### Setup Analysis with Element Modification

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-ele-removal-add.html

Initializes a model and database for an analysis involving element removal and addition.

```python
# Case
CASE_2 = 2

"""Ok, For case 2 I want to remove and add element during analysis."""

# Create model
model_info = triangleStruc(top_free=True, base_free=True, info=False)

# Create data base
ODB = opst.post.CreateODB(odb_tag=CASE_2, fiber_ele_tags="ALL", model_update=True)

# Linear timeSeries
ts = 1
ops.timeSeries("Linear", ts)

# Pattern for static analysis
pattern_1 = 100
ops.pattern("Plain", pattern_1, ts)
ops.load(model_info.ctrl_node, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0)
```

--------------------------------

### Setup Pushover Analysis

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-MRF-2Story-Concentrated-PanelZone.html

Sets up the parameters for a static pushover analysis, including defining lateral loads and analysis constraints.

```python
lat2 = 16.255
lat3 = 31.636

ops.timeSeries("Linear", 200)
ops.pattern("Plain", 200, 200)
ops.load(1205, lat2, 0.0, 0.0)
ops.load(2205, lat2, 0.0, 0.0)
ops.load(1305, lat3, 0.0, 0.0)
ops.load(2305, lat3, 0.0, 0.0)

IDctrlNode = 1305
IDctrlDOF = 1
Dmax = 0.1 * HBuilding
Dincr = 0.05

ops.wipeAnalysis()
ops.constraints("Plain")
ops.numberer("RCM")
ops.system("BandGeneral")
ops.test("NormUnbalance", 1.0e-5, 400)
ops.algorithm("Newton")
ops.integrator("DisplacementControl", IDctrlNode, IDctrlDOF, Dincr)
ops.analysis("Static")

```

--------------------------------

### Pushover Analysis Output Example

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-MRF-2Story-Concentrated-PanelZone.html

This is an example output showing the structure of displacement and reaction data loaded from an .odb file. It includes the shape and coordinates of the xarray DataArrays.

```text
OPSTOOL™ ::  Loading disp response data from G:\opstool\docs\.opstool.output\RespStepData-pushover.odb ...
OPSTOOL™ ::  Loading reaction response data from G:\opstool\docs\.opstool.output\RespStepData-pushover.odb ...
<xarray.DataArray 'disp' (time: 649, nodeTags: 72, DOFs: 6)> Size: 1MB
array([[[ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  0.0000000e+00],
        [ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  0.0000000e+00],
        [ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -4.4436118e-07],
        ...,
        [ 1.8685561e-04, -2.7262092e-02,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -4.1580705e-08],
        [ 1.8685561e-04, -2.7262092e-02,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -6.9950938e-09],
        [ 1.8694965e-04, -2.7277712e-02,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -6.8283303e-09]],

       [[ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  0.0000000e+00],
        [ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  0.0000000e+00],
        [ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -1.4927976e-04],
...
          0.0000000e+00, -1.0054388e-01],
        [ 3.1038769e+01,  1.1918640e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -9.6789598e-02],
        [ 3.2350239e+01,  1.1917404e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -9.6783288e-02]],

       [[ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  0.0000000e+00],
        [ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  0.0000000e+00],
        [ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -9.8876216e-02],
        ...,
        [ 3.1086489e+01,  1.1939133e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -1.0070825e-01],
        [ 3.1086489e+01,  1.1939133e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -9.6957892e-02],
        [ 3.2400238e+01,  1.1937901e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -9.6951604e-02]]],
      shape=(649, 72, 6), dtype=float32)
Coordinates:
  * time      (time) float32 3kB 0.0 0.06466 0.1293 0.194 ... 1.098 1.093 1.089
  * nodeTags  (nodeTags) int64 576B 11 21 31 32 33 ... 2306 2307 2308 2309 2310
  * DOFs      (DOFs) <U2 48B 'UX' 'UY' 'UZ' 'RX' 'RY' 'RZ'
<xarray.DataArray 'reaction' (time: 649, nodeTags: 72, DOFs: 6)> Size: 1MB
array([[[ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  7.9213899e-01],
        [ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  7.9221976e-01],
        [ 3.5074761e-04,  7.8933002e+02,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  5.1174906e-15],
        ...,
        [ 5.2678199e-03, -3.3429100e+01,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -1.3585577e-11],
        [-5.2678199e-03,  3.3429100e+01,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  1.3946830e-12],
        [ 6.2170668e-13,  8.3772989e-12,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -9.6687519e-12]],

       [[ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  3.9567642e+02],
        [ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  3.9567175e+02],
        [ 1.1783099e-01,  7.8933002e+02,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  0.0000000e+00],
...
          0.0000000e+00, -1.0266831e-08],
        [-1.7378375e+02,  2.6457239e+02,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -3.6235883e-07],
        [-1.7751367e-07,  1.6630082e-08,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  2.2146787e-07]],

       [[ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  1.6660080e+04],
        [ 0.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  1.6660518e+04],
        [ 7.8045967e+01,  7.8933002e+02,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  0.0000000e+00],
        ...,
        [ 1.7317819e+02, -2.6378641e+02,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00, -1.1087877e-08],
        [-1.7317812e+02,  2.6378647e+02,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  2.6137354e-07],
        [ 2.9309660e-08, -2.5756037e-09,  0.0000000e+00,  0.0000000e+00,
          0.0000000e+00,  2.9473085e-07]]],
      shape=(649, 72, 6), dtype=float32)

