SystemModel - milcapy

Overview

SystemModel is the primary class for building 2D structural analysis models in milcapy. It manages all model components including materials, sections, nodes, elements, loads, and analysis results.

Constructor

from milcapy import SystemModel

model = SystemModel()

Creates an empty structural model.

Materials

add_material()

Adds a material to the model.

model.add_material(
    name="concrete",
    modulus_elasticity=2.1e6,
    poisson_ratio=0.2,
    specific_weight=2400
)

name

str

required

Unique name for the material

modulus_elasticity

float

required

Modulus of elasticity (E) in force per area units

poisson_ratio

float

required

Poisson’s ratio (ν), must be in range (-1, 0.5)

specific_weight

float

default:"0.0"

Specific weight or density (kg/m³ or N/m³)

Material

Returns the created Material object

Sections

add_rectangular_section()

Adds a rectangular cross-section to the model.

model.add_rectangular_section(
    name="beam_section",
    material_name="concrete",
    base=0.3,
    height=0.5
)

name

str

required

Unique name for the section

material_name

str

required

Name of previously defined material

base

float

required

Width of the rectangular section

height

float

required

Height of the rectangular section

Section

RectangularSection

Returns the created Section object

add_circular_section()

Adds a circular cross-section to the model.

model.add_circular_section(
    name="column_section",
    material_name="steel",
    diameter=0.3
)

name

str

required

Unique name for the section

material_name

str

required

Name of previously defined material

diameter

float

required

Diameter of the circular section (must be positive)

Section

CircularSection

Returns the created Section object

add_generic_section()

Adds a generic section with custom geometric properties.

model.add_generic_section(
    name="custom_section",
    material_name="steel",
    area=0.05,
    inertia=0.0001,
    k_factor=0.85
)

name

str

required

Unique name for the section

material_name

str

required

Name of previously defined material

area

float

required

Cross-sectional area

inertia

float

required

Moment of inertia

k_factor

float

required

Shear coefficient factor (Ac = A * k_factor)

Section

GenericSection

Returns the created Section object

add_shell_section()

Adds a shell section for membrane/plate elements.

model.add_shell_section(
    name="wall_section",
    material_name="concrete",
    thickness=0.2
)

name

str

required

Unique name for the section

material_name

str

required

Name of previously defined material

thickness

float

required

Thickness of the shell element

ShellSection

Returns the created ShellSection object

Nodes

add_node()

Adds a node to the model.

model.add_node(id=1, x=0.0, y=0.0)
model.add_node(id=2, x=5.0, y=0.0)

int

required

Unique node identifier

float

required

X-coordinate of the node

float

required

Y-coordinate of the node

Node

Returns the created Node object

Members

add_member()

Adds a frame member (beam/column) to the model.

from milcapy import BeamTheoriesType

model.add_member(
    id=1,
    node_i_id=1,
    node_j_id=2,
    section_name="beam_section",
    beam_theory=BeamTheoriesType.TIMOSHENKO
)

int

required

Unique member identifier

node_i_id

int

required

ID of the start node

node_j_id

int

required

ID of the end node

section_name

str

required

Name of previously defined section

beam_theory

BeamTheoriesType | str

default:"BeamTheoriesType.TIMOSHENKO"

Beam theory to use: TIMOSHENKO or EULER_BERNOULLI

Member

Returns the created Member object

add_elastic_timoshenko_beam()

Adds a Timoshenko beam with axial stiffness.

model.add_elastic_timoshenko_beam(
    id=1,
    node_i_id=1,
    node_j_id=2,
    section_name="beam_section"
)

int

required

Unique member identifier

node_i_id

int

required

ID of the start node

node_j_id

int

required

ID of the end node

section_name

str

required

Name of previously defined section

add_elastic_euler_bernoulli_beam()

Adds an Euler-Bernoulli beam with axial stiffness.

model.add_elastic_euler_bernoulli_beam(
    id=1,
    node_i_id=1,
    node_j_id=2,
    section_name="beam_section"
)

int

required

Unique member identifier

node_i_id

int

required

ID of the start node

node_j_id

int

required

ID of the end node

section_name

str

required

Name of previously defined section

add_truss()

Adds a truss element (axial force only).

model.add_truss(
    id=1,
    node_i_id=1,
    node_j_id=2,
    section_name="truss_section"
)

int

required

Unique truss identifier

node_i_id

int

required

ID of the start node

node_j_id

int

required

ID of the end node

section_name

str

required

Name of previously defined section

Boundary Conditions

add_restraint()

Adds restraints (boundary conditions) to a node.

