fixed-displacement_elastic.py
da29a847c7bbmaster

fixed-displacement_elastic.py
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			import argparse
			import sys

			import GMatElastic
			import GooseFEM
			import numpy as np

			# mesh
			# ----

			# define mesh
			mesh = GooseFEM.Mesh.Quad4.Regular(5, 5)

			# mesh dimensions
			nelem = mesh.nelem
			nne = mesh.nne
			ndim = mesh.ndim

			# mesh definition, displacement, external forces
			coor = mesh.coor()
			conn = mesh.conn()
			dofs = mesh.dofs()
			disp = np.zeros_like(coor)
			fext = np.zeros_like(coor)

			# list of prescribed DOFs
			iip = np.concatenate(
			(
			dofs[mesh.nodesRightEdge(), 0],
			dofs[mesh.nodesTopEdge(), 1],
			dofs[mesh.nodesLeftEdge(), 0],
			dofs[mesh.nodesBottomEdge(), 1],
			)
			)

			# simulation variables
			# --------------------

			# vector definition
			vector = GooseFEM.VectorPartitioned(conn, dofs, iip)

			# allocate system matrix
			K = GooseFEM.MatrixPartitioned(conn, dofs, iip)
			Solver = GooseFEM.MatrixPartitionedSolver()

			# element definition
			elem = GooseFEM.Element.Quad4.QuadraturePlanar(vector.AsElement(coor))
			nip = elem.nip

			# material definition
			# -------------------

			mat = GMatElastic.Cartesian3d.Elastic2d(K=np.ones([nelem, nip]), G=np.ones([nelem, nip]))

			# solve
			# -----

			# strain
			ue = vector.AsElement(disp)
			elem.symGradN_vector(ue, mat.Eps)
			mat.refresh()

			# internal force
			fe = elem.Int_gradN_dot_tensor2_dV(mat.Sig)
			fint = vector.AssembleNode(fe)

			# stiffness matrix
			Ke = elem.Int_gradN_dot_tensor4_dot_gradNT_dV(mat.C)
			K.assemble(Ke)

			# residual
			fres = fext - fint

			# set fixed displacements
			disp[mesh.nodesRightEdge(), 0] = +0.2
			disp[mesh.nodesTopEdge(), 1] = -0.2
			disp[mesh.nodesLeftEdge(), 0] = 0.0 # not strictly needed: default == 0
			disp[mesh.nodesBottomEdge(), 1] = 0.0 # not strictly needed: default == 0

			# solve
			Solver.solve(K, fres, disp)

			# post-process
			# ------------

			# strain
			vector.asElement(disp, ue)
			elem.symGradN_vector(ue, mat.Eps)
			mat.refresh()

			# internal force
			elem.int_gradN_dot_tensor2_dV(mat.Sig, fe)
			vector.assembleNode(fe, fint)

			# apply reaction force
			vector.copy_p(fint, fext)

			# residual
			fres = fext - fint

			# print residual
			assert np.isclose(np.sum(np.abs(fres)) / np.sum(np.abs(fext)), 0)

			# plot
			# ----

			parser = argparse.ArgumentParser()
			parser.add_argument("--plot", action="store_true", help="Plot result")
			parser.add_argument("--save", type=str, help="Save plot (plot not shown)")
			args = parser.parse_args(sys.argv[1:])

			if args.plot:

			import GooseMPL as gplt
			import matplotlib.pyplot as plt

			plt.style.use(["goose", "goose-latex"])

			# average equivalent stress per element
			dV = elem.AsTensor(2, elem.dV)
			Sigav = np.average(mat.Sig, weights=dV, axis=1)
			sigeq = GMatElastic.Cartesian3d.Sigeq(Sigav)

			# plot
			fig, ax = plt.subplots()
			gplt.patch(coor=coor + disp, conn=conn, cindex=sigeq, cmap="jet", axis=ax, clim=(0, 0.1))
			gplt.patch(coor=coor, conn=conn, linestyle="--", axis=ax)

			# optional save
			if args.save is not None:
			fig.savefig(args.save)
			else:
			plt.show()

			plt.close(fig)

rGOOSEFEM/docs/examples/statics/fixed-displacement_elastic.pyda29a847c7bbmaster

fixed-displacement_elastic.pyView Options

rGOOSEFEM/docs/examples/statics/fixed-displacement_elastic.py
da29a847c7bbmaster

fixed-displacement_elastic.py
View Options