mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-21 18:33:36 +00:00
Jukka Aho
23204ee15b
- `empty!(problem)` -> `empty!(problem.assembly)` - `get_gdofs(element, ndim)` -> `get_gdofs(problem, element)`
381 lines
13 KiB
Julia
381 lines
13 KiB
Julia
# This file is a part of JuliaFEM.
|
|
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
|
|
|
|
using ForwardDiff
|
|
|
|
""" Find segment from slave element corresponding to master element nodes.
|
|
|
|
Parameters
|
|
----------
|
|
x1_, n1_
|
|
slave element geometry and normal direction
|
|
x2
|
|
master element node to project onto slave
|
|
|
|
Returns
|
|
-------
|
|
xi
|
|
dimensionless coordinate on slave corresponding to
|
|
projected master
|
|
|
|
"""
|
|
function project_from_master_to_slave_ad{E<:MortarElements2D}(
|
|
slave_element::Element{E}, x1_::DVTI, n1_::DVTI, x2::Vector;
|
|
tol=1.0e-10, max_iterations=20, debug=false)
|
|
|
|
""" Multiply basis / dbasis at `xi` with field. """
|
|
function mul(func, xi, field)
|
|
B = func(slave_element, [xi], time)
|
|
return sum(B[i]*field[i] for i=1:length(B))
|
|
end
|
|
|
|
x1(xi1) = mul(get_basis, xi1, x1_)
|
|
dx1(xi1) = mul(get_dbasis, xi1, x1_)
|
|
n1(xi1) = mul(get_basis, xi1, n1_)
|
|
dn1(xi1) = mul(get_dbasis, xi1, n1_)
|
|
cross2(a, b) = cross([a; 0], [b; 0])[3]
|
|
R(xi1) = cross2(x1(xi1)-x2, n1(xi1))
|
|
dR(xi1) = cross2(dx1(xi1), n1(xi1)) + cross2(x1(xi1)-x2, dn1(xi1))
|
|
|
|
xi1 = 0.0
|
|
xi1_next = 0.0
|
|
dxi1 = 0.0
|
|
for i=1:max_iterations
|
|
dxi1 = -R(xi1)/dR(xi1)
|
|
dxi1 = clamp.(dxi1, -0.3, 0.3)
|
|
xi1_next = clamp.(xi1 + dxi1, -1.0, 1.0)
|
|
if norm(xi1_next - xi1) < tol
|
|
return xi1_next
|
|
end
|
|
if debug
|
|
info("xi1 = $xi1")
|
|
info("R(xi1) = $(R(xi1))")
|
|
info("dR(xi1) = $(dR(xi1))")
|
|
info("dxi1 = $dxi1")
|
|
info("norm = $(norm(xi1_next - xi1))")
|
|
info("xi1_next = $xi1_next")
|
|
end
|
|
xi1 = xi1_next
|
|
end
|
|
|
|
info("x1 = $x1_")
|
|
info("n1 = $n1_")
|
|
info("x2 = $x2")
|
|
info("xi1 = $xi1, dxi1 = $dxi1")
|
|
info("-R(xi1) = $(-R(xi1))")
|
|
info("dR(xi1) = $(dR(xi1))")
|
|
error("find projection from master to slave: did not converge")
|
|
|
|
end
|
|
|
|
function project_from_slave_to_master_ad{E<:MortarElements2D}(
|
|
master_element::Element{E}, x1, n1, x2_;
|
|
tol=1.0e-10, max_iterations=20)
|
|
|
|
x2(xi2) = interpolate(vec(get_basis(master_element, [xi2], time)), x2_)
|
|
dx2(xi2) = interpolate(vec(get_dbasis(master_element, [xi2], time)), x2_)
|
|
cross2(a, b) = cross([a; 0], [b; 0])[3]
|
|
R(xi2) = cross2(x2(xi2)-x1, n1)
|
|
dR(xi2) = cross2(dx2(xi2), n1)
|
|
|
|
xi2 = 0.0
|
|
dxi2 = 0.0
|
|
for i=1:max_iterations
|
|
dxi2 = -R(xi2) / dR(xi2)
|
|
xi2 += dxi2
|
|
if norm(dxi2) < tol
|
|
return xi2
|
|
end
|
|
end
|
|
|
|
error("find projection from slave to master: did not converge, last val: $xi2 and $dxi2")
|
|
|
|
end
|
|
|
|
"""
|
|
Frictionless 2d finite sliding contact with forwarddiff.
