Analysis

Understanding the Analysis Component

The Analysis component is a core part of the Femora library that manages the configuration and execution of OpenSees analyses. It implements a comprehensive system for defining and controlling various types of structural analyses, including static, transient, and variable transient analyses.

The Analysis component combines several key subcomponents to define how an analysis is performed: - Constraint Handler: Manages how constraints are handled in the analysis - Numberer: Determines the equation numbering scheme - System: Defines the system of equations to be solved - Algorithm: Specifies the solution algorithm - Test: Defines the convergence criteria - Integrator: Controls the time integration scheme

Accessing the Analysis Component

There are two ways to access the Analysis component in your code:

1. Direct Access: Import and use the AnalysisManager class directly

   from femora.components.Analysis.analysis import AnalysisManager
   
   # Get the singleton instance
   analysis_manager = AnalysisManager()
   
   # Use the analysis manager directly
   analysis_manager.create_analysis(...)
   

2. Through Femora (Recommended): Access via the Femora class’s .analysis property

   import femora as fm
   
   # Create a Femora instance
   
   
   # Access the AnalysisManager through the .analysis property
   fm.analysis.create_analysis(...)
   

The second approach is recommended as it provides a unified interface to all of Femora’s components and ensures proper initialization of all dependencies.

How Analysis Works

The Analysis component provides several key capabilities:

1. Analysis Creation: Creates analysis objects of various types with appropriate parameters

2. Analysis Tracking: Keeps track of all analyses by both tag and name

3. Analysis Management: Provides methods to retrieve, update, and delete analyses

4. TCL Generation: Converts analysis configurations to OpenSees TCL commands

When an analysis is created, the Analysis component:

1. Validates that all required components are present and compatible

2. Assigns a unique numeric tag automatically

3. Registers it with the user-provided name (which must be unique)

4. Validates that all required parameters are present and valid for the analysis type

Note

Each analysis must have a unique name. The Analysis component uses this name as a key to retrieve analyses later. If you try to create an analysis with a name that already exists, the Analysis component will raise an error.

Analysis Types

The Analysis component supports three main types of analyses:

1. Static Analysis - Used for static loading conditions - Requires number of steps parameter - Uses static integrators

2. Transient Analysis - Used for dynamic loading conditions - Requires time step (dt) parameter - Can use either number of steps or final time - Uses transient integrators

3. Variable Transient Analysis - Used for dynamic loading with adaptive time stepping - Requires time step parameters (dt, dt_min, dt_max) - Requires desired iterations per step (jd) - Uses transient integrators

Analysis Components

Each analysis requires six key components:

1. Constraint Handler - Manages how constraints are handled in the analysis - Available types: Plain, Lagrange, Penalty, Transformation

2. Numberer - Determines the equation numbering scheme - Available types: Plain, RCM, AMD

3. System - Defines the system of equations to be solved - Available types: BandGeneral, BandSPD, ProfileSPD, SparseGeneral, SparseSPD

4. Algorithm - Specifies the solution algorithm - Available types: Newton, ModifiedNewton, KrylovNewton, BFGS, Broyden

5. Test - Defines the convergence criteria - Available types: NormDispIncr, NormUnbalance, EnergyIncr

6. Integrator - Controls the time integration scheme - Static types: LoadControl, DisplacementControl - Transient types: Newmark, HHT, CentralDifference

AnalysisManager API Reference

Analysis Creation

Creating analyses is one of the primary functions of the AnalysisManager. There are two main approaches:

1. Default Analysis Creation - Creates a pre-configured analysis with default components - Useful for quick setup of common analysis types

2. Custom Analysis Creation - Allows full control over all analysis components and parameters - Required for specialized or complex analyses

Example of creating a custom analysis:

from femora.components.Analysis.analysis import AnalysisManager
from femora.components.Analysis.constraint_handlers import PlainHandler
from femora.components.Analysis.numberers import PlainNumberer
from femora.components.Analysis.systems import BandGeneral
from femora.components.Analysis.algorithms import Newton
from femora.components.Analysis.convergenceTests import NormDispIncr
from femora.components.Analysis.integrators import LoadControl

# Get the analysis manager
analysis_manager = AnalysisManager()

# Create components
constraint_handler = PlainHandler()
numberer = PlainNumberer()
system = BandGeneral()
algorithm = Newton()
test = NormDispIncr(1.0e-6, 10)
integrator = LoadControl(1.0)

# Create the analysis
analysis = analysis_manager.create_analysis(
    name="my_static_analysis",
    analysis_type="Static",
    constraint_handler=constraint_handler,
    numberer=numberer,
    system=system,
    algorithm=algorithm,
    test=test,
    integrator=integrator,
    num_steps=10
)

Available Analysis Components

• Integrators
  • Static Integrators
    • LoadControl Integrator
    • DisplacementControl Integrator
    • ParallelDisplacementControl Integrator
    • MinUnbalDispNorm Integrator
    • ArcLength Integrator
  • Transient Integrators
    • Newmark Integrator
    • TRBDF2 Integrator
    • CentralDifference Integrator
    • HHT Integrator
    • GeneralizedAlpha Integrator
    • ExplicitDifference Integrator
    • PFEM Integrator

• Constraint Handlers
  • Plain constraint handler
  • Transformation constraint handler
  • Penalty constraint handler
  • Lagrange constraint handler
  • Auto constraint handler
• Equation Numberers
  • Plain Numberer
  • RCM Numberer
  • AMD Numberer
  • Parallel RCM Numberer
• System Solvers
  • Full General System
  • Band General System
  • Band SPD System
  • Profile SPD System
  • SuperLU System
  • UMFPACK System
  • MUMPS System
• Solution Algorithms
  • Linear Algorithm
  • Newton Algorithm
  • Modified Newton Algorithm
  • Newton Line Search Algorithm
  • Krylov Newton Algorithm
  • Secant Newton Algorithm
  • BFGS Algorithm
  • Broyden Algorithm
• Convergence Tests
  • Norm Disp Incr Convergence Test
  • Norm Unbalance Convergence Test
  • Energy Incr Convergence Test
  • Relative Norm Disp Incr Convergence Test
  • Relative Norm Unbalance Convergence Test
  • Relative Energy Incr Convergence Test
  • Relative Total Norm Disp Incr Convergence Test
  • Relative Total Norm Unbalance Convergence Test
  • Relative Total Energy Incr Convergence Test
  • Fixed Num Iter Convergence Test
  • NormDispAndUnbalance Convergence Test
  • Norm Disp Or Unbalance Convergence Test

Each analysis component type has its own documentation page with detailed parameter descriptions and usage examples.