How can I plot 2d FEM results using matplotlib?

问题:

I'm developing a 2D plane finite element tool. One of the features is the ability to visualize the stresses on a particular object.

This tool creates a quadrilateral mesh using the following data:

• nodes: numpy array [[x1 y1], [x2 y2], etc] -> x and y coordinates of every node in the mesh

• elements: numpy array [[1 2 3 4], [2 3 5 6]] -> every line of the array corresponds to the 4 points of one particular element of the mesh.

I was able to implement a method that plots the mesh:

import matplotlib.pyplot as plt
import matplotlib.collections
import matplotlib.cm as cm

import numpy as np


def showMeshPlot(nodes, elements):

    y = nodes[:,0]
    z = nodes[:,1]

    #https://stackoverflow.com/questions/49640311/matplotlib-unstructered-quadrilaterals-instead-of-triangles
    def quatplot(y,z, quatrangles, ax=None, **kwargs):

        if not ax: ax=plt.gca()
        yz = np.c_[y,z]
        verts= yz[quatrangles]
        pc = matplotlib.collections.PolyCollection(verts, **kwargs)
        ax.add_collection(pc)
        ax.autoscale()

    plt.figure()
    plt.gca().set_aspect('equal')

    quatplot(y,z, np.asarray(elements), ax=None, color="crimson", facecolor="None")
    if nodes:            
        plt.plot(y,z, marker="o", ls="", color="crimson")

    plt.title('This is the plot for: quad')
    plt.xlabel('Y Axis')
    plt.ylabel('Z Axis')


    plt.show()

nodes = np.array([[0,0], [0,0.5],[0,1],[0.5,0], [0.5,0.5], [0.5,1], [1,0], 
                  [1,0.5],[1,1]])
elements = np.array([[0,3,4,1],[1,4,5,2],[3,6,7,4],[4,7,8,5]])
stresses = np.array([1,2,3,4])

showMeshPlot(nodes, elements)

Which produces a plot like this:

Now, i have an 1D array with the stresses on the object, with the same length as the elements array.

My question is how can i visualize those stresses (with a scalar bar) using matplotlib? I looked into pcolormesh, but i couldn't understand how it could work with my data. Here's an example of what i want to achieve (credits to robbievanleeuwen):

Note: I couldn't replicate the above example because he uses a triangular mesh instead of quads.

Thanks in advance!

回答1:

A PolyCollection is a ScalarMappable. It can have an array of values, a colormap and a normalization set. Here you would supply the stresses array to the PolyCollection and choose some colormap to use. The rest is rearanging the function a bit, such that can take the additional data as input and creates a colorbar.

import matplotlib.pyplot as plt
import matplotlib.collections
import numpy as np


def showMeshPlot(nodes, elements, values):

    y = nodes[:,0]
    z = nodes[:,1]

    def quatplot(y,z, quatrangles, values, ax=None, **kwargs):

        if not ax: ax=plt.gca()
        yz = np.c_[y,z]
        verts= yz[quatrangles]
        pc = matplotlib.collections.PolyCollection(verts, **kwargs)
        pc.set_array(values)
        ax.add_collection(pc)
        ax.autoscale()
        return pc

    fig, ax = plt.subplots()
    ax.set_aspect('equal')

    pc = quatplot(y,z, np.asarray(elements), values, ax=ax, 
             edgecolor="crimson", cmap="rainbow")
    fig.colorbar(pc, ax=ax)        
    ax.plot(y,z, marker="o", ls="", color="crimson")

    ax.set(title='This is the plot for: quad', xlabel='Y Axis', ylabel='Z Axis')

    plt.show()

nodes = np.array([[0,0], [0,0.5],[0,1],[0.5,0], [0.5,0.5], [0.5,1], [1,0], 
                  [1,0.5],[1,1]])
elements = np.array([[0,3,4,1],[1,4,5,2],[3,6,7,4],[4,7,8,5]])
stresses = np.array([1,2,3,4])

showMeshPlot(nodes, elements, stresses)

回答2:

I think your best option is to use tricontour. You already have the triangulation, right?

It creates plots like this one:

(from here)

https://matplotlib.org/api/_as_gen/matplotlib.axes.Axes.tricontour.html