Lagrange Multipliers

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This command is used to construct a LagrangeMultiplier constraint handler, which enforces the constraints by introducing lagrange multiplies to the system of equation. The following is the command to construct a plain constraint handler:

constraints Lagrange <$alphaS $alphaM >

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$alphaS	<math>\alpha_S</math> factor on singe points. optional, default = 1.0
$alphaM	<math>\alpha_M</math> factor on multi-points, optional default = 1.0;

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NOTES:

• The lagrange multiplier method introduces new unknowns to the system of equations. The diagonal part of the system corresponding to these new unknowns is 0.0. This ensure that the system IS NOT symmetric positive definite.

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THEORY:

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Code Developed by: fmk

• Command_Manual
  • Tcl Commands
  • Modeling_Commands
    • model
    • uniaxialMaterial
    • ndMaterial
    • frictionModel
    • section
    • geometricTransf
    • element
    • node
    • sp commands
      • fix
      • fixX
      • fixY
      • fixZ
    • mp commands
      • equalDOF
      • rigidDiaphragm
      • rigidLink
    • timeSeries
    • pattern
    • mass
    • block commands
      • block2D
      • block3D
    • region
    • rayleigh
  • Analysis Commands
    • constraints Command
    • numberer Command
    • system Command
    • test Command
    • algorithm Command
    • integrator Command
    • analysis Command
    • eigen Command
    • analyze Command
  • Output Commands
    • recorder
    • record
    • print
    • printA
    • logFile
    • RealTime_Output_Commands
  • Misc Commands
    • eleResponse Command
    • getTime Command
    • getEleTags Command
    • getNodeTags
    • loadConst Command
    • nodeCoord Command
    • nodeDisp Command
    • nodeVel Command
    • nodeAccel Command
    • nodeEigenvector Command
    • nodeBounds
    • print Command
    • remove Command
    • reset Command
    • testIter
    • testNorms
    • wipe Command
    • exit Command
  • DataBase Commands
    • Template:DataBaseCommandsMenu

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This command is used to construct a Penalty constraint handler, which enforces the constraints using the penalty method. The following is the command to construct a plain constraint handler:

constraints Penalty $alphaS $alphaM

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$alphaS	penalty <math>\alpha_S</math> factor on single point constraints
$alphaM	penalty <math>\alpha_M</math> factor on multi-point constraints

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NOTES:

• The degree to which the constraints are enforced is dependent on the penalty values chosen. Problems can arise if these values are too small (constraint not enforced strongly enough) or too large (problems associated with conditioning of the system of equations).

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THEORY:

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Code Developed by: fmk