|
|
|
|
true/false flags: finite_sliding, friction, use_forwarddiff
|
|
"""
|
|
function assemble!(problem::Problem{Contact}, time::Float64,
|
|
::Type{Val{1}}, ::Type{Val{true}},
|
|
::Type{Val{false}}, ::Type{Val{true}})
|
|
|
|
props = problem.properties
|
|
field_dim = get_unknown_field_dimension(problem)
|
|
field_name = get_parent_field_name(problem)
|
|
slave_elements = get_slave_elements(problem)
|
|
|
|
function calculate_interface(x::Vector)
|
|
|
|
ndofs = round(Int, length(x)/2)
|
|
nnodes = round(Int, ndofs/field_dim)
|
|
u = reshape(x[1:ndofs], field_dim, nnodes)
|
|
la = reshape(x[ndofs+1:end], field_dim, nnodes)
|
|
fc = zeros(u)
|
|
gap = zeros(u)
|
|
C = zeros(la)
|
|
S = Set{Int64}()
|
|
|
|
# 1. update nodal normals for slave elements
|
|
Q = [0.0 -1.0; 1.0 0.0]
|
|
normals = zeros(u)
|
|
for element in slave_elements
|
|
conn = get_connectivity(element)
|
|
push!(S, conn...)
|
|
gdofs = get_gdofs(problem, element)
|
|
X_el = element("geometry", time)
|
|
x_el = tuple( (X_el[i] + u[:,j] for (i,j) in enumerate(conn))... )
|
|
#=
|
|
for ip in get_integration_points(element, 3)
|
|
dN = get_dbasis(element, ip, time)
|
|
N = element(ip, time)
|
|
t = sum([kron(dN[:,i], x_el[i]') for i=1:length(x_el)])
|
|
normals[:, conn] += ip.weight*Q*t'*N
|
|
end
|
|
=#
|
|
dN = get_dbasis(element, [0.0], time)
|
|
t = sum([kron(dN[:,i], x_el[i]') for i=1:length(x_el)])
|
|
n = Q*t'
|
|
n /= norm(n)
|
|
for c in conn
|
|
normals[:,c] += n
|
|
end
|
|
end
|
|
for i in 1:size(normals,2)
|
|
normals[:,i] /= norm(normals[:,i])
|
|
end
|
|
# swap element normals in 2d if they point to inside of body
|
|
if props.rotate_normals
|
|
for i=1:size(normals,2)
|
|
normals[:,i] = -normals[:,i]
|
|
end
|
|
end
|
|
normals2 = Dict()
|
|
for j in S
|
|
normals2[j] = normals[:,j]
|
|
end
|
|
update!(slave_elements, "normal", time => normals2)
|
|
|
|
# 2. loop all slave elements
|
|
for slave_element in slave_elements
|
|
|
|
slave_element_nodes = get_connectivity(slave_element)
|
|
X1 = slave_element("geometry", time)
|
|
u1 = ((u[:,i] for i in slave_element_nodes)...)
|
|
x1 = ((Xi+ui for (Xi,ui) in zip(X1,u1))...)
|
|
la1 = ((la[:,i] for i in slave_element_nodes)...)
|
|
n1 = ((normals[:,i] for i in slave_element_nodes)...)
|
|
nnodes = size(slave_element, 2)
|
|
|
|
# construct dual basis
|
|
De = zeros(nnodes, nnodes)
|
|
Me = zeros(nnodes, nnodes)
|
|
for master_element in slave_element("master elements", time)
|
|
|
|
master_element_nodes = get_connectivity(master_element)
|
|
X2 = master_element("geometry", time)
|
|
u2 = ((u[:,i] for i in master_element_nodes)...)
|
|
x2 = ((Xi+ui for (Xi,ui) in zip(X2,u2))...)