model.add_restraint(
    node_id=1,
    ux=True,   # Restrain X translation
    uy=True,   # Restrain Y translation
    rz=True    # Restrain Z rotation
)

node_id

int

required

ID of the node to restrain

bool

required

Restrain translation in X direction

bool

required

Restrain translation in Y direction

bool

required

Restrain rotation about Z axis

Load Patterns

add_load_pattern()

Creates a load pattern for organizing loads.

from milcapy import StateType

model.add_load_pattern(
    name="Live Load",
    self_weight_multiplier=0.0,
    state=StateType.ACTIVE
)

name

str

required

Unique name for the load pattern

self_weight_multiplier

float

default:"0.0"

Multiplier for self-weight (1.0 = full self-weight)

state

StateType | str

default:"StateType.ACTIVE"

Load pattern state: ACTIVE or INACTIVE

add_point_load()

Adds a point load to a node.

from milcapy import CoordinateSystemType

model.add_point_load(
    node_id=2,
    load_pattern_name="Live Load",
    fx=100.0,
    fy=-200.0,
    mz=50.0,
    CSys=CoordinateSystemType.GLOBAL
)

node_id

int

required

ID of the node to apply load

load_pattern_name

str

required

Name of the load pattern

float

default:"0.0"

Force in X direction

float

default:"0.0"

Force in Y direction

float

default:"0.0"

Moment about Z axis

CSys

CoordinateSystemType | str

default:"GLOBAL"

Coordinate system: GLOBAL or LOCAL

replace

bool

default:"False"

Replace existing load if True, otherwise add to existing

add_distributed_load()

Adds a distributed load to a member.

from milcapy import DirectionType, LoadType

model.add_distributed_load(
    member_id=1,
    load_pattern_name="Dead Load",
    load_start=-10.0,
    load_end=-10.0,
    CSys="LOCAL",
    direction=DirectionType.LOCAL_2,
    load_type=LoadType.FORCE
)

member_id

int

required

ID of the member to apply load

load_pattern_name

str

required

Name of the load pattern

load_start

float

default:"0.0"

Load magnitude at start of member

load_end

float

default:"0.0"

Load magnitude at end of member

CSys

CoordinateSystemType | str

default:"LOCAL"

Coordinate system: GLOBAL or LOCAL

direction

DirectionType | str

default:"LOCAL_2"

Load direction: LOCAL_1, LOCAL_2, X, Y, GRAVITY, etc.

load_type

LoadType | str

default:"FORCE"

Type of load: FORCE or MOMENT

replace

bool

default:"False"

Replace existing load if True

Analysis

solve()

Solves the structural model using the direct stiffness method.

results = model.solve()

# Or solve specific load patterns
results = model.solve(load_pattern_name=["Dead Load", "Live Load"])

load_pattern_name

list[str] | None

default:"None"

List of load pattern names to solve. If None, solves all active patterns.

results

Dict[str, Results]

Dictionary mapping load pattern names to Results objects

Results

get_results()

Retrieves analysis results for a specific load pattern.

results = model.get_results("Live Load")

# Access node displacements
displacements = results.get_node_displacements(2)
print(f"ux={displacements[0]}, uy={displacements[1]}, rz={displacements[2]}")

load_pattern_name

str

required

Name of the load pattern

Results

Results object containing displacements, reactions, and internal forces

get_global_stiffness_matrix()

Returns the assembled global stiffness matrix.

K = model.get_global_stiffness_matrix()

NDArray

Global stiffness matrix

get_global_load_vector()

Returns the global load vector for a load pattern.

F = model.get_global_load_vector("Live Load")

load_pattern_name

str

required

Name of the load pattern

NDArray

Global load vector

Visualization

show()

Launches the interactive model viewer window.

model.solve()
model.show()

The model must be solved before calling show(). The viewer displays the model geometry, loads, deformed shape, and internal force diagrams.

plot_model()

Creates a static plot of the model.

model.plot_model(
    load_pattern="Live Load",
    node_labels=True,
    member_labels=True
)

load_pattern

str | None

default:"None"

Load pattern to display loads for

node_labels

bool

default:"True"

Show node ID labels

member_labels

bool

default:"True"

Show member ID labels

Advanced Features

add_elastic_support()

Adds an elastic support (spring) to a node.

model.add_elastic_support(
    node_id=2,
    kx=1000.0,  # Spring stiffness in X
    ky=2000.0,  # Spring stiffness in Y
    krz=500.0,  # Rotational spring stiffness
    CSys="GLOBAL"
)

node_id

int

required

ID of the node

float | None

default:"None"

Spring stiffness in X direction

float | None

default:"None"

Spring stiffness in Y direction

krz

float | None

default:"None"

