## Nonlinear Structural Analysis (CI3-333)

### Module aims

• To present systematic procedures for geometric and material nonlinear structural analysis.
• To introduce and encourage the use of advanced nonlinear analysis software and to explore the significance of common nonlinear phenomena, particularly in relation to the structural response under extreme events.

### Learning outcomes

On successfully completing this course unit, students will be able to:

• Distinguish between linear and nonlinear structural analysis.
• Recognise types of problem for which nonlinear structural analysis is necessary.
• Understand principles of stability for multi-degree of freedom structural systems.
• Appreciate the basis of sophisticated and simplified buckling analysis methods.
• Use equilibrium paths to characterise the nonlinear structural response.
• Understand basic incremental iterative solution procedures for tracing equilibrium paths.
• Appreciate the fundamentals of nonlinear finite element discretisation, including geometric and material nonlinearity.
• Appreciate the use of hierarchic processes in tackling complex problems.
• Recognise the role of analogies in gaining greater understanding.
• Use nonlinear structural analysis software.
• Perform simplified buckling analysis.
• Use computers for simulations.
• Solve a nonlinear system of equations.
• Apply techniques of linear algebra.

### Module syllabus

• Fundamentals of geometric nonlinearity for discrete structural systems.
• Principles of stability and buckling analysis for discrete structural systems.
• Nonlinear solution procedures for tracing equilibrium paths.
• Geometrically nonlinear finite elements for one-dimensional structural systems.
• Materially nonlinear finite elements for one-dimensional structural systems.
• Nonlinear dynamic analysis of discrete structural systems (only MSc).
 No. Topic Staff 01 Lecture: Fundamentals of geometric nonlinearity for discrete structural systems. BAI 02 Lecture: Principles of stability and buckling analysis for discrete structural systems BAI 03 Lecture: Principles of stability and buckling analysis for discrete structural systems Tutorial BAI 04 Lecture: Principles of stability and buckling analysis for discrete structural systems Tutorial BAI 05 Lecture: Nonlinear solution procedures for tracing equilibrium paths Computer lab BAI 06 Lecture: Geometrically nonlinear finite elements for one-dimensional structural systems Project BAI 07 Lecture: Materially nonlinear finite elements for one-dimensional structural systems Project Computer lab BAI 08 Lecture: Materially nonlinear finite elements for one-dimensional structural systems Project BAI 09 Lecture: Nonlinear dynamic analysis of discrete structural systems Project Computer lab BAI 10 Lecture: Nonlinear dynamic analysis of discrete structural systems Project Computer lab BAI

### Teaching methods

Handouts are provided for the various topics, and extensive use is made of the visualiser to elaborate on concepts and application issues. All material, including handouts, visualiser lecture notes and solutions to tutorial problems, are placed on Blackboard for student access. Computer laboratory sessions are also provided making use of screen projection to introduce finite element analysis software.

### Assessments

Assessment will be via written examination and project coursework, with respective marks split of 70:30.