```

--------------------------------

### Pushover Analysis Output Log

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-2DFrame-Pushover.html

Example output log generated upon successful completion of the pushover analysis.

```text
OPSTOOL™ ::  All responses data with _odb_tag = 1 saved in G:\opstool\docs\.opstool.output\RespStepData-1.odb!
Pushover analysis completed.
```

--------------------------------

### Dynamic Analysis Configuration

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-PressureDependMultiYield-6.html

Prepares the model for dynamic analysis by resetting the time and wiping the previous analysis setup. This section is a placeholder for further dynamic analysis configuration.

```python
# ===============================================================
#  DYNAMIC ANALYSIS CONFIGURATION
# ===============================================================

```

--------------------------------

### Example DataArray for Stress Measures

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-PressureDependMultiYield-6.html

This is an example of the xarray.DataArray structure for 'StressMeasures', showing dimensions, shape, and coordinates for time, GaussPoints, eleTags, and measures.

```python
<xarray.DataArray 'StressMeasures' (time: 1601, GaussPoints: 8)> Size: 51kB
array([[1.541493  , 1.541493  , 1.541493  , ..., 1.541493  , 1.541493  ,
        1.541493  ],
       [1.541422  , 1.541422  , 1.541422  , ..., 1.541422  , 1.541422  ,
        1.541422  ],
       [1.5525209 , 1.5525209 , 1.5525209 , ..., 1.5525209 , 1.5525209 ,
        1.5525209 ],
       ...,
       [0.36760953, 0.36760953, 0.36760953, ..., 0.36760953, 0.36760953,
        0.36760953],
       [0.36760953, 0.36760953, 0.36760953, ..., 0.36760953, 0.36760953,
        0.36760953],
       [0.36760953, 0.36760953, 0.36760953, ..., 0.36760953, 0.36760953,
        0.36760953]], shape=(1601, 8), dtype=float32)
Coordinates:
  * time         (time) float32 6kB 0.0 0.01 0.02 0.03 ... 15.98 15.99 16.0
  * GaussPoints  (GaussPoints) int64 64B 1 2 3 4 5 6 7 8
    eleTags      int64 8B 1
    measures     <U9 36B 'tau_oct'
```

--------------------------------

### Configuring and Running Analysis

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-cantilever-roll-up.html

Sets up the static analysis parameters and executes the simulation steps.

```python
duration = 1.0
nsteps = 40
dt = duration / nsteps
dt_record = 0.2
ops.constraints("Transformation")
ops.numberer("RCM")
ops.system("UmfPack")
ops.test("NormDispIncr", 1.0e-5, 100, 0)
ops.algorithm("Newton")
ops.integrator("LoadControl", dt)
ops.analysis("Static")
```

```python
ODB = opst.post.CreateODB(odb_tag="CantileverBendingRollup", project_gauss_to_nodes="copy")
for _ in range(nsteps):
    ops.analyze(1)
    ODB.fetch_response_step()
ODB.save_response()
```

