# DDM-Based Response Sensitivity Computation Tcl Commands:
Created by: Quan Gu (Xiamen University, China), Joel P. Conte (UCSD), Michele
Barbato (LSU), Yong Li (UCSD)
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Sensitivity Analysis User Page
<!-- INTRODUCTION --> <h1>Introduction</h1> The
following Analysis commands are added to the interpreter to create the
Analysis and perform the analysis:
<!-- General commands --> <h1>General
Commands</h1>
::; <h3>reliability Command</h3>
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This command creates the reliability domain in which the sensitivity,
reliability and optimization components are kept. This reliability
domain is parallel to the finite element (FE) domain in OpenSees.
Currently, the commands for stand-alone sensitivity analysis (e.g.,
sensitivityIntegrator, sensitivityAlgorithm) are set in the reliability
domain only and, thus, the ‘reliability’ command must be used before any
stand-alone sensitivity analysis.
::; <h3>parameter
Command</h3>
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In DDM-based FE response sensitivity analysis, the sensitivity
parameters can be material, geometry or discrete loading parameters.
::; <h3>addToParameter Command</h3>
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In case that more objects (e.g., element, section) are mapped to an
existing parameter, the following command can be used to relate these
additional objects to the specific parameter.
::; <h3>updateParameter Command</h3>
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Once the parameters in FE model are defined, their value can be updated.
::; <h3>sensitivityIntegrator Command</h3>
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Define the sensitivity integrator.
::; <h3>sensitivityAlgorithm Command</h3>
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Define the sensitivity algorithm.
::; <h3>recorder
Commands</h3>
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To record the nodal response and response sensitivity.
<!-- Material Commands --> <h1>Material
Commands</h1>
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<h2>uniaxialMaterial commands</h2>
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Several uniaxial materials are available for DDM-based FE response
sensitivity computation.
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SteelMP Material
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This command is used to construct a uniaxial Menegotto-Pinto steel
material object.
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SmoothPSConcrete
Material
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This command is used to construct a uniaxial smoothed Popovics-Saenz
concrete material object.
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UniaxialJ2Plasticity Material
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This command is used to construct a uniaxial J2 Plasticity material
object with isotropic and kinematic hardening.
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Hardening
Material for Sensitivity
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This command is used to construct a uniaxial material object with
combined linear kinematic and isotropic hardening.
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Concrete01 Material
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This command is used to construct a uniaxial Kent-Scott-Park concrete
material object with degraded linear unloading/reloading stiffness
according to the work of Karsan-Jirsa and no tensile strength (refer to
http://peer.berkeley.edu).
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Steel01
Material for Sensitivity
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This command is used to construct a uniaxial bilinear steel material
object with kinematic hardening and optional isotropic hardening
described by a non-linear evolution equation (refer to http://peer.berkeley.edu).
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Elastic Material
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This command is used to construct a linear elastic uniaxial material
object (with optional material damping).
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<h2>nDmaterial
commands</h2>
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Currently, only one multi-axial material model has been extended for
DDM-based FE response sensitivity computation.
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MultiYieldSurfaceClay
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The ‘MultiYieldSurfaceClay’ is an elastic-plastic material in which
plasticity exhibits only in the deviatoric stress-strain response. The
volumetric stress-strain response is linear-elastic and is independent
of the deviatoric response. This material is implemented to simulate
monotonic or cyclic response of materials whose shear behavior is
pressure independent. Such materials include, for example, organic soils
or clay under fast (undrained) loading conditions.
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This material is available for sensitivity computation in both 2-D and
3-D models. It is another version of PressureIndependMultiYield
material. However there are three differences between this model and
PressureIndependMultiYield:
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1. This model uses the consistent tangent modulus instead of the
continuum tangent modulus.
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2. This model does not support the ‘updateMaterialStage’ command.
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3. This model does not support further discretization of the strain
increment in each iteration.
<!-- Section Commands --> <h1>Section
Commands</h1>
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Currently, only two cross-section models and the section aggregator have
been extended for DDM-based FE response sensitivity computation.
::; <h3>Section
Commands</h3>
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Fiber
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Both 2-D and 3-D fiber sections are available for response sensitivity
computation.
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Elastic
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Both 2-D and 3-D elastic sections are available for response sensitivity
computation.
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Aggregator
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This command is used to construct a SectionAggregator object which
groups previously-defined UniaxialMaterial objects into a single section
force-deformation model.
<!-- Element Commands --> <h1>Element
Commands</h1>
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Currently, several element types have been extended for DDM-based FE
response sensitivity computation.
::; <h3>Element
Commands</h3>
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dispBeamColumnWithSensitivity
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This command is used to construct a 2-D or 3-D distributed-plasticity
displacement-based beam-column (frame) element.
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quadWithSensitivity
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This command is used to construct a 2D four-node quadrilateral element
object based on a bilinear isoparametric formulation.
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bbarBrickWithSensitivity
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This command is used to construct an eight-node 3D brick element object
based on a trilinear isoparametric formulation.
<!-- Constraint Commands --> <h1>Constraint
Commands</h1>
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Currently, several element types have been extended for DDM-based FE
response sensitivity computation.
::; <h3>Constraint Commands</h3>
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Transformation
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This command is used to construct a multi-point constraint handler based
on the transformation equation method.