Patch test for mixed mesh of triangular and quadrilateral plate elements under in-plane loading

PatchMesher test for the mixed mesh of triangular and quadrilateral plate elements.

import math
import numpy as np

from femedu.examples import Example

from femedu.domain import System, Node
from femedu.solver import NewtonRaphsonSolver
from femedu.elements.linear import Quad, Triangle
from femedu.materials import PlaneStress
from femedu.mesher import *


class ExamplePlate04(Example):

    def problem(self):
        # ========== setting mesh parameters ==============

        Nx = 7        # number of elements in the mesh
        Ny = 6        # number of elements in the mesh
        Lx = 100.0    # length of plate in the x-direction
        Ly =  80.0    # length of plate in the y-direction

        # ========== setting material parameters ==============

        params = dict(
            E  = 20000.,    # Young's modulus
            nu = 0.250,     # Poisson's ratio
            t  = 1.00       # thickness of the plate
        )

        # ========== setting load parameters ==============

        px  = 10.0         # uniform load normal to x=const
        py  =  0.0         # uniform load normal to y=const
        pxy =  0.0         # uniform shear load on x=const and y=const

        # ========== setting analysis parameters ==============

        target_load_level = 1.00     # reference load
        max_steps = 2                # number of load steps: 2 -> [0.0, 1.0]

        # define a list of target load levels
        load_levels = np.linspace(0, target_load_level, max_steps)

        #
        # ==== Build the system model ====
        #

        model = System()
        model.setSolver(NewtonRaphsonSolver())

        # create reference points
        pt0 = (0,0)
        pt1 = (0.5*Lx,0)
        pt2 = (Lx,Ly)
        pt3 = (0,Ly)
        pt4 = (0.25*Lx, 0.0)
        pt5 = (0.65*Lx, Ly/2)
        pt6 = (0.55*Lx, Ly)
        pt7 = (0.0, Ly/2)
        pt8 = (0.325*Lx, 0.55*Ly)
        pt9 = (Lx,0.0)

        mesher1 = PatchMesher(model,
                             pt0, pt1, pt2, pt3, # corner nodes
                             pt4, pt5, pt6, pt7, # mid-side nodes
                             pt8)                # center node
        #nodes1, elements1 = mesher1.triangleMesh(Nx, Ny, LinearTriangle, PlaneStress(params))
        nodes1, elements1 = mesher1.quadMesh(Nx, Ny, Quad, PlaneStress(params))

        mesher2 = TriPatchMesher(model,
                                 pt1, pt9, pt2, # corner nodes
                                 None, None, pt5, # mid-side nodes
                                 )
        #mesher2.shift(1.25*Lx, Ly/2)
        nodes2, elements2 = mesher2.triangleMesh(Ny, Triangle, PlaneStress(params))
        #nodes2, elements2 = mesher2.quadMesh(Ny, Triangle, PlaneStress(params))

        # tie the patches together
        mesher1.tie(mesher2)

        nodes    = nodes1    + nodes2
        elements = elements1 + elements2

        # define support(s)

        ## find nodes at y==0 and x==0

        for node in nodes:
            X = node.getPos()
            if math.isclose(X[0], 0.0):
                node.fixDOF('ux')    # horizontal support left side
            if math.isclose(X[1], 0.0):
                node.fixDOF('uy')    # vertical support at y==0

        # ==== complete the reference load ====

        for elem, face in model.findFacesAlongLine((Lx, 0.0), (0.0, 1.0)):
            face.setLoad(px, 0.0)

        #model.report()

        model.plot(factor=0, title="undeformed system", show_bc=1, show_loads=1)

        model.setLoadFactor(10.0)
        model.solve()

        #model.report()

        model.plot(factor=25.)
        model.valuePlot('sxx', show_mesh=1)
        model.valuePlot('syy', show_mesh=1)
        model.valuePlot('sxy', show_mesh=1)

Run the example by creating an instance of the problem and executing it by calling Example.run()

if __name__ == "__main__":
    ex = ExamplePlate04()
    ex.run()

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+ Quad_926: nodes ( Node_741 Node_742 Node_750 Node_749 )
    material: list
    strain (0): xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress (0): xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
    strain (1): xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress (1): xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
    strain (2): xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress (2): xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
    strain (3): xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress (3): xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_961: nodes ( Node_776 Node_777 Node_778 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_932: nodes ( Node_756 Node_757 Node_763 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_932: nodes ( Node_756 Node_757 Node_763 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_941: nodes ( Node_762 Node_763 Node_768 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_942: nodes ( Node_763 Node_762 Node_756 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_941: nodes ( Node_762 Node_763 Node_768 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_949: nodes ( Node_767 Node_768 Node_772 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_950: nodes ( Node_768 Node_767 Node_762 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_949: nodes ( Node_767 Node_768 Node_772 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_955: nodes ( Node_771 Node_772 Node_775 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_956: nodes ( Node_772 Node_771 Node_767 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_955: nodes ( Node_771 Node_772 Node_775 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_959: nodes ( Node_774 Node_775 Node_777 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_960: nodes ( Node_775 Node_774 Node_771 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_959: nodes ( Node_774 Node_775 Node_777 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_961: nodes ( Node_776 Node_777 Node_778 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_962: nodes ( Node_777 Node_776 Node_774 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+ Triangle_961: nodes ( Node_776 Node_777 Node_778 )
    material: PlaneStress
    strain: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=-0.000e+00
    stress: xx=0.000e+00 yy=0.000e+00 xy=0.000e+00 zz=0.000e+00
+