--------------------------------

### Initialize Post-processing Environment

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-excavation.html

Imports necessary libraries for visualization and sets up plot properties.

```python
import matplotlib.pyplot as plt

import opstool as opst
import opstool.vis.pyvista as opsvis
```

```python
opsvis.set_plot_props(point_size=0, line_width=5, cmap="turbo")
opsvis.set_plot_props(
    scalar_bar_kargs={
        "label_font_size": 12,
        "title_font_size": 13,
        "position_x": 0.85,  # 0--1
    }
)
```

--------------------------------

### Execute Pushover Analysis and Save Results

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-2DFrame-Pushover.html

Initializes the Opstool ODB, runs the analysis loop, and saves the response data.

```python
ODB = opst.post.CreateODB(odb_tag=1, interpolate_beam_disp=11)

while ok == 0 and ops.nodeDisp(3, 1) < maxU:
    ok = ops.analyze(1)
    if ok != 0:
        print("KrylovNewton newton failed")
        break
    ODB.fetch_response_step()
ODB.save_response()
print("Pushover analysis completed.")
```

--------------------------------

### Import Libraries for OpenSeesPy Analysis

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-2DFrame-Pushover.html

Imports necessary libraries for plotting and OpenSeesPy operations. Ensure these libraries are installed before running the script.

```python
import matplotlib.pyplot as plt
import openseespy.opensees as ops

import opstool as opst
```

--------------------------------

### Initialize Gmsh Model

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-forma11c.html

Set up the Gmsh environment and add a new model.

```python
import json
import math

import gmsh
```

```python
gmsh.initialize()

gmsh.model.add("forma11c_gmsh")
```

--------------------------------

### Setting up the Model

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-cantilever-roll-up.html

Defines the model geometry, material properties, mesh, boundary conditions, and applied loads.

```python
ops.wipe()
ops.model("basic", "-ndm", 3, "-ndf", 6)
E = 1e4
h = 1.0
ops.section("ElasticMembranePlateSection", 1, E, 0.0, h)

# mesh
Lx = 20.0
Ly = 1.0
Nx = 20
Ny = 1
dLx = Lx / Nx
dLy = Ly / Ny
for j in range(Ny + 1):
    offset = j * (Nx + 1)
    jY = j * dLy
    for i in range(Nx + 1):
        iX = i * dLx
        ops.node(offset + i + 1, iX, jY, 0.0)
ele_id = 1
for j in range(Ny):
    for i in range(Nx):
        qids = (j * (Nx + 1) + i + 1, j * (Nx + 1) + i + 2, (j + 1) * (Nx + 1) + i + 2, (j + 1) * (Nx + 1) + i + 1)
        ops.element("ASDShellQ4", ele_id, *qids, 1, "-corotational")
        ele_id += 1

# fix
for j in range(Ny + 1):
    ops.fix(j * (Nx + 1) + 1, 1, 1, 1, 1, 1, 1)

# load
Nrolls = 2
M = Nrolls * 2.0 * np.pi * E * h**3 / 12 / Lx
dM = M / Ny / 2
ops.timeSeries("Linear", 1)
ops.pattern("Plain", 1, 1)
for j in range(Ny):
    i = Nx - 1
    n1 = j * (Nx + 1) + i + 2
    n2 = (j + 1) * (Nx + 1) + i + 2
    ops.load(n1, 0, 0, 0, 0, -dM, 0)
    ops.load(n2, 0, 0, 0, 0, -dM, 0)
```

--------------------------------

### Get Nodal Responses for Pushover Analysis

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-MRF-2Story-Concentrated-PanelZone.html

Use this function to retrieve displacement and reaction data from a pushover analysis. Ensure the 'pushover' odb_tag is correctly specified. The output is an xarray.DataArray.

```python
disp_pushover = opst.post.get_nodal_responses(odb_tag="pushover", resp_type="disp")
react_pushover = opst.post.get_nodal_responses(odb_tag="pushover", resp_type="reaction")
print(disp_pushover)
print(react_pushover)
```

