calculate the cross-sectional force of frame structure using python and API

ササザワヨウスケ — Sun, 14 Feb 2021 03:10:47 +0000

I tried to shoot with a python staged in a textbook of structural mechanics

For those who find structural mechanics difficult for some people, and who enjoy studying python but are not good at structural mechanics.
I would like to solve a structural mechanics problem using python.

The example to be taken up this time is

Draw the Q and M figures of the overhang shown in Figure 4.20.

I would like to solve it quickly with python and api.

Click here for all source code
https://colab.research.google.com/drive/11cMEEUSFgu3hVw0vLOo1PZhvwSiM-5Ys?usp=sharing

Commentary

In an environment called Google colaboratory that can be used without installing python provided free of charge by Google
Solve the problem.

Calculation flow

Generate input data
Let the API calculate the section force
Display the calculation result

1. Generate input data

Input data is recorded in this variable body.

body = dict()

Define a "node"

Define the coordinates and numbers of members and intersections of members in a skeleton structure such as a truss

n1 = {"x":0, "y":0, "z":0}
n2 = {"x":2, "y":0, "z":0}
n3 = {"x":6, "y":0, "z":0}

body["node"] = {
    "1": n1,
    "2": n2,
    "3": n3 
    }

Define a "member"

Define member numbers and the following information in the skeleton structure

ni: The leftmost point of the member
nj: Rightmost point of the member
e: Material number described later

body["member"] = {
    "1": {"ni":"1", "nj":"2", "e":"1"},
    "2": {"ni":"2", "nj":"3", "e":"1"}
        }

Define "element"

Define "element" means material

number and information below
In this problem, the material is uniform and there is no particular specification, so I entered an appropriate value.

E: Elastic modulus
G: Shear modulus
Xp: Coefficient of expansion
A: Cross-sectional area
J: Torsion constant
Iy: Moment of inertia of area around the y-axis
Iz: Moment of inertia of area around the z-axis

body["element"] = {
    "1":{
       "1":{ "E":20000000, "G":770000, "Xp":0.00001, "A":1.0, "J":1.0, "Iy":1.0, "Iz":1.0 }
      }
    }

Define fulcrum information

n: Fixed rating number
tx: 1 if the displacement in the x direction is fixed, 0 if not fixed
ty: 1, if the displacement in the y direction is fixed, 0 if not fixed
tz: 1 if the displacement in the z direction is fixed, 0 if not fixed
rx: 1 to fix rotation around x-axis, 0 otherwise
ry: 1, if the rotation around the y-axis is fixed, 0 if not fixed
rz: 1, if the rotation around the z-axis is fixed, 0 if not fixed

body["fix_node"] = { 
    "1":[
       {"n":"2","tx":1,"ty":1,"tz":1,"rx":0,"ry":0,"rz":0},
       {"n":"3","tx":0,"ty":1,"tz":1,"rx":0,"ry":0,"rz":0}
      ]
    }

Define load information

fix_node: fulcrum information number
element: Material information number
load_node
- n: Rating number to load the load
- tx: Load acting in the x direction
- ty: Load acting in the y direction
- tz: Load acting in the z direction
- rx: moment acting around the x-axis
- ry: Moment acting around the y-axis
- rz: moment acting around the z axis

body["load"] = {
      "1":{
         "fix_node": "1",
         "element": "1",
         "load_node":[
                      { "n":"1","tx":0,"ty":0,"tz":2,"rx":0,"ry":0,"rz":0 }
                      ]
        }
    }

2. Let the API calculate the section force

The calculation of the section force uses an API called StructuralEngine.
If you POST the above data here, it will calculate the section force.

response = requests.post(
    'https://asia-northeast1-the-structural-engine.cloudfunctions.net/frameWeb-2',
     json.dumps(body),
     headers={'Content-Type': 'application/json'})
result = response.json()   
print(result)

