use buffer and call assemble for one elements, also some tweaks for using sparsity pattern in FEMBase.jl

This commit is contained in:
Kristoffer Carlsson
2018-10-19 17:35:30 -04:00
parent 2394725a61
commit cd22d1a571
3 changed files with 209 additions and 193 deletions
+202 -186
View File
@@ -70,6 +70,15 @@ function assemble!(assembly::Assembly, problem::Problem{Elasticity},
end
end
function assemble!(assembly::Assembly, problem::Problem{Elasticity},
elements::Vector{<:Element}, time, formulation)
local_buffer = allocate_buffer(problem, elements)
assembler = FEMBase.start_assemble(assembly.K)
for element in elements
assemble_element!(assembly, assembler, problem, element, local_buffer, time, formulation)
end
end
include("problems_elasticity_2d.jl")
const Elasticity3DSurfaceElements = Union{Poi1,Tri3,Tri6,Quad4,Quad8,Quad9}
@@ -120,6 +129,16 @@ Parameters.@with_kw struct Elasticity3DLocalBuffers{B, T}
Bt_mul_S :: Vector{T} = zeros(ndofs)
end
function allocate_buffer(problem::Problem{Elasticity}, ::Vector{Element{El}}) where El<:Elasticity3DVolumeElements
dim = get_unknown_field_dimension(problem)
nnodes = length(El)
ndofs = dim*nnodes
return Elasticity3DLocalBuffers(ndofs=ndofs, dim=dim, bi = BasisInfo(El))
end
function reset_element!(buf::Elasticity3DLocalBuffers)
fill!(buf.Km, 0.0)
fill!(buf.Kg, 0.0)
@@ -148,9 +167,11 @@ function to_voigt!(strain_vec, strain)
end
""" Assemble 3d continuum elements in general solid mechanics problem. """
function assemble!(assembly::Assembly,
function assemble_element!(assembly::Assembly,
assembler::FEMBase.AssemblerSparsityPattern,
problem::Problem{Elasticity},
elements::Vector{Element{El}},
element::Element{El},
local_buffer::Elasticity3DLocalBuffers,
time, ::Type{Val{:continuum}}) where El<:Elasticity3DVolumeElements
props = problem.properties
dim = get_unknown_field_dimension(problem)
@@ -158,206 +179,201 @@ function assemble!(assembly::Assembly,
nnodes = length(El)
ndofs = dim*nnodes
buffer = Elasticity3DLocalBuffers(ndofs=ndofs, dim=dim, bi = BasisInfo(El))
Parameters.@unpack bi, BL, BNL, Km, Kg, f_int, f_ext, gradu, strain,
strain_vec, stress_vec, F, D, Dtan, Bt_mul_D, Bt_mul_D_mul_B, Bt_mul_S = local_buffer
u = element("displacement", time)
reset_element!(local_buffer)
for element in elements
Parameters.@unpack bi, BL, BNL, Km, Kg, f_int, f_ext, gradu, strain,
strain_vec, stress_vec, F, D, Dtan, Bt_mul_D, Bt_mul_D_mul_B, Bt_mul_S = buffer
u = element("displacement", time)
reset_element!(buffer)
for ip in get_integration_points(element)
reset_integration_point!(local_buffer)
X = element("geometry", time)
eval_basis!(bi, X, ip)
w = ip.weight*bi.detJ
N = bi.N
dN = bi.grad # deriatives of basis functions w.r.t. X, i.e. ∂N/∂X
grad!(bi, gradu, u) # displacement gradient ∇u
for ip in get_integration_points(element)
reset_integration_point!(buffer)
X = element("geometry", time)
