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Description
Fundamentals of finite-element modelling and analysis: energy method (variational formulation), Galerkin weak formulation, choice of elements and shape functions (conformity, accuracy, efficiency); mesh generation; isoparametric elements; time-stepping methods (implicit methods, explicit methods, stability); finite-difference approximation of differential equations; applications to 1D and 2D models taken from various areas of engineering: structural mechanics and dynamics (beams, frames, torsion, plates, membranes, vibration), heat/fluid flow, soil mechanics, etc.; nonlinear problems; limitations of finite-element approximation: shear and membrane locking, reduced integration, hourglassing; use of finite-element software. The module is self-contained and the only background required is simple linear algebra.
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Learning Outcomes
- Knowledge of how to discretise one- and two-dimensional structures using different kinds of finite elements, how to assemble elements and how to solve the resulting equations (statics and dynamics and including nonlinear problems)
- Knowledge of how to obtain approximate solutions to boundary-value problems using the Galerkin and energy methods
- Knowledge of limitations of finite-element approximations such as shear and membrane locking, reduced integration, hourglassing and nonconformity of finite-element meshes
- Knowledge of time-stepping methods for the numerical integration of ordinary differential equations obtained by finite-element discretisation - implicit, explicit methods and stability
- Understanding the concept of natural frequency, natural mode shape and resonance in multi-degree-of-freedom systems
- Understanding of how modern software packages can be used for finite-element modelling, with emphasis on how their output can be used in seismic design
- Knowledge of applications to bars, beams, frames, torsion, heat flow, fluid flow, membranes, plates
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 8th April 2024.
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