|
|
|
|
# calculate segmentation: we care only about endpoints
|
|
xi1a = project_from_master_to_slave_ad(slave_element, field(x1), field(n1), x2[1])
|
|
xi1b = project_from_master_to_slave_ad(slave_element, field(x1), field(n1), x2[2])
|
|
xi1 = clamp.([xi1a; xi1b], -1.0, 1.0)
|
|
l = 1/2*abs(xi1[2]-xi1[1])
|
|
isapprox(l, 0.0) && continue # no contribution in this master element
|
|
|
|
for ip in get_integration_points(slave_element, 3)
|
|
# jacobian of slave element in deformed state
|
|
dN = get_dbasis(slave_element, ip, time)
|
|
j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
|
|
w = ip.weight*norm(j)*l
|
|
xi = ip.coords[1]
|
|
xi_s = dot([1/2*(1-xi); 1/2*(1+xi)], xi1)
|
|
N1 = get_basis(slave_element, xi_s, time)
|
|
De += w*diagm(vec(N1))
|
|
Me += w*N1'*N1
|
|
end
|
|
end
|
|
|
|
Ae = De*inv(Me)
|
|
|
|
# 3. loop all master elements
|
|
for master_element in slave_element("master elements", time)
|
|
|
|
master_element_nodes = get_connectivity(master_element)
|
|
X2 = master_element("geometry", time)
|
|
u2 = ((u[:,i] for i in master_element_nodes)...)
|
|
x2 = ((Xi+ui for (Xi,ui) in zip(X2,u2))...)
|
|
|
|
#x1_midpoint = 1/2*(x1[1]+x1[2])
|
|
#x2_midpoint = 1/2*(x2[1]+x2[2])
|
|
#distance = ForwardDiff.get_value(norm(x2_midpoint - x1_midpoint))
|
|
#distance > props.maximum_distance && continue
|
|
|
|
# calculate segmentation: we care only about endpoints
|
|
xi1a = project_from_master_to_slave_ad(slave_element, field(x1), field(n1), x2[1])
|
|
xi1b = project_from_master_to_slave_ad(slave_element, field(x1), field(n1), x2[2])
|
|
xi1 = clamp.([xi1a; xi1b], -1.0, 1.0)
|
|
l = 1/2*abs(xi1[2]-xi1[1])
|
|
isapprox(l, 0.0) && continue # no contribution in this master element
|
|
|
|
slave_dofs = get_gdofs(problem, slave_element)
|
|
master_dofs = get_gdofs(problem, master_element)
|
|
|
|
# 4. loop integration points of segment
|
|
for ip in get_integration_points(slave_element, 3)
|
|
# jacobian of slave element in deformed state
|
|
dN = get_dbasis(slave_element, ip, time)
|
|
j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
|
|
w = ip.weight*norm(j)*l
|
|
|
|
# project gauss point from slave element to master element
|
|
xi = ip.coords[1]
|
|
xi_s = dot([1/2*(1-xi); 1/2*(1+xi)], xi1)
|
|
N1 = vec(get_basis(slave_element, xi_s, time))
|
|
x_s = interpolate(N1, x1) # coordinate in gauss point
|
|
n_s = interpolate(N1, n1) # normal direction in gauss point
|
|
t_s = Q'*n_s # tangent direction in gauss point
|
|
xi_m = project_from_slave_to_master_ad(master_element, x_s, n_s, x2)
|
|
N2 = vec(get_basis(master_element, xi_m, time))
|
|
x_m = interpolate(N2, x2)
|
|
Phi = Ae*N1
|
|
|
|
la_s = interpolate(Phi, la1) # traction force in gauss point
|
|
gn = -dot(n_s, x_s - x_m) # normal gap
|
|
|
|
fc[:,slave_element_nodes] += w*la_s*N1'
|
|
fc[:,master_element_nodes] -= w*la_s*N2'
|
|
gap[1,slave_element_nodes] += w*gn*Phi
|
|
#gap[1,slave_element_nodes] += w*gn*N1'