--------------------------------

### Model Configuration and Parameters

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-PressureDependMultiYield-6.html

Sets up material and physical parameters for a dry bbarBrick element with PressureDependMultiYield material. Includes elastic constants, time step, density, and body forces.

```python
# ===============================================================
#  MODEL CONFIGURATION & PARAMETERS
#  This script converts the original Tcl model into OpenSeesPy.
#  A dry bbarBrick element with PressureDependMultiYield material
#  is subjected to 1D sinusoidal base excitation.
# ===============================================================

ops.wipe()

# --- Material & physical parameters ---
friction = 31.40  # Friction angle of the soil
phaseTransform = 26.50  # Phase transformation angle
E1 = 93178.4  # Young's modulus
poisson1 = 0.40  # Poisson’s ratio

# Derived elastic constants
G1 = E1 / (2.0 * (1.0 + poisson1))  # Shear modulus
B1 = E1 / (3.0 * (1.0 - 2.0 * poisson1))  # Bulk modulus

gamma = 0.600  # Newmark gamma parameter

dt = 0.01  # Time step for dynamic analysis
numSteps = 1600  # Number of analysis steps

rhoS = 2.00  # Solid mass density (saturated)
rhoF = 0.00  # Fluid density (dry case → 0)
densityMult = 1.0  # Density multiplier

Bfluid = 2.2e6  # Fluid bulk modulus (unused in dry case)
fluid1 = 1  # Tag for fluid material (not used)
solid1 = 10  # Tag for solid material

accMul = 4.0  # Input acceleration scaling factor

pi = np.pi
inclination = 0.0  # Inclination angle of the element

massProportionalDamping = 0.0
InitStiffnessProportionalDamping = 0.001

# Body forces in global coordinates
bUnitWeightX = (rhoS - 0.0) * 9.81 * np.sin(inclination / 180.0 * pi) * densityMult
bUnitWeightY = 0.0
bUnitWeightZ = -(rhoS - rhoF) * 9.81 * np.cos(inclination / 180.0 * pi)

ndm = 3  # Spatial dimensions
ndf = 3  # Degrees of freedom per node for bricks

# ===============================================================
#  MODEL GENERATION
# ===============================================================
ops.model("Basic", "-ndm", ndm, "-ndf", ndf)

# --- PressureDependMultiYield material definition ---
ops.nDMaterial(
    "PressureDependMultiYield",
    solid1,
    ndm,
    rhoS * densityMult,
    G1,
    B1,
    friction,
    0.1,
    80,
    0.5,
    phaseTransform,
    0.17,
    0.4,
    10,
    10,
    0.015,
    1.0,
)

# --- Nodes of the brick element ---
ops.node(1, 0, 0, 0)
ops.node(2, 0, 0, 1)
ops.node(3, 0, 1, 0)
ops.node(4, 0, 1, 1)
ops.node(5, 1, 0, 0)
ops.node(6, 1, 0, 1)
ops.node(7, 1, 1, 0)
ops.node(8, 1, 1, 1)

# --- bbarBrick element ---
ops.element("bbarBrick", 1, 1, 5, 7, 3, 2, 6, 8, 4, solid1, bUnitWeightX, bUnitWeightY, bUnitWeightZ)

# Initially, set the material to "elastic stage"
ops.updateMaterialStage("-material", solid1, "-stage", 0)

# ===============================================================
#  BOUNDARY CONDITIONS
# ===============================================================
# Note: Brick elements use 3 DOFs (UX, UY, UZ). Rotations are not present.

ops.fix(1, 1, 1, 1)
ops.fix(2, 0, 1, 0)
ops.fix(3, 1, 1, 1)
ops.fix(4, 0, 1, 0)
ops.fix(5, 1, 1, 1)
ops.fix(6, 0, 1, 0)
ops.fix(7, 1, 1, 1)
ops.fix(8, 0, 1, 0)

# Equal DOF constraints (to tie boundary nodes)
ops.equalDOF(2, 4, 1, 3)
ops.equalDOF(2, 6, 1, 3)
ops.equalDOF(2, 8, 1, 3)

```

--------------------------------

### Importing Required Libraries for Opstool Analysis

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-MRF-2Story-Concentrated-PanelZone.html

