Purdue School of Engineering and Technology

Purdue School of Engineering and Technology

Advanced Finite Element Method for Solids

ME 65100 / 3 Cr. (3 Class)

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.  

T. Belytschko, W.K. Liu, and B. Moran, Nonlinear Finite Elements for Continua and Structures, 2nd Edition, John Wiley & Sons. And/or  Nam-Ho Kim, Introduction to Non-Linear Finite Element Analysis.  Springer.

ANSYS and LSDYNA  will be used.

After completion of this course, the students should be able to:

  • 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