Standard syllabus
Finite element methods · Graduate · Engineering
Topics
Weak form and element formulations
- Calculus of variations and Euler-Lagrange equations
- Weighted residual methods: Galerkin approach
- Weak form derivation for Poisson and elasticity problems
- Shape functions for 1D and 2D elements
- Isoparametric mapping and numerical integration
- Element stiffness and mass matrix assembly
- Patch test and element completeness
- Locking phenomena: shear and volumetric
- Mixed formulations and reduced integration
- A priori and a posteriori error estimates (intro)
Solvers and nonlinear extensions
- Direct versus iterative linear solvers
- Preconditioning and sparse matrix storage
- Newton-Raphson for nonlinear equilibrium
- Material nonlinearities: plasticity intro
- Contact algorithms: penalty and Lagrange multipliers
- Large deformation and updated Lagrangian formulations
- Dynamic FE: Newmark time integration
- Eigenvalue solvers for modal analysis
- Adaptive mesh refinement strategies
- Parallel FE on HPC clusters
What each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Weak form and element formulations
Calculus of variations and Euler-Lagrange equations
Coming soon - Solvers and nonlinear extensions
Direct versus iterative linear solvers
Coming soon - Implementation and software development
Building a 1D/2D FE code in MATLAB or Python
Coming soon - Research applications
Biomechanics FE: tissue and implant modeling
Coming soon
Pricing calculator
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$1,162 · Finite element methods · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.