horloadist

Calculate horizontal load distribution on multiple supports of a single shell assuming $EA \to \infty$ .

Caution! Do not blindly trust this calculation, but always check the plausibility of the results.

This project provides a tool for structural analysis using the horloadist library. You can define a 2D polygon in the x-y plane representing a shell, along with supports that represent walls and their bending stiffnesses around the x and y axes. Afterwards you can calculate the horizontal reaction forces on the support nodes (walls). Use NonLinSolve for solving systems iteratively with nonlinear wall bending stiffnesses taken from user created csv files.

Example Table Output of LinSolve

glo mass   centre [x,y] : 0.0000, 0.0000
glo stiff. centre [x,y] : 2.4672, -4.7664
loc stiff. centre [x,y] : 2.4672, -4.7664
EIx total               : 9.4
EIy total               : 34.4
EIw total               : 1,937.0

   node nr  glo x  glo y  loc x  loc y    loc xs      loc ys      EIx       EIy     % EIx     % EIy    % EIwx        % EIwy
0        1  -10.0    2.5  -10.0    2.5 -12.467197   7.266411  0.01125   3.12500  0.090820  0.001193  0.011723 -7.240963e-05
1        2  -12.5    0.0  -12.5    0.0 -14.967197   4.766411  3.12500   0.01125  0.000327  0.331345  0.000028 -2.414713e-02
2        3  -10.0   -2.5  -10.0   -2.5 -12.467197   2.266411  0.01125   3.12500  0.090820  0.001193  0.003656 -7.240963e-05
3        4    0.0    7.5    0.0    7.5  -2.467197  12.266411  0.01125   3.12500  0.090820  0.001193  0.019790 -1.432951e-05
4        5    2.5   -7.5    2.5   -7.5   0.032803  -2.733589  0.02250  25.00000  0.726559  0.002386 -0.035282  3.810425e-07
5        6    7.5    0.0    7.5    0.0   5.032803   4.766411  3.12500   0.01125  0.000327  0.331345  0.000028  8.119605e-03
6        7   12.5    5.0   12.5    5.0  10.032803   9.766411  3.12500   0.01125  0.000327  0.331345  0.000057  1.618629e-02


Fx, Fy                  : 0, -1
ex, ey                  : 2.4672, -4.7664
tor. Ts,x  =  Fx * ey   : -0.0000
tor. Ts,y  =  Fy * ex   : 2.4672
tor. Ts = Ts,x + Ts,y   : 2.4672

   node nr  Vx ~ EIx  Vy ~ EIy  Ts ~ EIwx     Ts ~ EIwy        Vx        Vy
0        1       0.0 -0.001193  -0.028923 -1.786488e-04 -0.028923 -0.001371
1        2       0.0 -0.331345  -0.000068 -5.957571e-02 -0.000068 -0.390921
2        3       0.0 -0.001193  -0.009021 -1.786488e-04 -0.009021 -0.001371
3        4       0.0 -0.001193  -0.048825 -3.535372e-05 -0.048825 -0.001228
4        5       0.0 -0.002386   0.087047  9.401069e-07  0.087047 -0.002385
5        6       0.0 -0.331345  -0.000068  2.003266e-02 -0.000068 -0.311313
6        7       0.0 -0.331345  -0.000140  3.993476e-02 -0.000140 -0.291411

Example Output of NonLinSolve

Output of plot_nlsolve from NONLIN_main.py in the examples directory:

Prerequisites

• horloadist library
• Python 3.x
• pandas
• numpy
• matplotlib
• datetime

Installation

install via pip:

pip install horloadist

Usage

The main script demonstrates how to use the horloadist library to create a structural model and solve it. Here's a brief overview of the process:

1. Import necessary classes from horloadist:

   from horloadist import SupportNode, Polygon, Stucture, LinSolve

2. Define helper functions for moment of inertia calculations:

   def globalIy(dx, dy):
      return dy*dx**3/12
    
   def globalIx(dx, dy):
      return dx*dy**3/12

3. Create support nodes using the SupportNode class.

4. Define the structure's shape using the Polygon class.

5. Create a Stucture object with the defined polygon and support nodes.

6. Solve the structure using LinSolve.

7. Print the results.

Example

The provided example creates a plate structure with seven support nodes and solves it for a specific load case.

# Create support nodes
w1 = SupportNode(nr=1, glob_x=-10.0,  glob_y=2.5, glob_kx=globalIy(5, 0.3), glob_ky=globalIx(5, 0.3))
# ... (other nodes)

# Define the plate
plate = Polygon([[-12.5,-7.5], [12.5, -7.5], [12.5, 7.5], [-12.5, 7.5]])

# Create and solve the structure
struc = Stucture(nodes=[w1, w2, w3, w4, w5, w6, w7], glo_mass_centre=plate.centroid)
sol = LinSolve(structure=struc, x_mass_force=0, y_mass_force=-1)

# Print results
struc.printTable()
sol.printTable()

Possible Further Improvements

• add plot for geometry and force-vectors
• add plot for bending stiffnesses imported from csv files
• add angle param for KX.globalRectangular(... , angle_from_x : float = ...)
• Add a ceiling recess

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.