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)
- Week01-CIVIL449-Revision Matrix Structural Analysis U1 (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-CIVIL449-Truss Frame Zero Length Elements U1 (File)
- 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 U2 (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)
- 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)
- Assignment #2: Nonlinear analysis of planar structures - Solution (File)
- Assignment #2: MATLAB code (Folder)
- Assignment #2: Python code (Folder)
- 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-Contro 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)
- 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)
- Assignment #3: Nonlinear analysis of planar structures - Solution (File)
- Assignment#3: MATLAB Code (Folder)
- Assignment #3: Python Code (Folder)
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)
Topics: Constitutive models based on continuum damage mechanics (CDM):
In-class assignment:
Assignment 04:
- General concepts in CDM
- Isotropic CDM model
- Orthotropic CDM model with and without irreversible strains
- Combination of continuum damage mechanics and plasticity models
In-class assignment:
- Euler forward return mapping
Assignment 04:
- Euler forward return mapping (non-associated flow)
- Euler backward return mapping (associated flow)
- Q & A week #13 (Forum)
- CIVIL 449 - Week 13 - Isotropic damage models (File)
- CIVIL 449 - Week - 13: Orthotropic damage models (File)
- In-class exercise: Euler forward return mapping (File)
9 December - 15 December
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
- Q & A week #14 (Forum)
- CIVIL 449 - Week 14 Smeared crack approach (File)
- CIVIL 449 Week 14 Mesh dependency (File)
- CIVIL 449 - Week 14 Application examples of constitutive models (File)
Provides an overview on case studies that use nonlinear analysis including the results from previous blind analysis contests as well as projects that benefitted from nonlinear analysis.
- CIVIL 449 - Week15 - Case Studies (File)
- Q & A week #15 (Forum)
- Exam 2019 (File)
- Exam 2019 Solution (File)
- CIVIL 449 - Week 15 - Modelling strategies for URM (File)