Initializes the environment by importing matplotlib, numpy, openseespy, and opstool.

```python
import matplotlib.pyplot as plt
import numpy as np
import openseespy.opensees as ops

import opstool as opst
```

--------------------------------

### Get 2D Entity Tags from GMSH Model

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-forma11c.html

Extract dimension entity tags, specifically filtering for 2D entities, from the GMSH model. These tags are used to define shell elements in the OpenSeesPy model.

```python
dim_entity_tags = GMSH2OPS.get_dim_entity_tags()
dim_entity_tags_2D = [item for item in dim_entity_tags if item[0] == 2]
```

--------------------------------

### Configure Basic Transient Analysis

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-MRF-2Story-Concentrated-PanelZone.html

Sets up the algorithm and integrator for a transient analysis in OpenSees.

```python
ops.algorithm("Newton")
ops.integrator("Newmark", 0.5, 0.25)
ops.analysis("Transient")
```

--------------------------------

### Configure Transient Analysis

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-MRF-2Story-Concentrated-PanelZone.html

Initializes the analysis environment with standard constraints, numberer, and system solvers.

```python
dt_analysis = dt
ops.wipeAnalysis()
ops.constraints("Plain")
ops.numberer("RCM")
ops.system("UmfPack")
# ops.test("NormDispIncr", 1.0e-8, 10)
```

--------------------------------

### Construct Model

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-double-layer-shallow-dome.html

Initialize the OpenSees domain and populate it with nodes and elements using list comprehensions.

```python
ops.wipe()
ops.model("basic", "-ndm", 3, "-ndf", 3)

# Adding nodes to the model object using list comprehensions
[ops.node(n + 1, *node_coords[n]) for n in range(nn)]
# Applying BC
[ops.fix(B_C[n][0], *B_C[n][1:]) for n in range(len(B_C))]
# Set Material
ops.uniaxialMaterial("Elastic", 1, E_list[0])

# Adding Elements
[
    ops.element(
        "corotTruss",
        e + 1,
        *connectivity[e],
        area_list[e],
        1,
        "-rho",
        rho * area_list[e],
        "-cMass",
        1,
    )
    for e in range(nel)
]
print(f"Number of Nodes: {nn}, Number of Elements: {nel}")
```

--------------------------------

### Configure Analysis Settings

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-double-layer-shallow-dome.html

Sets up various analysis parameters such as constraints, numberers, system solvers, integrators, and analysis type. Ensure all necessary parameters are defined before running the analysis.

```python
ops.constraints("Plain")
ops.numberer("Plain")
ops.system("ProfileSPD")
ops.test("NormUnbalance", 0.0000001, 100)
ops.algorithm("ModifiedNewton")
ops.integrator("Newmark", 0.5, 0.25)
ops.analysis("Transient")
```

--------------------------------

### Configure Time-History Analysis

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-PressureDependMultiYield-6.html

Sets up the time series, excitation, damping, and analysis parameters for a transient simulation.

```python
ops.timeSeries("Sine", 1, 0.0, 10.0, 1.0, "-factor", accMul)
ops.pattern("UniformExcitation", 1, 1, "-accel", 1)

ops.rayleigh(massProportionalDamping, 0.0, InitStiffnessProportionalDamping, 0.0)

beta = (gamma + 0.5) ** 2 / 4.0
ops.integrator("Newmark", gamma, beta)

ops.constraints("Penalty", 1e18, 1e18)
ops.test("NormDispIncr", 1e-10, 25, 0)
ops.algorithm("ModifiedNewton")
ops.system("ProfileSPD")
ops.numberer("Plain")
ops.analysis("VariableTransient")
```

--------------------------------

### Configure Static Analysis Pattern

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-ele-removal-add.html

Sets up a plain pattern for static analysis and applies a load to the control node.

```python
pattern = 100
ops.pattern("Plain", pattern, ts)
ops.load(model_info.ctrl_node, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0)
```

--------------------------------

### Importing Required Libraries

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-cantilever-roll-up.html

Initial imports for numerical computation, plotting, and OpenSeesPy integration.

```python
import matplotlib.pyplot as plt
import numpy as np
from openseespy import opensees as ops

import opstool as opst
```