eval_basis!(bi, X, ip)
w = ip.weight*bi.detJ
N = bi.N
dN = bi.grad # deriatives of basis functions w.r.t. X, i.e. ∂N/∂X
grad!(bi, gradu, u) # displacement gradient ∇u
# calculate strain tensor and deformation gradient
F[:,:] += I
if props.finite_strain
strain[:,:] = 1/2 * (gradu + gradu' + gradu'*gradu)
F[:,:] += gradu
else
strain[:,:] = 1/2 * (gradu + gradu')
end
# calculate strain tensor and deformation gradient
F[:,:] += I
if props.finite_strain
strain[:,:] = 1/2 * (gradu + gradu' + gradu'*gradu)
F[:,:] += gradu
else
strain[:,:] = 1/2 * (gradu + gradu')
to_voigt!(strain_vec, strain)
# material stiffness start
if props.finite_strain
for i=1:nnodes
BL[1, 3*(i-1)+1] = F[1,1]*dN[1,i]
BL[1, 3*(i-1)+2] = F[2,1]*dN[1,i]
BL[1, 3*(i-1)+3] = F[3,1]*dN[1,i]
BL[2, 3*(i-1)+1] = F[1,2]*dN[2,i]
BL[2, 3*(i-1)+2] = F[2,2]*dN[2,i]
BL[2, 3*(i-1)+3] = F[3,2]*dN[2,i]
BL[3, 3*(i-1)+1] = F[1,3]*dN[3,i]
BL[3, 3*(i-1)+2] = F[2,3]*dN[3,i]
BL[3, 3*(i-1)+3] = F[3,3]*dN[3,i]
BL[4, 3*(i-1)+1] = F[1,1]*dN[2,i] + F[1,2]*dN[1,i]
BL[4, 3*(i-1)+2] = F[2,1]*dN[2,i] + F[2,2]*dN[1,i]
BL[4, 3*(i-1)+3] = F[3,1]*dN[2,i] + F[3,2]*dN[1,i]
BL[5, 3*(i-1)+1] = F[1,2]*dN[3,i] + F[1,3]*dN[2,i]
BL[5, 3*(i-1)+2] = F[2,2]*dN[3,i] + F[2,3]*dN[2,i]
BL[5, 3*(i-1)+3] = F[3,2]*dN[3,i] + F[3,3]*dN[2,i]
BL[6, 3*(i-1)+1] = F[1,3]*dN[1,i] + F[1,1]*dN[3,i]
BL[6, 3*(i-1)+2] = F[2,3]*dN[1,i] + F[2,1]*dN[3,i]
BL[6, 3*(i-1)+3] = F[3,3]*dN[1,i] + F[3,1]*dN[3,i]
end
else
for i=1:nnodes
BL[1, 3*(i-1)+1] = dN[1,i]
BL[2, 3*(i-1)+2] = dN[2,i]
BL[3, 3*(i-1)+3] = dN[3,i]
BL[4, 3*(i-1)+1] = dN[2,i]
BL[4, 3*(i-1)+2] = dN[1,i]
BL[5, 3*(i-1)+2] = dN[3,i]
BL[5, 3*(i-1)+3] = dN[2,i]
BL[6, 3*(i-1)+1] = dN[3,i]
BL[6, 3*(i-1)+3] = dN[1,i]
end
end
# calculate stress
E = element("youngs modulus", ip, time)
nu = element("poissons ratio", ip, time)
la = E*nu/((1.0+nu)*(1.0-2.0*nu))
mu = E/(2.0*(1.0+nu))
D[1,1] = D[2,2] = D[3,3] = 2*mu + la
D[4,4] = D[5,5] = D[6,6] = mu
D[1,2] = D[2,1] = D[2,3] = D[3,2] = D[1,3] = D[3,1] = la
# determine material model
material_model = :linear_elasticity
if haskey(element, "plasticity")
material_model = :ideal_plasticity
end
# calculate stress vector based on material model
if material_model == :linear_elasticity
Dtan[:,:] = D[:,:]
stress_vec[:] = Dtan * strain_vec
end
if material_model == :ideal_plasticity
plastic_def = element("plasticity")[ip.id]
calculate_stress! = plastic_def["type"]
yield_surface_ = plastic_def["yield_surface"]
params = plastic_def["params"]
initialize_internal_params!(params, ip, Val{:type_3d})
if time == 0.0
error("Given step time = $(time). Please select time > 0.0")
end
to_voigt!(strain_vec, strain)
# material stiffness start
if props.finite_strain
for i=1:nnodes
BL[1, 3*(i-1)+1] = F[1,1]*dN[1,i]
BL[1, 3*(i-1)+2] = F[2,1]*dN[1,i]
BL[1, 3*(i-1)+3] = F[3,1]*dN[1,i]
BL[2, 3*(i-1)+1] = F[1,2]*dN[2,i]
BL[2, 3*(i-1)+2] = F[2,2]*dN[2,i]
BL[2, 3*(i-1)+3] = F[3,2]*dN[2,i]
