Meng 4553 (3 Crd Hrs) Finite Element Method & Applications in Design

Displacement approach for simple elements in structural mechanics. Generalization to three-dimensional elements. Overview of the finite element method (FEM), variational principles, transformation, assembly, boundary conditions, solutions, convergence and stability. Isoparametric elements. Applications to solid mechanics, heat conduction and coupled problems. Pre- and post processing. Integration of FEM in Computer Aided Design.

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  Prerequisites: MENG 3505, ENGR 3202, CSCE 1001.
  

1. 
   Classify PDEs, and recognize elliptic BVPs in the abstract.
   
2. 
   Derive the associated weak form for a BVP, and anticipate its solution space (Sobolov spaces).
   
3. 
   Understand key approximation theory for V-elliptic weak forms (Galerkin method).
   
4. 
   Be aware, and make use, of a-priori error estimates.
   
5. 
   Create mesh-descriptive data structures to handle general BVPs by FEM (focus on linear triangles).
   
6. 
   Solve large FE systems by the Cholesky factorization method while leveraging sparsity.
   
7. 
   Solve large FE systems by the CG method, leveraging hierarchical bases and matrix sparsity.
   
8. 
   Be aware, and make use, of Error Indicators and Error Estimators a-posteriori.
   
9. 
   Adaptively refine meshes to improve solution accuracy (with application to singularities).
   
10. 
    Program on MATLAB simple FE applications of steady-state heat transfer (with inhomogeneity) and linear elasticity (with anisotropy).
    
11. 
    Exposure to realistic FE applications in design (thermal, elastic, thermo-elastic).
    
12. 
    Mastery of realistic integration of FE procedures with key CAD software.
    
13. 
    Ability to correct designs via theoretical-implementational considerations from the FE Lectures.
    
14. 
    Ability to correctly place FE within a team design’s “big picture”, and use it to fulfill a “true” need.