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Mechanics of Solids and Structures 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. The FE part (as well as recapping relevant FE theory) 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 beings with idealised geometries were 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.

Mandatory Entry Requirements

None

Recommended Entry Requirements

None

None

None

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;

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 problems;

■ develop Hertzian contact theory from simple elasticity solutions (point loading of an elastic half-space) and use it to solve various engineering analysis and design problems;

■ determine stress fields using a first principles equilibrium approach for a variety of symmetric stress analysis problems (membrane theory for stresses in thin solids of revolution, rotating discs and shafts, bending of thin circular plates etc.);

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

■ 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