|
|
|
|
end # done integrating segment
|
|
|
|
end # master elements done
|
|
|
|
end # slave elements done
|
|
|
|
# at this point we have calculated contact force fc and gap for all slave elements.
|
|
# next task is to find out are they in contact or not and remove inactive nodes
|
|
|
|
state = problem.properties.contact_state_in_first_iteration
|
|
if problem.properties.iteration == 1
|
|
info("First contact iteration, initial contact state = $state")
|
|
if state == :AUTO
|
|
avg_gap = ForwardDiff.value(mean([gap[1, j] for j in S]))
|
|
std_gap = ForwardDiff.value(std([gap[1, j] for j in S]))
|
|
if (avg_gap < 1.0e-12) && (std_gap < 1.0e-12)
|
|
state = :ACTIVE
|
|
else
|
|
state = :UNKNOWN
|
|
end
|
|
info("Average weighted gap = $avg_gap, std gap = $std_gap, automatically determined contact state = $state")
|
|
end
|
|
end
|
|
|
|
is_active = Dict{Int, Bool}()
|
|
condition = Dict()
|
|
|
|
for j in S
|
|
if j in props.always_in_contact
|
|
is_active[j] = true
|
|
continue
|
|
end
|
|
lan = dot(normals[:,j], la[:,j])
|
|
condition[j] = ForwardDiff.value(lan - gap[1, j])
|
|
is_active[j] = condition[j] > 0
|
|
end
|
|
|
|
if problem.properties.iteration == 1 && state == :ACTIVE
|
|
for j in S
|
|
is_active[j] = true
|
|
end
|
|
end
|
|
|
|
if problem.properties.iteration == 1 && state == :INACTIVE
|
|
for j in S
|
|
is_active[j] = false
|
|
end
|
|
end
|
|
|
|
if Logging._root.level == DEBUG
|
|
debug("Summary of nodes")
|
|
for j in sort(collect(keys(is_active)))
|
|
n = map(ForwardDiff.value, normals[:,j])
|
|
debug("$j, c=$(condition[j]), s=$(is_active[j]), n=$n")
|
|
end
|
|
end
|
|
|
|
for j in S
|
|
|
|
if is_active[j]
|
|
n = normals[:,j]
|
|
t = Q'*n
|
|
lan = dot(n, la[:,j])
|
|
lat = dot(t, la[:,j])
|
|
C[1,j] += gap[1, j]
|
|
C[2,j] += lat
|
|
else
|
|
C[:,j] = la[:,j]
|
|
end
|
|
|
|
end
|
|
|
|
return vec([fc C])
|
|
|
|
end
|
|
|
|
# x doesn't mean deformed configuration here
|
|
x = [problem.assembly.u; problem.assembly.la]
|
|
if length(x) == 0
|
|
error("2d autodiff contact problem: initialize problem.assembly.u & la before solution")
|
|
end
|
|
|
|
A = ForwardDiff.jacobian(calculate_interface, x)
|
|
b = calculate_interface(x)
|
|
A = sparse(A)
|
|
b = sparse(b)
|
|
SparseArrays.droptol!(A, 1.0e-9)
|
|
SparseArrays.droptol!(b, 1.0e-9)
|
|
|
|
ndofs = round(Int, length(x)/2)
|
|
K = A[1:ndofs,1:ndofs]
|
|
C1 = A[1:ndofs,ndofs+1:end]
|
|
C2 = A[ndofs+1:end,1:ndofs]
|
|
D = A[ndofs+1:end,ndofs+1:end]
|
|
f = -b[1:ndofs]
|
|
g = -b[ndofs+1:end]
|
|
|
|
f += C1*problem.assembly.la
|
|
g += D*problem.assembly.la
|
|
|
|
#=
|
|
if !haskey(problem, "contact force")
|
|
problem.fields["contact force"] = Field(time => f)
|
|
else
|
|
update!(problem.fields["contact force"], time => f)
|
|
end
|
|
|
|
fc = problem.fields["contact force"]
|
|
|
|
if length(fc) > 1
|
|
# kick in generalized alpha rule for time integration
|
|
alpha = 0.5
|
|
info("Applying Generalized alpha time integration")
|
|
K = (1-alpha)*K
|
|
C1 = (1-alpha)*C1
|
|
f = alpha*fc[end-1].data
|
|
end
|
|
=#
|
|
|
|
problem.assembly.K = K
|
|
problem.assembly.C1 = transpose(C1)
|
|
problem.assembly.C2 = C2
|
|
problem.assembly.D = D
|
|
problem.assembly.f = sparse(f)
|
|
problem.assembly.g = sparse(g)
|
|
|
|
end
|
|
|