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unit_cube_mode_examples.jl
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unit_cube_mode_examples.jl
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module unit_cube_mode_examples
using FinEtools
using FinEtools.MeshExportModule
using FinEtoolsDeforLinear
using FinEtoolsDeforLinear.AlgoDeforLinearModule
using LinearAlgebra
using GEPHelpers: gep_smallest, check_M_orthogonality, check_K_orthogonality
using Arpack
function unit_cube_modes()
println("""
Vibration modes of unit cube of almost incompressible material.
%
Reference: Puso MA, Solberg J (2006) A stabilized nodally integrated
tetrahedral. International Journal for Numerical Methods in
Engineering 67: 841-867.
""")
t0 = time()
E = 1 * phun("PA")
nu = 0.499
rho = 1 * phun("KG/M^3")
a = 1 * phun("M")
b = a
h = a
n1 = 10# How many element edges per side?
na = n1
nb = n1
nh = n1
neigvs = 20 # how many eigenvalues
OmegaShift = (0.01 * 2 * pi)^2
MR = DeforModelRed3D
fens, fes = H20block(a, b, h, na, nb, nh)
geom = NodalField(fens.xyz)
u = NodalField(zeros(size(fens.xyz, 1), 3)) # displacement field
numberdofs!(u)
material = MatDeforElastIso(MR, rho, E, nu, 0.0)
femm = FEMMDeforLinear(MR, IntegDomain(fes, GaussRule(3, 2)), material)
@time K = stiffness(femm, geom, u)
femm = FEMMDeforLinear(MR, IntegDomain(fes, GaussRule(3, 3)), material)
@time M = mass(femm, geom, u)
d, v, nconv = gep_smallest(K + OmegaShift * M,
M, neigvs,
which = :SM)
d = d .- OmegaShift
fs = real(sqrt.(complex(d))) / (2 * pi)
println("Eigenvalues: $fs [Hz]")
@info check_K_orthogonality(d, v, K)
@info check_M_orthogonality(v, M)
@info norm(K * v - M * v * Diagonal(d))
vectors = []
File = "unit_cube_modes.vtk"
for mode in 1:neigvs
scattersysvec!(u, v[:, mode])
push!(vectors, ("mode$mode", deepcopy(u.values)))
end
vtkexportmesh(File, fens, fes; vectors = vectors)
true
end # unit_cube_modes
function unit_cube_modes_arnoldimethod()
println("""
Vibration modes of unit cube of almost incompressible material.
%
Reference: Puso MA, Solberg J (2006) A stabilized nodally integrated
tetrahedral. International Journal for Numerical Methods in
Engineering 67: 841-867.
""")
t0 = time()
E = 1 * phun("PA")
nu = 0.499
rho = 1 * phun("KG/M^3")
a = 1 * phun("M")
b = a
h = a
n1 = 10# How many element edges per side?
na = n1
nb = n1
nh = n1
neigvs = 20 # how many eigenvalues
OmegaShift = (0.01 * 2 * pi)^2
MR = DeforModelRed3D
fens, fes = H20block(a, b, h, na, nb, nh)
geom = NodalField(fens.xyz)
u = NodalField(zeros(size(fens.xyz, 1), 3)) # displacement field
numberdofs!(u)
material = MatDeforElastIso(MR, rho, E, nu, 0.0)
femm = FEMMDeforLinear(MR, IntegDomain(fes, GaussRule(3, 2)), material)
@time K = stiffness(femm, geom, u)
femm = FEMMDeforLinear(MR, IntegDomain(fes, GaussRule(3, 3)), material)
@time M = mass(femm, geom, u)
d, v, nconv = gep_smallest(K + OmegaShift * M,
M, neigvs; method = :ArnoldiMethod, orthogonalize = true,
which = :SM)
d = d .- OmegaShift
fs = real(sqrt.(complex(d))) / (2 * pi)
println("Eigenvalues: $fs [Hz]")
@info check_K_orthogonality(d, v, K)
@info check_M_orthogonality(v, M)
@info norm(K * v - M * v * Diagonal(d))
vectors = []
File = "unit_cube_modes_arnoldimethod.vtk"
for mode in 1:neigvs
scattersysvec!(u, v[:, mode])
push!(vectors, ("mode$mode", deepcopy(u.values)))
end
vtkexportmesh(File, fens, fes; vectors = vectors)
true
end # unit_cube_modes
function unit_cube_modes_algo()
println("""
% Vibration modes of unit cube of almost incompressible material.