BL[3, 3*(i-1)+1] = F[1,3]*dN[3,i]
BL[3, 3*(i-1)+2] = F[2,3]*dN[3,i]
BL[3, 3*(i-1)+3] = F[3,3]*dN[3,i]
BL[4, 3*(i-1)+1] = F[1,1]*dN[2,i] + F[1,2]*dN[1,i]
BL[4, 3*(i-1)+2] = F[2,1]*dN[2,i] + F[2,2]*dN[1,i]
BL[4, 3*(i-1)+3] = F[3,1]*dN[2,i] + F[3,2]*dN[1,i]
BL[5, 3*(i-1)+1] = F[1,2]*dN[3,i] + F[1,3]*dN[2,i]
BL[5, 3*(i-1)+2] = F[2,2]*dN[3,i] + F[2,3]*dN[2,i]
BL[5, 3*(i-1)+3] = F[3,2]*dN[3,i] + F[3,3]*dN[2,i]
BL[6, 3*(i-1)+1] = F[1,3]*dN[1,i] + F[1,1]*dN[3,i]
BL[6, 3*(i-1)+2] = F[2,3]*dN[1,i] + F[2,1]*dN[3,i]
BL[6, 3*(i-1)+3] = F[3,3]*dN[1,i] + F[3,1]*dN[3,i]
end
else
for i=1:nnodes
BL[1, 3*(i-1)+1] = dN[1,i]
BL[2, 3*(i-1)+2] = dN[2,i]
BL[3, 3*(i-1)+3] = dN[3,i]
BL[4, 3*(i-1)+1] = dN[2,i]
BL[4, 3*(i-1)+2] = dN[1,i]
BL[5, 3*(i-1)+2] = dN[3,i]
BL[5, 3*(i-1)+3] = dN[2,i]
BL[6, 3*(i-1)+1] = dN[3,i]
BL[6, 3*(i-1)+3] = dN[1,i]
end
end
# calculate stress
E = element("youngs modulus", ip, time)
nu = element("poissons ratio", ip, time)
la = E*nu/((1.0+nu)*(1.0-2.0*nu))
mu = E/(2.0*(1.0+nu))
D[1,1] = D[2,2] = D[3,3] = 2*mu + la
D[4,4] = D[5,5] = D[6,6] = mu
D[1,2] = D[2,1] = D[2,3] = D[3,2] = D[1,3] = D[3,1] = la
# determine material model
material_model = :linear_elasticity
if haskey(element, "plasticity")
material_model = :ideal_plasticity
end
# calculate stress vector based on material model
if material_model == :linear_elasticity
Dtan[:,:] = D[:,:]
stress_vec[:] = Dtan * strain_vec
end
if material_model == :ideal_plasticity
plastic_def = element("plasticity")[ip.id]
calculate_stress! = plastic_def["type"]
yield_surface_ = plastic_def["yield_surface"]
params = plastic_def["params"]
initialize_internal_params!(params, ip, Val{:type_3d})
if time == 0.0
error("Given step time = $(time). Please select time > 0.0")
end
t_last = ip("prev_time", time)
update!(ip, "prev_time", time => t_last)
dt = time - t_last
stress_last = ip("stress", t_last)
strain_last = ip("strain", t_last)
dstrain_vec = strain_vec - strain_last
fill!(stress_vec, 0.0)
fill!(Dtan, 0.0)
plastic_strain = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
calculate_stress!(stress_vec, stress_last, dstrain_vec, plastic_strain, D, params, Dtan, yield_surface_, time, dt, Val{:type_3d})
end
:strain in props.store_fields && update!(ip, "strain", time => strain_vec)
:stress in props.store_fields && update!(ip, "stress", time => stress_vec)
:stress11 in props.store_fields && update!(ip, "stress11", time => stress_vec[1])
:stress22 in props.store_fields && update!(ip, "stress22", time => stress_vec[2])
:stress33 in props.store_fields && update!(ip, "stress33", time => stress_vec[3])
:stress12 in props.store_fields && update!(ip, "stress12", time => stress_vec[4])
:stress23 in props.store_fields && update!(ip, "stress23", time => stress_vec[5])
:stress13 in props.store_fields && update!(ip, "stress13", time => stress_vec[6])
:plastic_strain in props.store_fields && update!(ip, "plastic_strain", time => plastic_strain)
