Finite Elements

A long-term vision in structural engineering is that we can accurately simulate the behaviour of real structures on the computer. The “displacement-based” finite element method, an extension of the stiffness method for hand calculations, is the most influential approach. I cover the notes on linear finite element analysis in CIVL 435, after an introduction in CIVL 332. Nonlinear and dynamic analysis further down the page are important subjects when I teach CIVL 509. I also given an introduction to structural dynamics in CIVL 332. 


LINEAR ANALYSIS
Notes
Computational Stiffness Method
Finite Element Method
Elements
Truss Elements
Euler Bernoulli Beam Elements
Timosheno Beam Elements
Frame Elements with P Delta
Frame Elements in Torsion
3D Linear Frame Elements
Q4 Elements in 2D Elasticity
M4 Elements for Plates
Examples
Buckling Modes for Two-storey Frame
Shear Wall Analysis
Static Condensation
Python
getTrussStiffness2D()
getFrameStiffness2D()
getQuad4Stiffness2D()
assembleStiffnessMatrix()
Linear Static Structural Analysis (Screenshot) (Alternative input)
MDOF Buckling Analysis (Screenshot)
CROSS-SECTION ANALYSIS
Notes
Computational Cross-section Analysis
Elements
T3 Elements in Torsion
Python
Thin-walled Cross-section Analysis (Screenshots)
Solid Cross-section Analysis (Screenshots)
NONLINEAR ANALYSIS
Notes
Governing Equations and Solution Techniques
Geometric Nonlinearity and the Snap-through Problem
Characteristics of Material Behaviour
Examples
Inelastic Stick Model with P-delta
Elements
Nonlinear Frame Elements
Frame Element with Concentrated Hinges
Truss Element with Geometric Nonlinearity
Frame Element with Geometric Nonlinearity
Python
G2 Examples (Screenshot)
G2 Linear Analysis
G2 Simple Newton-Raphson
G2 Model Class
G2 Element 1 Class
G2 Element 2 Class
G2 Element 3 Class
G2 Element 5 Class
G2 Element 12 Class
G2 Element 13 Class
G2 Element 15 Class
G2 Wide-Flange Section Class
G2 Bilinear Material Class
G2 Uniaxial Plasticity Class
G2 Uniaxial Material Tester (Screenshot)
G2 Quadrature
DYNAMIC ANALYSIS
Notes
Multi-Degree-of-Freedom Dynamics
Mass Matrix for Truss and Frame Elements
Time-stepping Algorithms
Examples
Modes of Vibration for Two-storey Frame
Python
probabilisticGroundMotion()
MDOF Dynamic Analysis with Probabilistic Ground Motion (Screenshot)