Course 21 | Advanced Engineering Methods
Finite Element Methods
Turn mechanics and numerical methods into checked structural and thermal simulations.
Course snapshot
- Purpose
- Integrates mechanics and numerical methods into checked stress, deformation, heat, vibration, and validation work.
- Prerequisites
- Related advanced methods
- Used in Career Directions
Choose later
How to study this course
- Define the physical problem
- Choose idealization
- Assign material and boundary conditions
- Mesh responsibly
- Solve
- Compare with a hand estimate
- Check convergence and stress interpretation
How this course is designed
Original course map
This course uses an original MechCompass module order using prerequisite logic, standard engineering practice, and evidence tasks. Suggested references are optional and listed separately.
Stiffness, assembled
Almost everything is one idea applied again: write an element stiffness matrix, assemble the elements into a global K, apply boundary conditions, and solve Ku = F. Each module is a new element.
Always a hand check
FEA is only as good as its validation. Every module pairs the matrix result with a closed-form benchmark, so a colorful contour is never trusted on its own.
The 10 modules
01 | Module
Introduction to the Finite Element Method
What FEM is, the general steps, and the element stiffness idea.
02 | Module
The Direct Stiffness Method: Spring Elements
Assembling element matrices, applying boundary conditions, and solving Ku = F.
03 | Module
Bar and Truss Elements
The bar stiffness AE/L, coordinate transformation, and member forces.
04 | Module
Beam Elements
The 4-by-4 beam stiffness matrix and bending deflections.
05 | Module
Shape Functions and Interpolation
Interpolation, natural coordinates, and the properties shape functions must have.
06 | Module
Plane Stress and the Constant-Strain Triangle
Two-dimensional elasticity, the CST element, and the B and D matrices.
07 | Module
Isoparametric Formulation and Gauss Quadrature
Mapped elements, the Jacobian, and numerical integration.
08 | Module
Finite Elements for Heat Transfer
The conductance matrix and solving for temperatures and heat flow.
09 | Module
Dynamics and Modal Analysis
The mass matrix and natural frequencies from an eigenvalue problem.
10 | Module
Convergence, Errors, and Modeling
Mesh refinement, error, equilibrium checks, and validation.