Rotational spring stiffness about Z

CSys

CoordinateSystemType | str

default:"GLOBAL"

Coordinate system for the spring

add_end_length_offset()

Adds rigid end offsets to a member (rigid arms).

model.add_end_length_offset(
    member_id=1,
    la=0.2,  # Offset at start node
    lb=0.3,  # Offset at end node
    qla=True,  # Apply loads on rigid arm at start
    qlb=True,  # Apply loads on rigid arm at end
    fla=1.0,   # Rigidity factor at start
    flb=1.0    # Rigidity factor at end
)

member_id

int

required

ID of the member

float

default:"0"

Length offset at start node

float

default:"0"

Length offset at end node

qla

bool

default:"True"

Apply loads on rigid arm at start

qlb

bool

default:"True"

Apply loads on rigid arm at end

fla

float

default:"1"

Rigidity factor for start offset (1.0 = fully rigid)

flb

float

default:"1"

Rigidity factor for end offset (1.0 = fully rigid)

add_releases()

Adds member end releases.

model.add_releases(
    member_id=1,
    pi=False,  # Axial release at start
    vi=False,  # Shear release at start
    mi=True,   # Moment release at start (pinned)
    pj=False,  # Axial release at end
    vj=False,  # Shear release at end
    mj=False   # Moment release at end
)

member_id

int

required

ID of the member

bool

default:"False"

Release axial force at start node

bool

default:"False"

Release shear force at start node

bool

default:"False"

Release moment at start node

bool

default:"False"

Release axial force at end node

bool

default:"False"

Release shear force at end node

bool

default:"False"

Release moment at end node

Cannot release both ends for the same force type (e.g., pi=True and pj=True is invalid)

Example

from milcapy import SystemModel, BeamTheoriesType

# Create model
model = SystemModel()

# Define material
model.add_material(
    name="concrete",
    modulus_elasticity=2.1e6,
    poisson_ratio=0.2,
    specific_weight=2400
)

# Define section
model.add_rectangular_section(
    name="beam_30x50",
    material_name="concrete",
    base=0.3,
    height=0.5
)

# Create nodes
model.add_node(1, 0, 0)
model.add_node(2, 5, 0)
model.add_node(3, 10, 0)

# Create members
model.add_member(1, 1, 2, "beam_30x50", BeamTheoriesType.TIMOSHENKO)
model.add_member(2, 2, 3, "beam_30x50", BeamTheoriesType.TIMOSHENKO)

# Apply supports
model.add_restraint(1, True, True, True)  # Fixed
model.add_restraint(3, False, True, False)  # Roller

# Add loads
model.add_load_pattern("Dead Load", self_weight_multiplier=1.0)
model.add_distributed_load(1, "Dead Load", load_start=-10, load_end=-10)
model.add_distributed_load(2, "Dead Load", load_start=-10, load_end=-10)

model.add_load_pattern("Live Load")
model.add_point_load(2, "Live Load", fy=-50.0)

# Solve
results = model.solve()

# Get results
node_2_disp = model.get_results("Live Load").get_node_displacements(2)
print(f"Node 2 vertical displacement: {node_2_disp[1]:.6f}")

# Visualize
model.show()

Core API

Materials & Sections

Nodes & Elements

Loads & Boundary Conditions

Analysis & Results

Enums & Types

​Overview

​Constructor

​Materials

​add_material()

​Sections

​add_rectangular_section()

​add_circular_section()

​add_generic_section()

​add_shell_section()

​Nodes

​add_node()

​Members

​add_member()

​add_elastic_timoshenko_beam()

​add_elastic_euler_bernoulli_beam()

​add_truss()

​Boundary Conditions

​add_restraint()

​Load Patterns

​add_load_pattern()

​add_point_load()

​add_distributed_load()

​Analysis

​solve()

​Results

​get_results()

​get_global_stiffness_matrix()

​get_global_load_vector()

​Visualization

​show()

​plot_model()

​Advanced Features

​add_elastic_support()

​add_end_length_offset()

​add_releases()

​Example

Build docs developers (and LLMs) love

Overview

Constructor

Materials

add_material()

Sections

add_rectangular_section()

add_circular_section()

add_generic_section()

add_shell_section()

Nodes

add_node()

Members

add_member()

add_elastic_timoshenko_beam()

add_elastic_euler_bernoulli_beam()

add_truss()

Boundary Conditions

add_restraint()

Load Patterns

add_load_pattern()

add_point_load()

add_distributed_load()

Analysis

solve()

Results

get_results()

get_global_stiffness_matrix()

get_global_load_vector()

Visualization

show()

plot_model()

Advanced Features

add_elastic_support()

add_end_length_offset()

add_releases()

Example