Nonlinear analysis of structures
CIVIL-449
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Introduction
- Introduction to course
- Revision: Matrix structural analysis (direct stiffness method)
- Week01-CIVIL449-Introduction (File)
- Weeks-01-02-CIVIL449-Revision-Truss-Frame Zero Length Elements (File)
- 01-In Class Exercise: Matrix Structural Analysis (File)
- 01-In Class Exercise-Suggested Solution (File)
- Q & A Week#1 (Forum)
- Assignment#1-Analysis of elastic structures - Solution (File)
- Assignment#1-Source Code-MATLAB (Folder)
- Assignment#1-Source Code-Python (Folder)
- Formulation of basic static equilibrium in matrix form
- Static decomposition
- Solution of linear problems
- 02-In Class Exercise-Matrix Structural Analysis Programming (File)
- 02-CIVIL-449-Matrix Structural Analysis Programming Solution (File)
- Q & A Week#2 (Forum)
- Truss elements
- Frame (beam-column) elements
- Zero-length elements
- Local to global coordination transformations
- Code number technique for assembling the global stiffness matrix
- 03-In Class Exercise-Truss Frame ZeroLength Elements (File)
- 03-CIVIL-449-Truss Frame ZeroLength Elements Solution (File)
- Q & A Week#3 (Forum)
- Nonlinear geometric effects
- Geometric stiffness matrix
- Limit load analysis
- Basic reference systems for frame elements
- Formulations for linear and corotational transformations
- Week04 & 05-CIVIL449-NonlinearGeometry U3 (File)
- 04-In Class Exercise-Geometric Stiffness Matrix (File)
- 04-In Class Exercise-Geometric Stiffness Matrix Solution (File)
- Q & A Week#4 (Forum)
- Source Code: Example on Slide21 (File)
- Source Code: Example on Slide23 (File)
- Assignment #2: Nonlinear analysis of planar structures - Solution (File)
- Assignment #2: Python code (Folder)
- Assignment #2: MATLAB code (Folder)
- Reading Material#1-Yaw-Corotational Transformation 2D Elements (File)
- Reading Material#2-Battini-Corotational beam elements in instability problems (File)
- Iterative techniques for solution of nonlinear equations
- Incremental approach to equilibrium
- Load-displacement constraint methods
- Weeks 05 & 06-CIVIL449-Iterative_Solution_Techniques U2 (File)
- 05-In Class Exercise-IterativeTechniques (in class programming exercise) (File)
- 05-In Class Exercise-IterativeTechniques Solution (File)
- Source Code: Week5-InClass Exercise: Exo1a (File)
- Source Code: Week5-InClass Exercise: Exo1b (File)
- Source Code: Week5-InClass Exercise: Exo2a (File)
- Source Code: Week5-InClass Exercise: Exo2b (File)
- Q & A Week#5 (Forum)
- Displacement control
- Arc-length control
- Analytical examples for demonstrating the use of control methods
- 06-In Class Exercise-Control Methods (in class programming exercise) (File)
- 06-In Class Exercise-Control Methods Solution (File)
- Source Code: Week6-InClass Exercise: Exo1a (File)
- Source Code: Week6-InClass Exercise: Exo1b (File)
- Q & A Week#6 (Forum)
- Reading Material#1-Poliotti et al-2017-Implementation Unified Library of Solvers (File)
- Reading Material#2-Ramm-1981-Strategies for Tracing Nonlinear Response (File)
- Reading Material#3-Vasios-2015-Implementation of Arc Length Method (File)
- Study Break
- Material nonlinearity
- Constitutive formulations for concentrated plasticity models
- Assessment models for steel and reinforced concrete members
- Week08-CIVIL449-Material Nonlinearity and Concentrated Plasticity (File)
- Week08-CIVIL449-Material Nonlinearity and Concentrated Plasticity Solution (File)
- Source Code: Week8-InClass Exercise: Exo2 (File)
- Source Code: Week8-InClass Exercise: Exo3 (File)
- 08-CIVIL-449-Resistance Models (in-class exercise on resistance models) (File)
- 08-CIVIL-449-Concentrated Plasticity (in-class calculation and programming exercise) (File)
