beam_width = 2.
pressure = 2.
domainCorners = np.array([[0., 0.], [0, beam_width], [beam_length, 0.],
[beam_length, beam_width]])
geomDomain = Quadrilateral(domainCorners)
model_data = dict()
model_data["E"] = 1e3
model_data["nu"] = 0.25
model_data["state"] = "plane stress"
numElemU = 20
numElemV = 10
numGauss = 4
#xPhys, yPhys = myQuad.getRandomIntPts(numPtsU*numPtsV)
xPhys, yPhys, Wint = geomDomain.getQuadIntPts(numElemU, numElemV, numGauss)
data_type = "float32"
Xint = np.concatenate((xPhys, yPhys), axis=1).astype(data_type)
Wint = np.array(Wint).astype(data_type)
# prepare boundary points in the fromat Xbnd = [Xcoord, Ycoord, norm_x, norm_y] and
# Wbnd for boundary integration weights and
# Ybnd = [trac_x, trac_y], where Xcoord, Ycoord are the x and y coordinates of the point,
# norm_x, norm_y are the x and y components of the unit normals
# trac_x, trac_y are the x and y components of the traction vector at each point
#boundary for x=beam_length, include both the x and y directions
xPhysBnd, yPhysBnd, xNorm, yNorm, Wbnd = geomDomain.getQuadEdgePts(
numElemV, numGauss, 2)
Xbnd = np.concatenate((xPhysBnd, yPhysBnd, xNorm, yNorm),
xmin = 0
xmax = 1
ymin = 0
ymax = 1
domainCorners = np.array([[xmin, ymin], [xmin, ymax], [xmax, ymin],
[xmax, ymax]])
myQuad = Quadrilateral(domainCorners)
numPtsU = 80
numPtsV = 80
numElemU = 20
numElemV = 20
numGauss = 4
boundary_weight = 1e4
xPhys, yPhys, Wint = myQuad.getQuadIntPts(numElemU, numElemV, numGauss)
data_type = "float32"
Xint = np.concatenate((xPhys, yPhys), axis=1).astype(data_type)
Wint = Wint.astype(data_type)
Yint = rhs_fun(Xint[:, [0]], Xint[:, [1]])
xPhysBnd, yPhysBnd, _, _ = myQuad.getUnifEdgePts(numPtsU, numPtsV,
[1, 1, 1, 1])
Xbnd = np.concatenate((xPhysBnd, yPhysBnd), axis=1).astype(data_type)
Ybnd = exact_sol(Xbnd[:, [0]], Xbnd[:, [1]])
Wbnd = boundary_weight * np.ones_like(Ybnd).astype(data_type)
#plot the boundary and interior points
plt.scatter(Xint[:, 0], Xint[:, 1], s=0.5)
plt.scatter(Xbnd[:, 0], Xbnd[:, 1], s=1, c='red')