This module will provide you with an introduction to the principles of machine learning in healthcare and biomedicine, covering the key concepts involved in...

Machine Learning in Healthcare and Biomedicine (CHME0016)

FINITE ELEMENTS|GALERKIN APPROXIMATION|ENERGY METHOD|SHAPE FUNCTIONS|STIFFNESS MATRIX|MASS MATR

Fundamentals of finite-element modelling and analysis: energy method (variational formulation), Galerkin weak formulation, choice of elements and shape...

Finite-Element Modelling and Numerical Methods (CEGE0038)

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.

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