- 08-CIVIL-449-Resistance Models solution (File)
- Assignment #3: Nonlinear analysis of planar structures - Solution (File)
- Assignment#3: MATLAB Code (Folder)
- Assignment #3: Python Code (Folder)
- Q & A week #8 (Forum)
- Reading Material#1: Steel column modelling - Lignos et al. - 2019 (File)
- Reading Material#2: Steel beam modelling - Lignos et al. - 2011 (File)
- Reading Material#3: RC member modelling - Haselton et al. - 2008 (File)
- Reading Material#4: RC member modelling - Panagiotakos and Fardis - 2001 (File)
- Distributed plasticity
- Basic element formulations
- Constitutive formulations for steel materials
- Constitutive formulations for reinforced concrete
- Cross-sectional analysis
- Week09-CIVIL449-Distributed Plasticity Constitutive Formulations (File)
- Q & A week #9 (Forum)
- Reading Material#1: Hartloper et al. - 2021 - Constitutive Modeling of Structural Steels (File)
- Reading Material#2: Hartloper et al. - 2023 - Uniaxial Cyclic and Tensile Tests Steels (File)
- Reading Material#3: Mander-1988 - Theoretical Stress‐Strain Model for Confined Concrete (File)
Discusses element formulations for fiber-based elements.
- Displacement-based elements
- Force-based elements
- State determination of sections
- Week10-CIVIL449-Section Analysis Element Formulations U2 (File)
- Week10-CIVIL-449-Section Analysis of Displacement based Elements (File)
- Week10-CIVIL-449-Section Analysis of Displacement based Elements-Solution (File)
- Q & A week #10 (Forum)
- Reading Material#1: Taucer et al. - 1991 - Fiber-based Beam Column Elements (File)
- Reading Material#2: Constraint Transformations (File)
- Week10-CIVIL-449-Displacement based Elements (File)
Discusses Integration methods for element formulations
- Gauss quadrature
- Gauss Lobatto
- Gauss Radau
- Element stiffness matrix and force vectors
- Examples for element stiffness matrix assembly
- Examples on tapered elements
- Week11-CIVIL449-Integration Methods U2 (File)
- Week11-CIVIL-449-Numerical Integration (File)
- Week11-CIVIL-449-Sectional Analysis (File)
- Week11-CIVIL-449-Sectional Analysis Solution (File)
- Week11-CIVIL-449-Numerical Integration solution U1 (File)
- Week11-CIVIL449-Enforcement Constraints (File)
- Source Code: Week11-InClass Exercise (File)
- Q & A week #11 (Forum)
Topics: Constitutive models based on plasticity:
- Overview of idealized material models
- Concept of yield surface
- Theory of plasticity - Formulation
- Euler Forward incremental method (Explicit)
- Euler Backward incremental method (Implicit)
- Euler forward return mapping
- Euler forward return mapping (non-associated flow)
- Euler backward return mapping (associated flow)
- CIVIL 449 - Week 12 - Plasticity based constitutive models (File)
- Q & A week #12 (Forum)
- In-class exercise: Euler forward return mapping (File)
9 December - 15 December
Topics: Constitutive models based on continuum damage mechanics (CDM):
- General concepts in CDM
- Isotropic CDM model
- Orthotropic CDM model with and without irreversible strains
- Combination of continuum damage mechanics and plasticity model
- Constitutive models based on the smeared crack approach
- Q & A week #13 (Forum)
- CIVIL 449 - Week 13 - Isotropic damage models (File)
- CIVIL 449 - Week - 13: Orthotropic damage models (File)
- CIVIL 449 - Week 14 Smeared crack approach (File)
Topics:
- Constitutive models based on the smeared crack approach
- Concepts of mesh size and directional dependency
- Application examples of constitutive models in continuum finite element approaches
- CIVIL 449 Week 14 Mesh dependency (File)
- CIVIL 449 - Week 14 Application examples of constitutive models (File)
- Q & A week #14 (Forum)