem-solving strategies for the formulation of the finite element method and how it can be applied to complex engineering problems.
LO3 Systematically and critically organise and apply advanced knowledge of finite element method towards solution of complex engineering mechanics problems.
LO4 Systematically and critically analyse and evaluate the validity of results generated from a finite element simulation of complex problems.

Computational mechanics and the finite element methods
Introduction to Engineering Mechanics; Computational mechanics; numerical methods; finite element methods; finite element solver types; finite element software.
Types of Finite Element Methods (FEM): Generalized FEM; XFEM; Spectral Methods; Meshfree Methods; Discontinuous Galerkin Method; Finite Element Limit Analysis.

Numerical skills for FE studies
Brief Introduction to MATLAB; Matrices; Equations of linear systems; programming; scripts; Python programming languages; object-oriented programming; Visualization of 2D and 3D data; Contour plotting.

Direct Stiffness Method
Discretization of a domain; Direct stiffness method; Displacement and Force matrix equations; member and structural stiffness matrix; Internal and external forces on members/bars/trusses.

FE solver design principles:
Principles of an FE Solver: Pre-processor; Simulation Engine; Post-processor; Plug-ins; Structural of typical FE keyword files; FE solver design based on the direct stiffness method.

FEM Modelling Principles: Geometry/Virtual domain design
Virtual domains; Converting physical domains to virtual domains; Representative volume elements; length scale effects on domain choice; Strategies for creating virtual domains for FE study; Quantifying suitability of chosen domain for FE study.

FEM Modelling Principles: Mesh
Finite element meshes; nodes; elements; element shapes and dimensions; classification of elements; meshing algorithms; meshing software; meshing strategies; mesh density; mesh convergence; choice of suitable mesh for a given study; Periodic and non-periodic meshes; aspect ratio of elements.
FEM Modelling Principles: The Mathematics of Element Formulation
1D linear elements; 2D elements; 3D elements; formulation for two-noded 1D linear elements; Strain-displacement matrix; element-level stiffness matrix; element formulation for 2D elements: quadrilaterals, triangles; element formulation for 3D elements: tetrahedra; hexahedra; Lagrangian element formulation.

FEM Modelling Principles: Loads and Boundary Conditions.
Boundary condition types: Dirichlet, Neuman, Robin and Periodic BCs; Mathematics of boundary conditions; Differences between loads and boundary conditions; Periodic Boundary conditions: influence of mesh types; Periodic and non-periodic meshes; Strategies for the implementation of periodic boundary conditions within FE solvers; multi-freedom constraints equations; Periodic boundary conditions and micromechanics; Comparison of the effect on model predictions of the four boundary conditions types.

Seminar & Practical/Hands-on sessions
Complex problems will be tackled during laboratory classes to ensure that students can translate the FE theory to the analysis of such complex real-life (practical) problems. Laboratory sessions will be based on practical problems that the module tutor has solved. Students will be encouraged to replicate the solution of the module tutor using different pedagogic approaches. The laboratory case-study scenario will be structured to focus on creating a link between the principles of the finite element methods and the practical skills needed in solving practical engineering problems.

Lecture
Principles of the Finite Element Method will be introduced in lectures. This is usually for the first two-hour slot where theories that define the FE process will be taught and demonstrated.

Group Study
Students will be put into groups and assigned projects (as part of the assessment expectation of the course) and encouraged to work in group, document their progress, reflect of their learning, and develop a group report of their original solutions to complex engineering problems. They will be given opportunities to present their findings to the class, assessed and reflected in a group study structure.

Self-directed learning
Students are encouraged to work on self-directed learning. This will be in the form of hands-on tutorial videos provided by the course tutor covering all aspects of the module (each dealing with a complex problem) and the students will be encouraged to attempt these tasks using a formative assessment structure. These videos will be taken outside the normal lecture or laboratory sessions so that students can self-direct their learning. Feedbacks will be provided generally and personally of progress made by the students.

Portfolio: 50% weighting, 50% pass mark.
Learning Outcomes: 1 - 4.
Outline Details: Individual case study report submitted with a Group report on solutions to a practical problem. 2000 words.

Coursework: 50% weighting, 50% pass mark.
Learning Outcomes: 1 - 4.
Outline Details: Take home coursework where student show answers to open-ended design-style questions. 1000 words.

Formative Assessment:
Tutorials, Observations,
Questioning, Discussion, Constructive Quizzes,
Practice Lab Report, case study activities