{'1': {'disg': {'1': {'dx': 0.0, 'dy': 0.0, 'dz': 8e-07, 'rx': 0.0, 'ry': 4.666666666666666e-07, 'rz': 0.0}, '2': {'dx': 0.0, 'dy': 0.0, 'dz': 0.0, 'rx': 0.0, 'ry': 2.6666666666666667e-07, 'rz': 0.0}, '3': {'dx': 0.0, 'dy': 0.0, 'dz': 0.0, 'rx': 0.0, 'ry': -1.333333333333333e-07, 'rz': 0.0}}, 'reac': {'2': {'tx': 0.0, 'ty': 0.0, 'tz': -1.0000000000000016, 'mx': 0.0, 'my': 0.0, 'mz': 0.0}, '3': {'tx': 0.0, 'ty': 0.0, 'tz': 1.0000000000000002, 'mx': 0.0, 'my': 0.0, 'mz': 0.0}}, 'fsec': {'1': {'P1': {'fxi': -0.0, 'fyi': -0.0, 'fzi': -2.0000000000000018, 'mxi': 0.0, 'myi': -3.552713678800501e-15, 'mzi': 0.0, 'fxj': 0.0, 'fyj': 0.0, 'fzj': -2.0000000000000018, 'mxj': -0.0, 'myj': 4.000000000000002, 'mzj': -0.0, 'L': 2.0}}, '2': {'P1': {'fxi': -0.0, 'fyi': -0.0, 'fzi': 1.0000000000000002, 'mxi': 0.0, 'myi': 4.0, 'mzi': 0.0, 'fxj': 0.0, 'fyj': 0.0, 'fzj': 1.0000000000000002, 'mxj': -0.0, 'myj': -4.440892098500626e-16, 'mzj': -0.0, 'L': 4.0}}}}}

3. Display the calculation result

Draw Q and M diagrams from the analysis results obtained by the API.

Extract information on section force

Since the information is stored in the following hierarchy, it is taken out and drawn.

"1": Case number
- "1", "2": Part number
- fsec: Cross-sectional force
  - P1: Points of interest
  - fzi: Shear force on the left side in the z-axis direction
  - fzj: Shear force on the right side in the z-axis direction
  - myi: Bending moment on the left side around the y-axis
  - myj: Bending moment on the right side around the y-axis

# Take out the information of Case 1
case1 = result['1']

# Extract section force information
fsec = case1['fsec']

# Take out the information of member number 1
member1 = fsec['1']['P1']

# Take out the information of member number 2
member2 = fsec['2']['P1']

Draw Q and M diagrams

# X-coordinate of member
x = [n1 ['x'], n2 ['x'], n2 ['x'], n3 ['x']]
# Y coordinate of member
y = [n1 ['y'], n2 ['y'], n2 ['y'], n3 ['y']]
# Shear force
yQ = [member1 ['fzi'], member1 ['fzj'], member2 ['fzi'], member2 ['fzj']]
# Bending moment
yM = [member1 ['myi'], member1 ['myj'], member2 ['myi'], member2 ['myj']]

Draw a diagram from the above information.

fig = plt.figure()

ax1 = fig.add_subplot(1, 2, 1)
ax1.set_ylim([2, -3])
ax1.set_xlim([-1, 7])
ax1.plot(x, y, marker ='o', color = "darkblue")
ax1.plot(x, yQ, color = "lightblue")
ax1.fill_between( x, yQ, color="lightblue", alpha=0.2)
ax1.set_title("Q")


ax2 = fig.add_subplot(1, 2, 2)
ax2.set_ylim([-1, 5])
ax2.set_xlim([-1, 7])
ax2.plot(x, y, marker ='o', color = "darkblue")
ax2.plot(x, yM, color = "lightblue")
ax2.fill_between( x, yM, color="lightblue", alpha=0.2)
ax2.set_title("M")

The answers matched

Summary

I tried to solve the problem described in the textbook of structural mechanics with python

Even if you are not good at structural mechanics, if you have python, you can proceed without understanding
I hope you will deepen your understanding of structural mechanics while playing around.

DEV Community: ササザワヨウスケ