Finite Elements | Prof Terje Haukaas

LINEAR FINITE ELEMENT ANALYSIS: Notes; Computational Stiffness Method; Static Condensation, Settlements, Springs, Dependencies; Finite Element Concepts; Elements; Truss Elements; Euler Bernoulli Beam Elements; Timoshenko Beam Elements; Frame Elements with P Delta; Frame Elements with Stability Functions; Frame Elements in Torsion; 3D Linear Frame Elements; Q4 Elements in 2D Elasticity; M4 Elements for Plates; Examples; Stiffness vs Flexibility Matrix; Shear Wall Analysis; Beam with Rigid Part; Static Condensation; Python; getTrussStiffness2D(); getFrameStiffness2D(); getQuad4Stiffness2D(); assembleStiffnessMatrix(); Linear Static Structural Analysis (Screenshot) (Alternative input); OpenSees; OpenSees Linear Elastic Cantilever

COMPUTATIONAL 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)

PLASTICITY: Notes; Plastic Capacity Analysis by Hand; Computational Plastic Capacity Analysis; Stress-based Failure Criteria; Examples; Plastic Capacity Examples; Computational Plastic Capacity Analysis for a Frame; Python; Generic Plastic Capacity Analysis (Screenshot)

NONLINEAR FINITE ELEMENT ANALYSIS: Notes; Governing Equations and Solution Algorithms; Load Incrementation Strategies; Geometric Nonlinearity; Material Nonlinearity; Nonlinear Dynamic Analysis; Elements; Concentrated Plasticity Elements; Distributed Plasticity Elements; Truss Elements with Geometric Nonlinearity; Materials; Uniaxial Plasticity Material Model; Bouc-Wen Material Model; Examples; Buckling Modes for Two-storey Frame; Inelastic Stick Model with P-delta; Shallow Truss Snap-through; Python; Nonlinear 2DOF Load Control (Screenshot); Nonlinear 2DOF Displacement Control (Screenshot); MDOF Buckling Analysis (Screenshot)

G2: G2 is a Python code for nonlinear static and dynamic structural analysis. It originated with a Matlab code created by Professor Fenves for a course on nonlinear analysis that I took at UC Berkeley around the time OpenSees changed name from G3. Several modifications and a also extensions related to the direct differentiation method are introduced in the Python code posted here. You can view the G2 code in the links below, and you can download the full package here: G2.zip (updated April 4, 2024).; Elements; Element 1 (Linear elastic truss element); Element 2 (Truss element with path-dependent material); Element 3 (Truss element with moderate displacements); Element 5 (Linear elastic frame element); Element 6 (Frame element with P-delta); Element 7 (Concentrated plasticity frame element: Elastic-perfectly-plastic, i.e., end releases); Element 8 (Concentrated plasticity frame element: Two-component parallel system); Element 9 (Concentrated plasticity frame element: One-component series system with uniaxial materials); Element 10 (Concentrated plasticity frame element: Rigid interior with path-dependent hinge materials); Element 12 (Distributed plasticity frame element: Displacement-based); Element 13 (Distributed plasticity frame element: Force-based); Sections; Rectangular; Wide-flange; Uniaxial Materials; Bilinear; Plasticity; Bouc-Wen; Analysis Types; Linear Static; Linear Dynamic; Nonlinear Static; Nonlinear Dynamic; SDOF Nonlinear Dynamic; Auxiliary Files; Model; Quadrature; Examples; Example 1 (Response spectra); Example 2 (Ductility demand); Example 3 (Nonlinear static truss); Example 4 (Material visualizer); Example 5 (Material tester); Example 6 (Nonlinear static cantilever); Example 7 (Nonlinear static frame); Example 8 (P-M interation); Example 9 (Snap-through); Example 10 (Nonlinear dynamic SDOF); Example 11 (Nonlinear dynamic cantilever); Example 12 (Nonlinear dynamic high-rise); Example 13 (Static OpenSees comparison); Example 14 (Dynamic OpenSees comparison); Example 15 (Linear static with DDM); Example 16 (Linear dynamic with DDM); Example 17 (Finite element reliability analysis with FOSM and DDM); Ground Motions; El Centro; Read PEER Record; Half Sine Wave

OpenSees: OpenSees is an open-source software framework for nonlinear structural analysis, originating at UC Berkeley. It is a powerful tool that is popular in earthquake engineering. OpenSees is object-oriented and consists of many “classes” from which “objects” are instantiated at run-time. There are several ways to run OpenSees; you can compile an executable file yourself, you can use the OpenSeesPy interface for Python, which is done here, or you can use the old Tcl interface.; Examples; OpenSees Uniaxial Material Tester; OpenSees Nonlinear Static Cantilever; OpenSees Nonlinear Dynamic Frame; El Centro Ground Motion; OpenSeesPy (examples in external links); Nonlinear Truss Analysis; Nonlinear Frame Analysis; Moment Curvature Analysis; Nonlinear Dynamic Analysis; Portwood Digital (examples in external links); Patch Test; Load Patterns and Time Series; Constraint Types; Beam with Finite-length Plastic Region; Localization Problem; Timoshenko Beam; Shell Elements; Shell Mesh; Plotting Curvature along Element; Analysis of Cable; Eccentrically Loaded Bolt Group; Arc-length Load Incrementation Method; Geometric Nonlinearity; Hollow Steel Cross-sections; Circular Cross-section Fibre Mesh; Rectangular Cross-section Fibre Mesh; Axial-moment (P-M) Interaction; Section Aggregation; Torsion and Fibres; Hysteretic Pinching (I); Hysteretic Pinching (II); Concrete Material Models; Multi-directional Ground Motion; Modal Damping; Modal and Rayleigh Damping; Quick Modal Damping; Careful with Modal Damping; Incremental Dynamic Analysis (IDA)