# AE40038: Nonlinear Finite Element Method

AE40038 | |
---|---|

Course name | Nonlinear Finite Element Method |

Offered by | Aerospace Engineering |

Credits | 3 |

L-T-P | 3-0-0 |

Previous Year Grade Distribution | |

{{{grades}}} | |

Semester | Spring |

## Contents

# Syllabus[edit | edit source]

## Syllabus mentioned in ERP[edit | edit source]

Prerequisites: AE40003 3 - 0 - 0: 3 CreditsSources of nonlinearities in structural problems: material, geometry, forces, boundary conditions; General features of nonlinear response: equilibrium trajectories, path dependencies, critical points, Geometrically nonlinear finite elements: residual and incremental forms. Finite element Total Lagrangian and corotational formulations, FEM nonlinear equilibrium equations: initial stress, tangent and secant stiffness, geometric stiffness; Solution of nonlinear equations: classification, incremental control techniques, augmented equation methods, incremental and pseudo-force methods, Newton Methods, Secant (quasi-Newton) methods, Acceleration and line search, dynamic relaxation, determination and transversal of critical points. Computer implementation: model definition, element level calculation, equation assembly, nonlinear equation solver, residual evaluation, post-processing, Nonlinear constitutive models, Applications to structural stability analysis and bifurcations, nonlinear static analysis and nonlinear transient problems (implicit vs. explicit time integration techniques), Treatment of constraints