Finite Element Methods in Engineering

Trusses: element and global geometries

Mathematical Foundations: overview of finite-elements in one dimension, weighted residuals, Galerkin method and weak form, shape and weight functions, one-dimensional elements, time-dependent problems, applications to heat transfer and mechanics

Two-dimensional Problems: review of 2D heat transfer and mechanics, 2D elements, linear and quadratic, rectangular and triangular elements, practical - 2D heat flow

Three-dimensional problems: review of 3D mechanics, 3D elements, grid generation, solution singularities, modelling failure, practical – 3D mechanics

Introduction to Design Optimisation: the design cycle; design as an optimisation process; objective and constraints; gradient-based versus heuristic methods; multi-objective problems

Hydrocodes: background, Lagrangian and Eulerian approaches, time-integration, artificial viscosity, methods for material contact and large deformations, overview of material and explosive modelling, applications, practical – impact problem

Material modelling: stress-strain relations, equations of state, case studies

Dynamic Problems: finite element methods to determine natural frequencies.