Overview After solving your model, milcapy stores all results in Results objects that you can query to extract displacements, reactions, internal forces, stresses, and strains.
Getting Results Retrieve the Results object for a specific load pattern:
model.solve() # Get results for a specific load pattern results = model.get_results( "Dead Load" )
Model-Level Results Get global displacement and reaction vectors for the entire model:
# Global displacement vector (length = 3 * number_of_nodes) displacements = results.get_model_displacements() # Global reaction vector (length = 3 * number_of_nodes) reactions = results.get_model_reactions()
The global vectors are organized as [Ux1, Uy1, Rz1, Ux2, Uy2, Rz2, ...] where subscripts indicate node numbers.
Node Results Extract displacements and reactions at individual nodes:
# Get displacements for node 5 node_disp = results.get_node_displacements( node_id = 5 ) # Returns: np.array([Ux, Uy, Rz]) # Get reactions for node 1 node_react = results.get_node_reactions( node_id = 1 ) # Returns: np.array([Rx, Ry, Mz])
Example: Node Results from milcapy import SystemModel model = SystemModel() # ... define model ... model.solve() results = model.get_results( "Dead Load" ) # Check displacement at node 3 disp = results.get_node_displacements( 3 ) print ( f "Node 3 - Ux: { disp[ 0 ] :.6f} , Uy: { disp[ 1 ] :.6f} , Rz: { disp[ 2 ] :.6f} " ) # Check reactions at support (node 1) react = results.get_node_reactions( 1 ) print ( f "Node 1 - Rx: { react[ 0 ] :.2f} , Ry: { react[ 1 ] :.2f} , Mz: { react[ 2 ] :.2f} " )
Member Results For frame and beam elements, extract detailed results including forces and diagrams:
End Forces and Displacements # Get member end displacements [Uxi, Uyi, Rzi, Uxj, Uyj, Rzj] member_disp = results.get_member_displacements( member_id = 2 ) # Get member end forces [Ni, Vi, Mi, Nj, Vj, Mj] member_forces = results.get_member_internal_forces( member_id = 2 )
Force Diagrams Along Member # Get axial force diagram N = results.get_member_axial_force( member_id = 2 ) # Get shear force diagram V = results.get_member_shear_force( member_id = 2 ) # Get bending moment diagram M = results.get_member_bending_moment( member_id = 2 ) # Get x-coordinates for diagrams x_vals = results.get_member_x_val( member_id = 2 )
Displacement Diagrams # Get deflection (transverse displacement) deflection = results.get_member_deflection( member_id = 2 ) # Get slope (rotation) slope = results.get_member_slope( member_id = 2 ) # Get axial displacement axial_disp = results.get_member_axial_displacement( member_id = 2 )
Complete Member Results Dictionary # Get all results for a member member_results = results.get_results_member( member_id = 2 ) # Returns a dict with keys: 'displacements', 'internal_forces', # 'axial_forces', 'shear_forces', 'bending_moments', # 'deflections', 'slopes', 'axial_displacements', 'x_val'
Truss Results For truss elements:
# Get truss end displacements [Uxi, Uxj] truss_disp = results.get_truss_displacements( truss_id = 10 ) # Get truss internal forces [Ni, Nj] truss_forces = results.get_truss_internal_forces( truss_id = 10 ) # Get axial force diagram truss_axial = results.get_truss_axial_force( truss_id = 10 ) # Get axial displacement diagram truss_axial_disp = results.get_truss_axial_displacement( truss_id = 10 ) # Get all truss results truss_results = results.get_results_truss( truss_id = 10 )
Finite Element Results (Membranes) CST Elements (Constant Strain Triangle) # Get nodal displacements [Ux1, Uy1, Ux2, Uy2, Ux3, Uy3] cst_disp = results.get_cst_displacements( cst_id = 15 ) # Get strains [εx, εy, γxy] cst_strains = results.get_cst_strains( cst_id = 15 ) # Get stresses [σx, σy, τxy] cst_stresses = results.get_cst_stresses( cst_id = 15 )
Membrane Q6/Q6I Elements # For Q6 elements (3 DOF per node) q6_disp = results.get_membrane_q3dof_displacements( membrane_q3dof_id = 20 ) # Returns: [Ux1, Uy1, Rz1, Ux2, Uy2, Rz2, Ux3, Uy3, Rz3, Ux4, Uy4, Rz4] # For Q6I/Q4/Q8 elements (2 DOF per node) q6i_disp = results.get_membrane_q2dof_displacements( membrane_q2dof_id = 21 ) # Returns: [Ux1, Uy1, Ux2, Uy2, Ux3, Uy3, Ux4, Uy4]
Exporting Results to DataFrames Convert results to pandas DataFrames for easy export and analysis:
import pandas as pd model.solve() results = model.get_results( "Dead Load" ) # Get node and element results as DataFrames df_nodes, df_elements = results.get_dataframes() # Node DataFrame columns: # ['node_id', 'Ux', 'Uy', 'Rz', 'ReacFx', 'ReacFy', 'ReacMz'] print (df_nodes.head()) # Element DataFrame columns: # ['ele_id', 'Uxi', 'Uyi', 'Rzi', 'Uxj', 'Uyj', 'Rzj', # 'Ni', 'Vi', 'Mi', 'Nj', 'Vj', 'Mj'] print (df_elements.head()) # Export to CSV df_nodes.to_csv( "node_results.csv" , index = False ) df_elements.to_csv( "element_results.csv" , index = False )
Complete Example from milcapy import SystemModel, BeamTheoriesType import numpy as np model = SystemModel() # Build model model.add_material( "steel" , modulus_elasticity = 2e8 , poisson_ratio = 0.3 ) model.add_rectangular_section( "beam" , "steel" , base = 0.2 , height = 0.4 ) 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" ) model.add_member( 2 , 2 , 3 , "beam" ) model.add_restraint( 1 , ux = True , uy = True , rz = True ) model.add_restraint( 3 , ux = False , uy = True , rz = False ) model.add_load_pattern( "Load" ) model.add_point_load( 2 , "Load" , fy =- 50 ) model.add_distributed_load( 1 , "Load" , load_start =- 10 , load_end =- 10 ) # Solve and extract results model.solve() results = model.get_results( "Load" ) # Node results print ( " \n === NODE RESULTS ===" ) for node_id in [ 1 , 2 , 3 ]: disp = results.get_node_displacements(node_id) react = results.get_node_reactions(node_id) print ( f "Node { node_id } :" ) print ( f " Displacement: Ux= { disp[ 0 ] :.6f} , Uy= { disp[ 1 ] :.6f} , Rz= { disp[ 2 ] :.6f} " ) print ( f " Reactions: Rx= { react[ 0 ] :.2f} , Ry= { react[ 1 ] :.2f} , Mz= { react[ 2 ] :.2f} " ) # Member results print ( " \n === MEMBER RESULTS ===" ) for member_id in [ 1 , 2 ]: forces = results.get_member_internal_forces(member_id) print ( f "Member { member_id } :" ) print ( f " Node i: N= { forces[ 0 ] :.2f} , V= { forces[ 1 ] :.2f} , M= { forces[ 2 ] :.2f} " ) print ( f " Node j: N= { forces[ 3 ] :.2f} , V= { forces[ 4 ] :.2f} , M= { forces[ 5 ] :.2f} " ) # Max moment M_diagram = results.get_member_bending_moment(member_id) M_max = np.max(np.abs(M_diagram)) print ( f " Max moment: { M_max :.2f} " )
Results Object Structure The Results class stores data in the following structure:
results.model = { "displacements" : np.ndarray, # Global displacement vector "reactions" : np.ndarray # Global reaction vector } results.nodes = { node_id: { "displacements" : np.ndarray, # [Ux, Uy, Rz] "reactions" : np.ndarray # [Rx, Ry, Mz] } } results.members = { member_id: { "displacements" : np.ndarray, # [Uxi, Uyi, Rzi, Uxj, Uyj, Rzj] "internal_forces" : np.ndarray, # [Ni, Vi, Mi, Nj, Vj, Mj] "x_val" : np.ndarray, # x-coordinates "axial_forces" : np.ndarray, # N(x) "shear_forces" : np.ndarray, # V(x) "bending_moments" : np.ndarray, # M(x) "deflections" : np.ndarray, # y(x) "slopes" : np.ndarray, # θ(x) "axial_displacements" : np.ndarray # u(x) } } results.trusses = { truss_id: { "displacements" : np.ndarray, "internal_forces" : np.ndarray, "axial_forces" : np.ndarray, "axial_displacements" : np.ndarray } } results. CST = { cst_id: { "displacements" : np.ndarray, "strains" : np.ndarray, "stresses" : np.ndarray } }
Next Steps
Visualization Visualize results with interactive plots
Model Building Learn more about building structural models
