Advanced Finite Element Method for Solids
ME 65100/ 3 Cr.
This course is designed to teach students advanced non-linear finite element techniques for solid mechanics stress and heat transfer analysis. Those include techniques for modeling: 2D/3D continua; beams; plates; large rotations; geometric non-linearity; material non-linearity; material plasticity; heat transfer; modeling thermo-mechanical systems; frequency domain solutions; quasi-static solutions; time domain solutions; modeling of frictional contact; and modeling rigid-bodies. Applications of the modeling techniques taught in this course will be introduced. Those include: static and dynamic stress-analysis of mechanical components (such as gears, cams, chains and belts) with material and geometric non-linearity; modal analysis of mechanical components; metal forming and crashworthiness analysis.
Primary Track: Solid Mechanics & CAE, Materials
- Available Online: No
- Credit by Exam: No
- Laptop Required: No
TextbooksNonlinear Finite Elements for Continua and Structures, Belytschko, Liu, and Moran, Wiley, 2nd or later Edition
- Understand continuum mechanics principles including stress and strain measures.
- Understand tensor and indicial notation applied to continuum mechanics.
- Understand the governing partial differential equations for modeling beams, plates, 2D/3D solids, heat transfer in solids and thermo-mechanical modeling of solids.
- Understand element shape functions for 2D, 3D elements.
- Understand Gauss quadrature for performing surface and volume integrals for 2D and 3D finite elements.
- Derive the semi-discrete finite element equations for 2D/3D continua with geometric and material non-linearity using the Galerkin method.
- Derive the semi-discrete finite element equations for heat transfer and thermo-mechanical systems using the Galerkin method.
- Solve quasi-static governing equations for solids and heat transfer.
- Solve time-dependent equations of motion using implicit and explicit methods.
- Calculate the natural frequencies and mode-shapes for solid mechanics problems.
- Implement finite element techniques in computer programs.
- Linear Algebra Review
- Lagrangian and Eulerian Finite Element Methods
- Continuum Mechanics Review
- 1D, 2D and 3D finite Element shape functions
- Numerical Integration
- Heat Transfer in 1D, 2D, and 3D
- Nonlinear solid mechanics
- Thermo-mechanical modeling
- Solving systems of linear algebraic equations
- Transient Dynamics
- Contact and friction
- Rigid body dynamics
- Model analysis
- Mesh Generation
- Nonlinear fluid dynamic networks
- Electrical Networks
- Electrostatic problems