%
% Reference: Puso MA, Solberg J (2006) A stabilized nodally integrated
% tetrahedral. International Journal for Numerical Methods in
% Engineering 67: 841-867.""")
t0 = time()
E = 1 * phun("PA")
nu = 0.499
rho = 1 * phun("KG/M^3")
a = 1 * phun("M")
b = a
h = a
n1 = 2# How many element edges per side?
na = n1
nb = n1
nh = n1
neigvs = 20 # how many eigenvalues
omega_shift = (0.1 * 2 * pi)^2
fens, fes = H20block(a, b, h, na, nb, nh)
# Make the region
MR = DeforModelRed3D
material = MatDeforElastIso(MR, rho, E, nu, 0.0)
region1 = FDataDict("femm" => FEMMDeforLinear(MR, IntegDomain(fes, GaussRule(3, 2)),
material), "femm_mass" => FEMMDeforLinear(MR, IntegDomain(fes, GaussRule(3, 3)),
material))
# Make model data
modeldata = FDataDict("fens" => fens, "regions" => [region1],
"omega_shift" => omega_shift, "neigvs" => neigvs)
# Solve
modeldata = AlgoDeforLinearModule.modal(modeldata)
fs = modeldata["omega"] / (2 * pi)
println("Eigenvalues: $fs [Hz]")
modeldata["postprocessing"] = FDataDict("file" => "unit_cube_mode",
"mode" => 10)
modeldata = AlgoDeforLinearModule.exportmode(modeldata)
@async run(`"paraview.exe" $(modeldata["postprocessing"]["file"]*"1.vtk")`)
true
end # unit_cube_modes_algo
function unit_cube_modes_export()
println("""
Vibration modes of unit cube of almost incompressible material.
This example EXPORTS the model to Abaqus.
Reference: Puso MA, Solberg J (2006) A stabilized nodally integrated
tetrahedral. International Journal for Numerical Methods in
Engineering 67: 841-867.
""")
t0 = time()
E = 1 * phun("PA")
nu = 0.499
rho = 1 * phun("KG/M^3")
a = 1 * phun("M")
b = a
h = a
n1 = 5# How many element edges per side?
na = n1
nb = n1
nh = n1
neigvs = 20 # how many eigenvalues
OmegaShift = (0.01 * 2 * pi)^2
MR = DeforModelRed3D
fens, fes = H20block(a, b, h, na, nb, nh)
geom = NodalField(fens.xyz)
u = NodalField(zeros(size(fens.xyz, 1), 3)) # displacement field
numberdofs!(u)
material = MatDeforElastIso(MR, rho, E, nu, 0.0)
femm = FEMMDeforLinear(MR, IntegDomain(fes, GaussRule(3, 2)), material)
K = stiffness(femm, geom, u)
femm = FEMMDeforLinear(MR, IntegDomain(fes, GaussRule(3, 3)), material)
M = mass(femm, geom, u)
d, v, nconv = gep_smallest(K + OmegaShift * M, M, neigvs, which = :SM)
d = d .- OmegaShift
fs = real(sqrt.(complex(d))) / (2 * pi)
println("Eigenvalues: $fs [Hz]")
mode = 7
scattersysvec!(u, v[:, mode])
File = "unit_cube_modes.vtk"
vtkexportmesh(File, fens, fes; vectors = [("mode$mode", u.values)])
@async run(`"paraview.exe" $File`)
AE = AbaqusExporter("unit_cube_modes_h20")
# AE.ios = STDOUT;
HEADING(AE, "Vibration modes of unit cube of almost incompressible material.")
