Holiday
ENG I工一 212 TnT5T6
To introduce advanced finite element methods (FEMs) for linear and nonlinear solid, mechanics, multi- field variational principles, total Lagrangian and updated Lagrangian formulations, nonlinear material models and numerical procedures for path independent (hyperelasticity) and path dependent (plasticity) problems. Optional topics includes FEMs for fluid flow problem and meshfree methods. Prerequisites: Finite Elements Methods, Linear Elasticity
Course keywords: Nonlinear Finite Element Method; Incompressible Material; Hyperelasticity; Elastoplasticity; FEniCS Course Description To introduce advanced finite element methods (FEMs) for linear and nonlinear solid, mechanics, multi-field variational principles, total Lagrangian and updated Lagrangian formulations, nonlinear material models and numerical procedures for path independent (hyperelasticity) and path dependent (plasticity) problems. Optional topics includes FEMs for fluid flow problem and meshfree methods. Prerequisites: Finite Elements Methods, Linear Elasticity Lecture Material In-class notes, and lecture handouts will be given. There is no required textbook for this course. However, textbooks in the reference are recommended. The FEniCS with Google Colab will be used as the simulation platform. Reference T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover, 2000. Belytschko, T., Liu, W. K., and Moran, B., and Khalil Elkhodary, "Nonlinear Finite Elements for Continua and Structures”, 2nd Edition, John Wiley & Sons, 2014. Finite Element in Computer Science (FEniCS): https://fenicsproject.org/ Evaluation Homework 30%; Computer Assignment 35%; Final Project 35% Use of the AI Conditionally open; please specify how generative AI will be used in course output Course Outline (Syllabus) 0. Fundamental Knowledge Strong form and Weak Form Galerkin Equation Basics of Finite Element Formulation Introduction to FEniCS, Google Colab and Paraview 1. Constrained Problems Numerical Difficulties in Nearly Incompressible and Incompressible Elasticity Volumetric Locking and Remedies Reduced Integration with Hourglass Stabilization, Selective Reduced Integration Reissner-Mindlin Plates and Shear Locking (Optional) Shear Locking and Remedies (Optional) 2. Multi-Field Variational Principles Hu-Washizu Variational Principle Hellinger-Reissner Variational principle Complementary Energy Principle Hybrid Stress Formulation Mixed (up) formulation for Incompressible Problems 3. Large Deformation Problems in Solid Mechanics Nonlinear solver: Newton Raphson methods Total and updated Lagrangian formulation History independent materials: hyperelasticity History dependent materials: plasticity Linearized buckling problems Contact problems 4. Finite Element Methods for Fluid Problems (Optional Topics) Advection-diffusion (AD) problem and its numerical difficulties Petrov-Galerkin formulation for AD problems Navier-Stokes equations Streamline upwind Petrov–Galerkin (SUPG) formulation Variational Multiscale Stabilization (VMS) formulation Arbitrary Lagrangian Eulerian method (ALE) for Fluid-Structure Interaction problem 5. Meshfree methods (Optional Topics) Moving Least-Squares Approximation Reproducing Kernel Approximation Galerkin Meshfree Methods for Solving PDEs
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Average Percentage 83.25
Std. Deviation 2.17
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