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Overview

Once you’ve defined your model geometry, materials, sections, loads, and boundary conditions, you can solve the structural analysis using milcapy’s linear static solver. The solver uses the Direct Stiffness Method and Finite Element Method to compute displacements, reactions, and internal forces.

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Basic Solve Command

The simplest way to solve your model is to call the solve() method: 
from milcapy import SystemModel

model = SystemModel()
# ... define materials, sections, nodes, elements, loads, etc.

# Solve all active load patterns
model.solve()

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Solving Specific Load Patterns

You can solve for specific load patterns by passing their names as a list: 
# Solve only specific load patterns
model.solve(load_pattern_name=["Dead Load", "Live Load"])
If load_pattern_name is None (default), all active load patterns will be solved.

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What Happens During Solve?

When you call solve(), milcapy performs the following steps:
  1. Assembly - Constructs the global stiffness matrix (K) and load vector (F)
  2. Boundary Conditions - Applies restraints, elastic supports, and prescribed displacements
  3. Solution - Solves the system K·u = F using numpy.linalg.solve()
  4. Post-Processing - Computes reactions, internal forces, and member diagrams

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Load Pattern States

Only load patterns with state=StateType.ACTIVE will be analyzed: 
# Create active load pattern (default)
model.add_load_pattern("Dead Load", state="ACTIVE")

# Create inactive load pattern
model.add_load_pattern("Wind Load", state="INACTIVE")

# Change state later
model.set_state_load_pattern("Wind Load", "ACTIVE")

model.solve()  # Only solves active patterns

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Analysis Methods

Milcapy uses the LinearStaticAnalysis class internally, which implements:
  • Direct Stiffness Method for frame and truss elements
  • Finite Element Method for membrane elements (CST, Q4, Q6, Q6I, Q8)
  • Closed-form solutions for 1D elements (beams and trusses)

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Solution Output

During the solve process, you’ll see timing information printed to the console: 
Tiempo de solucion: 0.0234 para el Load Pattern: Dead Load
Tiempo de solucion: 0.0198 para el Load Pattern: Live Load

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Complete Example

from milcapy import SystemModel, BeamTheoriesType

model = SystemModel()

# Define materials and sections
model.add_material("concrete", modulus_elasticity=2.5e6, poisson_ratio=0.2)
model.add_rectangular_section("beam", "concrete", base=0.3, height=0.5)

# Define geometry
model.add_node(1, 0, 0)
model.add_node(2, 5, 0)
model.add_node(3, 10, 0)

model.add_member(1, 1, 2, "beam", BeamTheoriesType.TIMOSHENKO)
model.add_member(2, 2, 3, "beam", BeamTheoriesType.TIMOSHENKO)

# Boundary conditions
model.add_restraint(1, ux=True, uy=True, rz=True)
model.add_restraint(3, ux=False, uy=True, rz=False)

# Load patterns
model.add_load_pattern("Dead Load")
model.add_point_load(2, "Dead Load", fx=0, fy=-100, mz=0)

model.add_load_pattern("Live Load")
model.add_distributed_load(1, "Live Load", load_start=-10, load_end=-10)

# Solve the model
model.solve()

print("Analysis complete!")

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Advanced Options

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Post-Processing Resolution

Control the number of points used for member force diagrams: 
# Set number of evaluation points (default is 17)
model.postprocessing_options.n = 100

model.solve()

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Accessing Global Matrices

After solving, you can access the assembled global matrices: 
model.solve()

# Get global stiffness matrix
K_global = model.global_stiffness_matrix

# Get global load vector for specific pattern
F_global = model.global_load_vector["Dead Load"]

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Troubleshooting

Singular Matrix Error: If the model is unstable or has insufficient restraints, you may get a singular matrix error. Ensure your model has proper support conditions.

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Common Issues

  1. No restraints defined - Model needs at least one support
  2. Unstable mechanism - Check for missing restraints or releases
  3. Inactive load patterns - Verify patterns are set to ACTIVE

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Next Steps

Results Extraction

Learn how to extract and interpret analysis results

Visualization

Visualize your model and results interactively

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