--------------------------------

### Import Libraries for OpenSeesPy and Opstool

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-forma11c.html

Import the OpenSeesPy and Opstool libraries to begin the analysis.

```python
import openseespy.opensees as ops

import opstool as opst
```

--------------------------------

### Initialize OpenSeesPy Model and Define Material

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-forma11c.html

Initialize the OpenSeesPy model with basic parameters and define an elastic isotropic material. This sets up the fundamental properties for the structural elements.

```python
ops.wipe()
ops.model("basic", "-ndm", 3, "-ndf", 6)
E, nu, rho = 2.76e10, 0.166, 2244.0  # Pa, kg/m3
ops.nDMaterial("ElasticIsotropic", 1, E, nu, rho)
secTag = 11
ops.section("PlateFiber", secTag, 1, 0.305)
```

--------------------------------

### Run Pushover Analysis Loop and Record ODB

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-MRF-2Story-Concentrated-PanelZone.html

Executes the pushover analysis using a SmartAnalyze object, splitting the analysis into segments and recording the response to an ODB file.

```python
smart_analysis = opst.anlys.SmartAnalyze(
    analysis_type="Static",
    testTol=1.0e-6,
    testType="NormDispIncr",
    testIterTimes=100,
    tryAddTestTimes=True,  # add test times to the analysis
    testIterTimesMore=[250, 500, 1000],
    tryAlterAlgoTypes=False,  # fix algorithm
    algoTypes=[40],  # algorithm is KrylovNewton
    relaxation=0.5,
    minStep=1e-6,  # minimum step size for substepping
    debugMode=True,
    printPer=100,
)
segs = smart_analysis.static_split(targets=[0, Dmax], maxStep=Dincr)

ODB = opst.post.CreateODB(odb_tag="pushover", interpolate_beam_disp=True)
for seg in segs:
    smart_analysis.StaticAnalyze(node=IDctrlNode, dof=IDctrlDOF, seg=seg)
    ODB.fetch_response_step()
ODB.save_response()
print("Pushover complete")

```

--------------------------------

### Perform static analysis with analysisLib

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-ele-removal-add.html

Executes a static analysis using a control node and displacement targets. Requires an initialized CreateODB object and OpenSees environment.

```python
def analysisLib(
    targets: Union[list, tuple, np.ndarray],
    patternTag: int,
    ctrl_node: int,
    ODB: opst.post.CreateODB,
) -> tuple[np.ndarray, np.ndarray]:
    """
    # Static analysis function

    :param targets: Displacement path
    :param patternTag: Pattern tag
    :param ctrl_node: Control node tag
    :param ODB: CreateODB object

    :return: Displacement and force
    """

    ops.system("BandGeneral")
    ops.constraints("Transformation")
    ops.numberer("RCM")

    analysis = opst.anlys.SmartAnalyze("Static")
    segs = analysis.static_split(targets=targets, maxStep=0.01 * UNIT.m)

    force_lambda: Union[list, float] = [0.0]
    node_disp: Union[list, float] = [0.0]
    for seg in segs:
        ok = analysis.StaticAnalyze(node=ctrl_node, dof=2, seg=seg)  # node tag 1, dof 2
        if ok < 0:
            raise RuntimeError("Analysis failed")  # noqa: TRY003

        # Fetch response
        ODB.fetch_response_step()
        force_lambda.append(ops.getLoadFactor(patternTag))
        node_disp.append(ops.nodeDisp(ctrl_node, 2))

    return np.array(node_disp), np.array(force_lambda)
```