COMMENT(AE, "The first six frequencies are rigid body modes.")
COMMENT(AE, "The first nonzero frequency (7) should be around 0.26 Hz")
PART(AE, "part1")
END_PART(AE)
ASSEMBLY(AE, "ASSEM1")
INSTANCE(AE, "INSTNC1", "PART1")
NODE(AE, fens.xyz)
COMMENT(AE, "The hybrid form of the serendipity hexahedron is chosen because")
COMMENT(AE, "the material is nearly incompressible.")
ELEMENT(AE, "c3d20rh", "AllElements", 1, connasarray(fes))
ORIENTATION(AE, "GlobalOrientation", vec([1.0 0 0]), vec([0 1.0 0]))
SOLID_SECTION(AE, "elasticity", "GlobalOrientation", "AllElements")
END_INSTANCE(AE)
END_ASSEMBLY(AE)
MATERIAL(AE, "elasticity")
ELASTIC(AE, E, nu)
DENSITY(AE, rho)
STEP_FREQUENCY(AE, neigvs)
END_STEP(AE)
close(AE)
true
end # unit_cube_modes_export
function unit_cube_modes_msh8_algo()
println("""
% Vibration modes of unit cube of almost incompressible material.
% Mean-strain hexahedron.
% Reference: Puso MA, Solberg J (2006) A stabilized nodally integrated
% tetrahedral. International Journal for Numerical Methods in
% Engineering 67: 841-867.""")
t0 = time()
E = 1 * phun("PA")
nu = 0.499
rho = 1 * phun("KG/M^3")
a = 1 * phun("M")
b = a
h = a
n1 = 8 # How many element edges per side?
na = n1
nb = n1
nh = n1
neigvs = 20 # how many eigenvalues
omega_shift = (0.1 * 2 * pi)^2
fens, fes = H8block(a, b, h, na, nb, nh)
# Make the region
MR = DeforModelRed3D
material = MatDeforElastIso(MR, rho, E, nu, 0.0)
region1 = FDataDict("femm" => FEMMDeforLinearMSH8(MR, IntegDomain(fes, GaussRule(3, 2)),
material),
"femm_mass" => FEMMDeforLinearMSH8(MR, IntegDomain(fes, GaussRule(3, 3)),
material))
# Make model data
modeldata = FDataDict("fens" => fens, "regions" => [region1],
"omega_shift" => omega_shift, "neigvs" => neigvs)
# Solve
modeldata = AlgoDeforLinearModule.modal(modeldata)
fs = modeldata["omega"] / (2 * pi)
println("Eigenvalues: $fs [Hz]")
modeldata["postprocessing"] = FDataDict("file" => "unit_cube_mode",
"mode" => 10)
modeldata = AlgoDeforLinearModule.exportmode(modeldata)
@async run(`"paraview.exe" $(modeldata["postprocessing"]["file"]*"1.vtk")`)
true
end # unit_cube_modes_msh8_algo
function allrun()
println("#####################################################")
println("# unit_cube_modes ")
unit_cube_modes()
println("#####################################################")
println("# unit_cube_modes_arnoldimethod ")
unit_cube_modes_arnoldimethod()
# println("#####################################################")
# println("# unit_cube_modes_algo ")
# unit_cube_modes_algo()
# println("#####################################################")
# println("# unit_cube_modes_export ")
# unit_cube_modes_export()
# println("#####################################################")
# println("# unit_cube_modes_msh8_algo ")
# unit_cube_modes_msh8_algo()
return true
end # function allrun
@info "All examples may be executed with "
println("using .$(@__MODULE__); $(@__MODULE__).allrun()")
end # module
nothing