The module will provide a holistic understanding of the advanced analytical methods and computational approaches used in the analysis of solids. This module builds on the solid mechanics syllabus delivered before the third year. It will provide you with a sound understanding of elasticity theory, plastic deformation, failure criterions and its application to stress analysis. The module will introduce you to the application of numerical methods, including the finite difference and finite element method applicable for solving linear partial differential equations, particularly for stress analysis in solids. 

• LO1. Apply basic elasticity theory and use stress functions to solve plane problems. (AHEP4 C1/M1)

• LO2. Analyse torsion problems involving non-circular bars and tubes both analytically and using a numerical method. (AHEP4 C2/M2) 

• LO3. Evaluate plastic yielding and predict stress distributions in pressure vessels using appropriate yield criteria. (AHEP4 C1/M1, C2/M2) 

• LO4. Apply fundamental numerical methods, such as finite difference and finite element techniques, to analyse stress and displacement in structural systems. (AHEP4 C2/M2) 

The Engineering Council sets the overall requirements for the AHEP (Accreditation for Higher Education Programmes). It is the standard used by the UK engineering profession to assess the competence and commitment of individual engineers and technicians and is in its 4th iteration. Link: ahep-fourth-edition

The module will be delivered through a blend of face-to-face teaching (such as lectures, guided study, tutorials, and formative feedback sessions), and online learning material (such as recorded lectures, quizzes, numerical examples and sample tutorial problems). These are used to elucidate the fundamentals and application of solid mechanics theory to a wide range of interesting problems, with emphasis throughout on real engineering configurations. 

A comprehensive set of tutorial sheets is issued, designed to develop your understanding and firm confidence in applying the knowledge gained during the course. Successful completion of the tutorial sheets is of crucial importance in helping you achieve all the intended learning outcomes of the module. 

Throughout the module, you will develop your academic skills in independent and critical thinking. You will need to: 

• Recognise and comprehend the essential nature of a particular solid mechanics problem; 

• Choose and successfully apply appropriate methods for obtaining stresses and deformations in real engineering situations. 

Professional & Practical Skills (AHEP4): 

• C1: Apply knowledge of mathematics, statistics, natural science and engineering principles to the solution of complex problems. Some of the knowledge will be at the forefront of the particular subject of study. 
  • M1 Apply a comprehensive knowledge of mathematics, statistics, natural science and engineering principles to the solution of complex problems. Much of the knowledge will be at the forefront of the particular subject of study and informed by a critical awareness of new developments and the wider context of engineering. 
• C2 Analyse complex problems to reach substantiated conclusions using first principles of mathematics, statistics, natural science and engineering principles 
  • M2 Formulate and analyse complex problems to reach substantiated conclusions. This will involve evaluating available data using first principles of mathematics, statistics, natural science and engineering principles, and using engineering judgment to work with information that may be uncertain or incomplete, discussing the limitations of the techniques employed. 

Transferable/Employability Skills (Graduate Attributes): 

• Collaboration Skills: 
  • C1: Contribute positively and effectively when working in a team, having an impact from the outset 
  • C2: Demonstrate enthusiasm and the ability to motivate themselves, and positively influence others in meeting agreed responsibilities 
• Effective Communicators: 
  • EC2: Communicate complex ideas effectively to diverse audiences 
  • EC3: Contribute to discussions, negotiate and present with impact 
• Ethically, socially and environmentally aware: 
  • ESEA1: Consider own personal and professional ethical, social and environmental responsibilities, and act as global citizens 
  • ESEA5: Be mindful of the Climate Emergency and the UN’s Sustainable Development Goals 
• Independent and critical thinkers 
  • ICT1: Identify, define and analyse complex issues and ideas, exercising critical judgement in evaluating sources of information 
  • ICT3: Investigate problems and offer effective solutions, reflecting on and learning from successes and failures 
• Innovative, enterprising and commercially aware: 
  • IECA1: Generate original ideas and apply creative, imaginative and innovative thinking in response to identified needs and problems 
• Reflective & Resilient 
  • RR1: Actively reflect on own studies, achievements and self-identity 
  • RR2: Demonstrate resilience, adaptability and creativity in dealing with challenges, and be open to change 

Summative assessment 

The module is assessed through a written examination (LO 1-4) scheduled during the Spring Semester Examination Period.   

Formative Assessment 

Formative assessment is provided through tutorials which are delivered throughout the module.  

THE OPPORTUNITY FOR REASSESSMENT IN THIS MODULE: 

The re-assessment for this module will consist of a 2-hour written examination.  

Opportunities for re-assessment are 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 the 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. 

Equations of Elasticity:, 

Plane Stress and Plane Strain: 

Two-dimensional Problems in Cartesian Coordinates:  

Problems in Polar Coordinates: 

Stress at a point (3D): 

Torsion of Prismatic Bars and Tubes: 

Deformation Beyond the Elastic Limit: 

Pressure Vessels: 

The Finite Difference Method for linear PDEs: 

Introduction to the Finite Element Method in Elasticity: