STRUCTURAL_FEA

Overview

The PyniteFEA package used in this function provides a Python interface for 3D static analysis of elastic structures. This example function only returns support reactions for 3D frames and beams, but much more is possible with the library. See the PyniteFEA documentation for details.

This example function is provided as-is without any representation or warranty of correctness. DO NOT USE for production applications without your own testing and validation.

Usage

To use this function in Excel, provide lists of nodes, members, materials, sections, supports, and loads as 2D arrays.


=STRUCTURAL_FEA(nodes, members, materials, sections, supports, nodal_loads)

Arguments

Argument	Type	Required	Description	Example
nodes	list[list]	Required	List of nodes: [name, x, y, z]	[[“N1”,0,0,0],[“N2”,168,0,0]]
members	list[list]	Required	List of members: [name, i-node, j-node, material, section]	[[“M1”,“N1”,“N2”,“Steel”,“W8x24”]]
materials	list[list]	Required	List of materials: [name, E, G, nu, rho]	[[“Steel”,29000,11200,0.3,0.284/12**3]]
sections	list[list]	Required	List of sections: [name, A, Iy, Iz, J]	[[“W8x24”,7.08,18.3,82.7,0.346]]
supports	list[list]	Required	List of supports: [node, DX, DY, DZ, RX, RY, RZ] (bools)	[[“N1”,TRUE,TRUE,TRUE,TRUE,FALSE,FALSE]]
nodal_loads	list[list]	Required	List of nodal loads: [node, direction, value]	[[“N2”,“FY”,-5]]

Returns

Output Type	Type	Description	Example
reactions	list[list]	Support reactions: [node, DX, DY, DZ, RX, RY, RZ]	[[“N1”,0.0,5.0,0.0,0.0,0.0,0.0]]
error	varies	Error message if calculation fails	”Error: Invalid input”

Example

Space Frame Nodal Loads

nodes:

name	x	y	z
N1	0	0	0
N2	-100	0	0
N3	0	0	-100
N4	0	-100	0

members:

name	i-node	j-node	material	section
M1	N2	N1	Steel	MySection
M2	N3	N1	Steel	MySection
M3	N4	N1	Steel	MySection

materials:

name	E	G	nu	rho
Steel	30000	10000	0.3	0.0002836

sections:

name	A	Iy	Iz	J
MySection	10	100	100	50

supports:

node	DX	DY	DZ	RX	RY	RZ
N2	TRUE	TRUE	TRUE	TRUE	TRUE	TRUE
N3	TRUE	TRUE	TRUE	TRUE	TRUE	TRUE
N4	TRUE	TRUE	TRUE	TRUE	TRUE	TRUE

nodal_loads:

node	direction	value
N1	FY	-50
N1	MX	-1000

Output: reactions

node	DX	DY	DZ	RX	RY	RZ
N2	-0.213	0.318	0.0526	19.98	-3.17	19.0
N3	0.0295	7.70	7.06	-265	0.940	0.517
N4	0.183	42.0	-7.11	-236	-0.0890	-6.07

Python Code


import micropip
await micropip.install('PyniteFEA')
from Pynite import FEModel3D
 
def structural_fea(nodes, members, materials, sections, supports, nodal_loads):
    """
    Performs 3D finite element analysis using the Pynite package and returns support reactions.  This function is provided as an example only without any representation or warranty of correctness. DO NOT rely on for production use without your own testing and validation.
 
    Args:
        nodes (list[list]): List of nodes: [name, x, y, z].
        members (list[list]): List of members: [name, i-node, j-node, material, section].
        materials (list[list]): List of materials: [name, E, G, nu, rho].
        sections (list[list]): List of sections: [name, A, Iy, Iz, J].
        supports (list[list]): List of supports: [node, DX, DY, DZ, RX, RY, RZ] (bools).
        nodal_loads (list[list]): List of nodal loads: [node, direction, value].
 
    Returns:
        reactions (list[list]): Support reactions: [node, DX, DY, DZ, RX, RY, RZ].
        If an error occurs, returns a list[list[str]] with the error message.
    """
    try:
        model = FEModel3D()
        # Add materials
        for m in materials:
            model.add_material(str(m[0]), float(m[1]), float(m[2]), float(m[3]), float(m[4]))
        # Add sections
        for s in sections:
            model.add_section(str(s[0]), float(s[1]), float(s[2]), float(s[3]), float(s[4]))
        # Add nodes
        for n in nodes:
            model.add_node(str(n[0]), float(n[1]), float(n[2]), float(n[3]))
        # Add members
        for mem in members:
            model.add_member(str(mem[0]), str(mem[1]), str(mem[2]), str(mem[3]), str(mem[4]))
        # Add supports
        for sup in supports:
            model.def_support(str(sup[0]), bool(sup[1]), bool(sup[2]), bool(sup[3]), bool(sup[4]), bool(sup[5]), bool(sup[6]))
        # Add nodal loads
        for ld in nodal_loads:
            model.add_node_load(str(ld[0]), str(ld[1]), float(ld[2]))
        # Analyze
        model.analyze()
        # Get reactions
        reactions = []
        for sup in supports:
            node = model.nodes[str(sup[0])]
            reactions.append([
                str(sup[0]),
                float(node.RxnFX['Combo 1']),
                float(node.RxnFY['Combo 1']),
                float(node.RxnFZ['Combo 1']),
                float(node.RxnMX['Combo 1']),
                float(node.RxnMY['Combo 1']),
                float(node.RxnMZ['Combo 1'])
            ])
        return reactions
    except Exception as e:
        # Return error as list[list[str]] to match output format
        return [[str(e)]]

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