--------------------------------

### Configure zeroLength and zeroLengthSection Elements

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-ele-removal-add.html

This configuration handles cases where both the top and base are free, setting up both zeroLength and zeroLengthSection elements. It involves creating nodes for both, defining the main and left elements, and then the zero-length elements.

```python
print("CASE: zeroLength & zeroLengthSection")

        ops.node(nodeTag_top_link, 0.0, 0.0, 1.2 * UNIT.m)  # For top zeroLength
        ops.node(nodeTag_base_link, 0.0, 0.0, 0.2 * UNIT.m)  # For base zeroLengthSection
        ops.element(
            "dispBeamColumn",
            eleTag_main,
            *(nodeTag_top, nodeTag_base_link),
            transf_ver,
            npTag_1,
        )  # Single vertical element
        ops.element(
            "dispBeamColumn",
            eleTag_left,
            *(nodeTag_top, nodeTag_left_base),
            transf_ver,
            npTag_2,
        )  # Left oblique element

        mats = (elasticTag, elasticTag, elasticTag, elasticTag, elasticTag, elasticTag)
        ops.element(
            "zeroLength",
            eleTag_top_link,
            *(nodeTag_top_link, nodeTag_top),
            "-mat",
            *mats,
            "-dir",
            *(1, 2, 3, 4, 5, 6),
            "-orient",
            *(0, 0, -1),
            *(0, -1, 0),
        )

        ops.equalDOF(*(nodeTag_base, nodeTag_base_link), *(1, 2, 3))
        ops.element(
            "zeroLengthSection",
            eleTag_base_link,
            *(nodeTag_base_link, nodeTag_base),
            secTag_2,
            "-orient",
            *(0, 0, -1),
            *(0, -1, 0),
        )

        return_val = RETURN_VAL(
            ctrl_node=nodeTag_top_link,
            remove_ele=eleTag_left,
            add_ele=(
                "dispBeamColumn",
                eleTag_right,
                *(nodeTag_top, nodeTag_right_base),
                transf_ver,
                npTag_2,
            ),
            top_link_ele=eleTag_top_link,
            base_link_ele=eleTag_base_link,
        )
```

--------------------------------

### Configure Pushover Animation Parameters

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-MRF-2Story-Concentrated-PanelZone.html

Sets animation properties such as interpolation, scaling, and output file format. Ensure the output filename extension matches the desired format for compatibility.

```python
    interpolate_beam_disp=True,
    defo_scale=2.0,
    framerate=30,
    savefig="pushover_disp_animation.mp4",  # mp4 more efficient but gif more widely supported
).close()
```

--------------------------------

### Create Output Database (ODB)

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-excavation.html

Initializes the ODB object for saving analysis results. Set model_update=True if elements/nodes will be removed. save_every controls the frequency of saving, and compute_mechanical_measures enables calculation of derived quantities.

```python
ODB = opst.post.CreateODB(
    odb_tag=1,
    model_update=True,
    save_every=8,  # every 8 analysis steps will be saved
    compute_mechanical_measures=True,
    project_gauss_to_nodes="copy",
)
```

--------------------------------

### Import Dependencies

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-double-layer-shallow-dome.html

Initial imports for numerical computation, plotting, and OpenSees integration.

```python
import matplotlib.pyplot as plt
import numpy as np
import openseespy.opensees as ops

import opstool as opst
import opstool.vis.plotly as opsvis

# import opstool.vis.pyvista as opsvis
```

