Mechanics of Solids 4 looks at determining stress fields in solids using both theory and the finite element (FE) method and affords students the opportunity of comparing both approaches. The course divides equally between the theoretical and finite element approaches. The theoretical part of the course uses the theory of elasticity to determine elastic stress fields in idealised solids using both the stress function approach and a first principles equilibrium approach. It also includes some focus on applying the theory to suitable real world engineering problems where stresses need to be determined. The FE part (as well as recapping relevant FE theory from year 3) takes a decidedly practical and industry-orientated approach to solving 2D and 3D stress analysis problems and focuses on the steps a practicing FE engineer would follow in solving various types of problems. The FE work begins with idealised geometries where results are compared with theory and progresses towards more complex problems, which are not amenable to theoretical treatment.

3 lectures per week and 1 lab per week.

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50% Written Exam

50% Coursework Reports

The aims of this course are to:

■ equip students with the tools to solve stress analysis problems and determine stress fields in components using both theory and the finite element method;

■ encourage students to critically compare theoretical and computational approaches in stress analysis;

■ equip students with the relevant theory to solve elastic solid mechanics problems and apply this theory to practical engineering scenarios;

■ equip students with practical skills in various aspects of finite element analysis and enable them to solve a variety of idealised and real-world stress analysis problems.

By the end of this course, students will be able to:

■ determine stress fields using the theory of elasticity (stress function approach) for various simple 2D problems in Cartesian and polar coordinates;

■ describe the differences between the 'Strength of Materials' approach and the 'Theory of Elasticity' approach

■ understand Hertzian contact theory and use it to solve various real world engineering contact problems;

■ understand how to account for adhesion in contact mechanics problems (in particular, using the Johnson, Kendell and Roberts JKR approach) and understand the possible engineering and real world scenarios where adhesion is appreciable;

■ determine stress fields using a first principles equilibrium approach for a variety of symmetric stress analysis problems (in particular, to determine the stress fields in rotating discs and shafts);

■ use a commercial finite element (FE) package to solve both idealised and real-word (2D and 3D) stress analysis problems;

■ explain the fundamental finite element theory underpinning computational stress analysis solutions for 2D and 3D problems;

■ correctly account for practical finite element modelling considerations such as: software selection, geometry modelling, element selection, partitioning, material model, meshing approach and mesh convergence, boundary conditions and loading, contact scenarios, solution procedures and post-processing;

■ critically compare theoretical and computational approaches to solving solid mechanics problems;

■ assess the likelihood of failure in components where the stress field has been determined by either finite element analysis or theory.

Satisfactory attendance at lectures and attendance at degree examination

Students must attend the timetabled laboratory classes.