Simple beam modeling

try:
    import piplite
    await piplite.install(['ipywidgets==7.7.0', 'ipyflex', 'plotly', 'cosapp'])
except:
    pass

from cosapp.ports import Port
from cosapp.systems import System
import numpy as np

class GeometryPort(Port):
    def setup(self):
        self.add_variable("visible", True, desc="Should this geometry be shown?")
        self.add_variable("shape", None, desc="Geometrical object")
class BeamGeo(System):
    
    def setup(self):
        self.add_inward("file","path")
        self.add_inward("mesh_size",100)
        self.add_inward('width', 0.5, unit = 'm')
        self.add_inward('height',0.5, unit = 'm')
        self.add_inward('length', 5., unit = 'm')
        self.add_outward('I', desc='Second area moment')
        self.add_outward('grid', np.zeros(1))
        self.add_outward("section", [])
        self.add_output(GeometryPort, 'geom')
    def compute(self):
        self.I = self.width*self.height**3/12.
        self.grid = np.array([i*self.length/self.mesh_size for i in range(0,int(self.mesh_size)+1)])
        section = [[],[]]
        for i in range(0,100):
            section[0].append((- 0.5 + i/100.)*self.width)
            section[1].append(-0.5*self.height)
        for i in range(0,100):
            section[0].append(0.5*self.width)
            section[1].append((- 0.5 + i/100.)*self.height) 
        for i in range(0,100):
            section[0].append((0.5 - i/100.)*self.width)
            section[1].append(0.5*self.height)  
        for i in range(0,100):
            section[0].append( -0.5*self.width)
            section[1].append((0.5 - i/100.)*self.height)  
        self.section = section

class BeamMeca(System):
    def setup(self):
        
        self.add_inward('E', 270, desc = "Young modulus",  valid_range = [100,150],limits = [50,200])
        self.add_inward("grid", np.zeros(101), valid_range = [2,4],limits = [-np.inf,10] )
        self.add_inward("I", 1., desc='Second area moment' )
        self.add_inward("force", -1., desc='Force value', unit = 'N' )
        self.add_inward("position", 0.5, desc="force relative position",limits= [0.2,0.3], valid_range = [0.1,0.8] )
        self.add_outward("M", np.zeros(1), desc = "Bending moments" )
        self.add_outward("Q", np.zeros(1), desc = "Shear forces" )
        self.add_outward("W", np.zeros(1), desc = "Deflections" )
        self.add_outward("maxW", 0, desc = "Max deflections" )
        self.add_outward("f_position", 0.5, desc="force  position")
        self.add_outward("maxW_loc", 0, desc = "Max deflections location" )
    def compute(self):
        if self.position > 1.:
            position = 0.99
        elif self.position < 0:
            position = 0.
        else:
            position = self.position
        mesh_size = len(self.grid)
        L = self.grid[-1]
        b = (1.- position)*L
        a = position*L
        M =[]
        Q = []
        W = []
        for i in range(0, int(mesh_size*position)):
            x = self.grid[i]
            M.append(self.force*b*x/L)
            Q.append(self.force*b/L)
            W.append(self.force*b*x*(L**2 - b**2 - x**2)/(6*L*self.E*self.I))  
        for j in range(int(mesh_size*position), mesh_size):
            x = self.grid[j]
            M.append(self.force*a*(L - x)/L)
            Q.append(self.force*(b/L-1))
            W.append(self.force*b*x*(L**2 - b**2 - x**2)/(6*L*self.E*self.I)+ self.force*(x-a)**3/(6*self.E*self.I))
        self.M = np.array(M)
        self.Q = np.array(Q) 
        self.W = np.array(W)
        self.maxW_loc = int(np.argmax(np.absolute(self.W)))-1
        self.maxW = self.W[self.maxW_loc]
        self.f_position = mesh_size*position

class Main(System):
    def setup(self):
        self.add_inward("maintest",0)
        self.add_child(BeamGeo("geo"))
        self.add_child(BeamMeca("meca"))
        self.connect(self.geo.outwards, self.meca.inwards, ["I", "grid"])

main = Main("main")
main.run_drivers()

import ipywidgets
import ipyflex
import plotly.graph_objects as go

widget_M = go.FigureWidget(go.Bar(
    y=main.meca.M,
    # marker_color='rgba(91, 91, 91, 0.73)',
    name='M',
))
widget_Q = go.FigureWidget(go.Scatter(
    y=main.meca.Q ,
    # marker_color='rgba(91, 91, 91, 0.73)',
    name='M',
))
widget_W = go.FigureWidget(go.Bar(
    y=main.meca.W,
    # marker_color='rgba(91, 91, 91, 0.73)',
    name='M',
), layout_yaxis_range=[-10,0])

E_slider = ipywidgets.FloatSlider(    value=150,
    min=50,
    max=250,description='Young modulus:',
                                 continuous_update=False,)
def on_E_change(change):
    main.meca.E = change['new']
    main.run_drivers()
    widget_M.data[0].y = main.meca.M
    widget_Q.data[0].y = main.meca.Q
    widget_W.data[0].y = main.meca.W
E_slider.observe(on_E_change, names='value')

position_slider = ipywidgets.FloatSlider(    value=0.5,
    min=0.1,
    max=0.8,
                                         continuous_update=False,
                                        description='Force position',)
def on_position_change(change):
    main.meca.position = change['new']
    main.run_drivers()
    widget_M.data[0].y = main.meca.M
    widget_Q.data[0].y = main.meca.Q
    widget_W.data[0].y = main.meca.W
position_slider.observe(on_position_change, names='value')
control = ipywidgets.VBox([E_slider, position_slider])

widget_dict = {'Moment': widget_M, 'Deflection': widget_W, 'Shear forces':widget_Q, 'Control':  control}
w = ipyflex.FlexLayout(widget_dict, 
                       template='beam.json',
                       editable=False,
                       header={'title':'Simply supported beam', 'buttons':[]},
                      )