#Km += w*BL'*Dtan*BL
mul!(Bt_mul_D, transpose(BL), Dtan)
mul!(Bt_mul_D_mul_B, Bt_mul_D, BL)
rmul!(Bt_mul_D_mul_B, w)
for i=1:ndofs^2
@inbounds Km[i] += Bt_mul_D_mul_B[i]
end
# material stiffness end
if props.geometric_stiffness
# take geometric stiffness into account
for i=1:size(dN, 2)
BNL[1, 3*(i-1)+1] = dN[1,i]
BNL[2, 3*(i-1)+1] = dN[2,i]
BNL[3, 3*(i-1)+1] = dN[3,i]
BNL[4, 3*(i-1)+2] = dN[1,i]
BNL[5, 3*(i-1)+2] = dN[2,i]
BNL[6, 3*(i-1)+2] = dN[3,i]
BNL[7, 3*(i-1)+3] = dN[1,i]
BNL[8, 3*(i-1)+3] = dN[2,i]
BNL[9, 3*(i-1)+3] = dN[3,i]
end
S3 = zeros(3*dim, 3*dim)
S3[1,1] = stress_vec[1]
S3[2,2] = stress_vec[2]
S3[3,3] = stress_vec[3]
S3[1,2] = S3[2,1] = stress_vec[4]
S3[2,3] = S3[3,2] = stress_vec[5]
S3[1,3] = S3[3,1] = stress_vec[6]
S3[4:6,4:6] = S3[7:9,7:9] = S3[1:3,1:3]
Kg += w*BNL'*S3*BNL
end
# internal load
mul!(Bt_mul_S, transpose(BL), stress_vec)
rmul!(Bt_mul_S, w)
for i=1:ndofs
@inbounds f_int[i] += Bt_mul_S[i]
end
# external load start
if haskey(element, "displacement load")
T = element("displacement load", ip, time)
f_ext += w*vec(T*N)
end
for i=1:dim
if haskey(element, "displacement load $i")
b = element("displacement load $i", ip, time)
f_ext[i:dim:end] += w*vec(b*N)
end
end
# external load end
t_last = ip("prev_time", time)
update!(ip, "prev_time", time => t_last)
dt = time - t_last
stress_last = ip("stress", t_last)
strain_last = ip("strain", t_last)
dstrain_vec = strain_vec - strain_last
fill!(stress_vec, 0.0)
fill!(Dtan, 0.0)
plastic_strain = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
calculate_stress!(stress_vec, stress_last, dstrain_vec, plastic_strain, D, params, Dtan, yield_surface_, time, dt, Val{:type_3d})
end
gdofs = get_gdofs(problem, element)
:strain in props.store_fields && update!(ip, "strain", time => strain_vec)
:stress in props.store_fields && update!(ip, "stress", time => stress_vec)
:stress11 in props.store_fields && update!(ip, "stress11", time => stress_vec[1])
:stress22 in props.store_fields && update!(ip, "stress22", time => stress_vec[2])
:stress33 in props.store_fields && update!(ip, "stress33", time => stress_vec[3])
:stress12 in props.store_fields && update!(ip, "stress12", time => stress_vec[4])
:stress23 in props.store_fields && update!(ip, "stress23", time => stress_vec[5])
:stress13 in props.store_fields && update!(ip, "stress13", time => stress_vec[6])
:plastic_strain in props.store_fields && update!(ip, "plastic_strain", time => plastic_strain)
# add contributions to K, Kg, f
add!(assembly.K, gdofs, gdofs, Km)
#Km += w*BL'*Dtan*BL
mul!(Bt_mul_D, transpose(BL), Dtan)
mul!(Bt_mul_D_mul_B, Bt_mul_D, BL)
rmul!(Bt_mul_D_mul_B, w)
for i=1:ndofs^2
@inbounds Km[i] += Bt_mul_D_mul_B[i]
end
# material stiffness end
if props.geometric_stiffness
add!(assembly.Kg, gdofs, gdofs, Kg)
# take geometric stiffness into account
for i=1:size(dN, 2)