--------------------------------

### Initialize triangle structure

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-ele-removal-add.html

Creates a triangle structure model with optional top and base link elements using OpenSees commands.

```python
def triangleStruc(top_free: bool = False, base_free: bool = False, info: bool = True) -> RETURN_VAL:
    """
    # Create a simple triangle structure

    :param top_free: if True, add zeroLength element to the top
    :param base_free: if True, add zeroLengthSection element to the base
    :param info: if True, print section element information

    :return a namedtuple with the following values:
    - :ctrl_node: the control node for static analysis
    - :remove_ele: the element to be removed
    - :add_ele: the element to be added
    - :top_link_ele: the top zeroLength element
    - :base_link_ele: the base zeroLengthSection element
    """

    "# ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- -----"
    # Initialize
    ops.wipe()
    ops.model("basic", "-ndm", 3, "-ndf", 6)

    # For vertical element
    transf_ver = 1
    ops.geomTransf("PDelta", transf_ver, *(-1, 0, 0))
    # For other element
    transf_other = 2
    ops.geomTransf("PDelta", transf_other, *(0, 0, 1))

    "# ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- -----"
    # Steel material
    steelTag = 10
    ops.uniaxialMaterial("Steel02", steelTag, 400 * UNIT.mpa, 206 * UNIT.gpa, 0.01)

    # Elastic no tension material
    ENTTag = 20
    ops.uniaxialMaterial("ENT", ENTTag, 200 * UNIT.gpa)

    # Elastic material
    elasticTag = 30
    ops.uniaxialMaterial("Elastic", elasticTag, 1.0e6)

    "# ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- -----"
    # Define vertical element section
    secTag_1 = 1
    W_1 = 10.0 * UNIT.cm
    H_1 = 10.0 * UNIT.cm
    sec_props_1 = secCreate(sec_name="vertical", secTag=secTag_1, matTag=steelTag, w=W_1, h=H_1, info=info)

    # Define vertical base link element section
    secTag_2 = 2
    sec_props_2 = secCreate(
        sec_name="vertical base",
        secTag=secTag_2,
        matTag=ENTTag,
        w=W_1,
        h=H_1,
        info=info,
    )

    # Define other element section
    secTag_3 = 3
    W_2 = 2.0 * UNIT.cm
    H_2 = 2.0 * UNIT.cm
    sec_props_3 = secCreate(sec_name="oblique", secTag=secTag_3, matTag=steelTag, w=W_2, h=H_2, info=info)

    "# ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- -----"
    # Node Tags
    nodeTag_base = 1
    nodeTag_top = 2
    nodeTag_base_link = 3  # Base link node
    nodeTag_top_link = 4  # Top link node
    nodeTag_left_base = 5
    nodeTag_right_base = 6

    # Element Tags
    eleTag_main = 1
    eleTag_left = 2
    eleTag_right = 3
    eleTag_base_link = 4  # Base link element
    eleTag_top_link = 5  # Top link element

    "# ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- -----"
    # Create nodes
    ops.node(nodeTag_base, 0.0, 0.0, 0.0)
    ops.node(nodeTag_top, 0.0, 0.0, 1.0 * UNIT.m)
    ops.node(nodeTag_left_base, 0.0, -1.0 * UNIT.m, 0.0)
    ops.node(nodeTag_right_base, 0.0, 1.0 * UNIT.m, 0.0)

    # Nodes fix
    ops.fix(nodeTag_base, 1, 1, 1, 1, 1, 1)
    ops.fix(nodeTag_left_base, 1, 1, 1, 1, 1, 1)
    ops.fix(nodeTag_right_base, 1, 1, 1, 1, 1, 1)

    # Integration
    npTag_1 = 1
    npTag_2 = 2
    ops.beamIntegration("Legendre", npTag_1, secTag_1, 5)
    ops.beamIntegration("Legendre", npTag_2, secTag_3, 5)

    "# ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- -----"
    """
    Note:
        In order to check the local axes of zeroLength and zeroLengthSection, the length of zeroLength and zeroLengthSection elements is not zero.
        It causes opensees warning but does not affect the results.
    """

    if top_free and not base_free:
        print("CASE: zeroLength")

        ops.node(nodeTag_top_link, 0.0, 0.0, 1.2 * UNIT.m)  # For top zeroLength
        ops.element(
            "dispBeamColumn",
            eleTag_main,
            *(nodeTag_top, nodeTag_base),
            transf_ver,
            npTag_1,
        )  # Single vertical element
        ops.element(
            "dispBeamColumn",
            eleTag_left,
            *(nodeTag_top, nodeTag_left_base),
            transf_ver,
            npTag_2,
        )  # Left oblique element

        mats = (elasticTag, elasticTag, elasticTag, elasticTag, elasticTag, elasticTag)
        ops.element(
            "zeroLength",
            eleTag_top_link,
            *(nodeTag_top_link, nodeTag_top),
            "-mat",
            *mats,
            "-dir",
            *(1, 2, 3, 4, 5, 6),
            "-orient",
            *(0, 0, -1),
            *(0, -1, 0),
        )
```

--------------------------------

### Import openseespy library

Source: https://opstool-doc.readthedocs.io/en/latest/_sphinx_gallery_examples/examples/postprocessing/ex-excavation.html

Imports the necessary openseespy library for finite element analysis.

```python
import openseespy.opensees as ops
```