BNL[1, 3*(i-1)+1] = dN[1,i]
BNL[2, 3*(i-1)+1] = dN[2,i]
BNL[3, 3*(i-1)+1] = dN[3,i]
BNL[4, 3*(i-1)+2] = dN[1,i]
BNL[5, 3*(i-1)+2] = dN[2,i]
BNL[6, 3*(i-1)+2] = dN[3,i]
BNL[7, 3*(i-1)+3] = dN[1,i]
BNL[8, 3*(i-1)+3] = dN[2,i]
BNL[9, 3*(i-1)+3] = dN[3,i]
end
S3 = zeros(3*dim, 3*dim)
S3[1,1] = stress_vec[1]
S3[2,2] = stress_vec[2]
S3[3,3] = stress_vec[3]
S3[1,2] = S3[2,1] = stress_vec[4]
S3[2,3] = S3[3,2] = stress_vec[5]
S3[1,3] = S3[3,1] = stress_vec[6]
S3[4:6,4:6] = S3[7:9,7:9] = S3[1:3,1:3]
Kg += w*BNL'*S3*BNL
end
add!(assembly.f, gdofs, f_ext - f_int)
# internal load
mul!(Bt_mul_S, transpose(BL), stress_vec)
rmul!(Bt_mul_S, w)
for i=1:ndofs
@inbounds f_int[i] += Bt_mul_S[i]
end
# external load start
if haskey(element, "displacement load")
T = element("displacement load", ip, time)
f_ext += w*vec(T*N)
end
for i=1:dim
if haskey(element, "displacement load $i")
b = element("displacement load $i", ip, time)
f_ext[i:dim:end] += w*vec(b*N)
end
end
# external load end
end
gdofs = get_gdofs(problem, element)
# add contributions to K, Kg, f
FEMBase.assemble_local_matrix!(assembler, gdofs, Km)
if props.geometric_stiffness
add!(assembly.Kg, gdofs, gdofs, Kg)
end
add!(assembly.f, gdofs, f_ext - f_int)
return nothing
end
+5 -5
View File
@@ -57,15 +57,16 @@ problems must have unique node ids.
function get_field_assembly(solver::Solver)
problems = get_field_problems(solver)
problem = problems[1]
M = SparseMatrixCOO()
K = SparseMatrixCOO()
K = spzeros(size(problems[1].assembly.K)...)
Kg = SparseMatrixCOO()
f = SparseMatrixCOO()
fg = SparseMatrixCOO()
for problem in problems
append!(M, problem.assembly.M)
append!(K, problem.assembly.K)
K += problem.assembly.K
append!(Kg, problem.assembly.Kg)
append!(f, problem.assembly.f)
append!(fg, problem.assembly.fg)
@@ -74,7 +75,6 @@ function get_field_assembly(solver::Solver)
N = size(K, 1)
M = sparse(M, N, N)
K = sparse(K, N, N)
if nnz(K) == 0
@warn("Field assembly seems to be empty. Check that elements are ",
"pushed to problem and formulation is correct.")
@@ -142,7 +142,7 @@ function get_boundary_assembly(solver::Solver, N)
g = spzeros(N, 1)
for problem in get_boundary_problems(solver)
assembly = problem.assembly
K_ = sparse(assembly.K, N, N)
# K_ = assembly.K
C1_ = sparse(assembly.C1, N, N)
C2_ = sparse(assembly.C2, N, N)
D_ = sparse(assembly.D, N, N)
@@ -167,7 +167,7 @@ function get_boundary_assembly(solver::Solver, N)
error("overconstrained dofs, not solving problem.")
end
K += K_
#K += K_
C1 += C1_
C2 += C2_
D += D_
@@ -25,8 +25,8 @@ update!(element, "geometry", X)
update!(element, "displacement", u)
problem = Problem(Elasticity, "tet10", 3)
add_element!(problem, element)
time = 0.0
assemble!(problem, time)
ttime = 0.0
assemble!(problem, ttime)
eigs = real(eigvals(Matrix(problem.assembly.K)))
eigs_expected = [8809.45, 4936.01, 2880.56, 2491.66, 2004.85,
1632.49, 1264.32, 1212.42, 817.905,