/
mortar2dad.jl
265 lines (215 loc) · 8.93 KB
/
mortar2dad.jl
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# This file is a part of JuliaFEM.
# License is MIT: see https://github.com/JuliaFEM/MortarContact2DAD.jl/blob/master/LICENSE
mutable struct Mortar2DAD <: BoundaryProblem
master_elements :: Vector{Element}
end
function Mortar2DAD()
return Mortar2DAD([])
end
function FEMBase.add_elements!(::Problem{Mortar2DAD}, ::Any)
error("use `add_slave_elements!` and `add_master_elements!` to add ",
"elements to the Mortar2D problem.")
end
function FEMBase.add_slave_elements!(problem::Problem{Mortar2DAD}, elements)
for element in elements
push!(problem.elements, element)
end
end
function FEMBase.add_master_elements!(problem::Problem{Mortar2DAD}, elements)
for element in elements
push!(problem.properties.master_elements, element)
end
end
function FEMBase.get_slave_elements(problem::Problem{Mortar2DAD})
return problem.elements
end
function FEMBase.get_master_elements(problem::Problem{Mortar2DAD})
return problem.properties.master_elements
end
function get_slave_dofs(problem::Problem{Mortar2DAD})
dofs = Int64[]
for element in get_slave_elements(problem)
append!(dofs, get_gdofs(problem, element))
end
return sort(unique(dofs))
end
function get_master_dofs(problem::Problem{Mortar2DAD})
dofs = Int64[]
for element in get_master_elements(problem)
append!(dofs, get_gdofs(problem, element))
end
return sort(unique(dofs))
end
function project_from_master_to_slave_ad(slave_element::Element{E}, x1_, n1_, x2, time;
tol=1.0e-9, max_iterations=5) where {E<:MortarElements2D}
x1(xi1) = interpolate(vec(get_basis(slave_element, [xi1], time)), x1_)
dx1(xi1) = interpolate(vec(get_dbasis(slave_element, [xi1], time)), x1_)
n1(xi1) = interpolate(vec(get_basis(slave_element, [xi1], time)), n1_)
dn1(xi1) = interpolate(vec(get_dbasis(slave_element, [xi1], time)), 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
dxi1 = 0.0
for i=1:max_iterations
dxi1 = -R(xi1)/dR(xi1)
xi1 += dxi1
if norm(dxi1) < tol
return xi1
end
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(
master_element::Element{E}, x1, n1, x2_, time;
tol=1.0e-10, max_iterations=20) where E<:MortarElements2D
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
""" 2d mesh tie using ForwardDiff.
Construct .. + fc*la and C(d,la)=0
"""
function FEMBase.assemble_elements!(problem::Problem{Mortar2DAD}, assembly::Assembly,
elements::Vector{Element{Seg2}}, time::Float64)
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
tangents = zeros(u)
for element in slave_elements
conn = get_connectivity(element)
push!(S, conn...)
X1 = element("geometry", time)
u1 = ((u[:,i] for i in conn)...)
x1 = map(+, X1, u1)
dN = get_dbasis(element, [0.0], time)
tangent = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
for nid in conn
tangents[:,nid] += tangent[:]
end
end
Q = [0.0 -1.0; 1.0 0.0]
normals = zeros(u)
for j in S
tangents[:,j] /= norm(tangents[:,j])
normals[:,j] = Q*tangents[:,j]
end
#update!(slave_elements, "normal", time => Dict(j => normals[:,j] for j in S))
#update!(slave_elements, "tangent", time => Dict(j => tangents[:,j] for j in S))
# 2. loop all slave elements
for slave_element in slave_elements
nsl = length(slave_element)
slave_element_nodes = get_connectivity(slave_element)
X1 = slave_element("geometry", time)
u1 = ((u[:,i] for i in slave_element_nodes)...)
x1 = map(+, X1, u1)
la1 = ((la[:,i] for i in slave_element_nodes)...)
n1 = ((normals[:,i] for i in slave_element_nodes)...)
# 3. loop all master elements
for master_element in get_master_elements(problem)
nm = length(master_element)
master_element_nodes = get_connectivity(master_element)
X2 = master_element("geometry", time)
u2 = ((u[:,i] for i in master_element_nodes)...)
x2 = map(+, X2, u2)
# 3.1 calculate segmentation
xi1a = project_from_master_to_slave_ad(slave_element, x1, n1, x2[1], time)
xi1b = project_from_master_to_slave_ad(slave_element, x1, n1, x2[2], time)
# xi1a = project_from_master_to_slave(slave_element, X2[1], time)
# xi1b = project_from_master_to_slave(slave_element, X2[2], time)
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
De = zeros(nsl, nsl)
Me = zeros(nsl, nsl)
# 3.3. loop integration points of one integration segment and calculate
# local mortar matrices
for ip in get_integration_points(slave_element, 3)
detJ = slave_element(ip, time, Val{:detJ})
w = ip.weight*detJ*l
#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 = vec(get_basis(slave_element, xi_s, time))
Phi = N1
# project gauss point from slave element to master element in direction n_s
x_s = interpolate(N1, x1) # coordinate in gauss point
n_s = interpolate(N1, n1) # normal direction in gauss point
#xi_m = project_from_slave_to_master(master_element, X_s, n_s, time)
xi_m = project_from_slave_to_master_ad(master_element, x_s, n_s, x2, time)
N2 = vec(get_basis(master_element, xi_m, time))
x_m = interpolate(N2, x2)
la_s = interpolate(Phi, la1)
gn = dot(n_s, x_s-x_m)
u_s = interpolate(N1, u1)
u_m = interpolate(N2, u2)
X_s = interpolate(N1, X1)
X_m = interpolate(N2, X2)
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[:,slave_element_nodes] += w*(u_s-u_m)*Phi'
# if props.adjust
# G = w*(X_s-X_m)*Phi'
# gap[:,slave_element_nodes] += G
# end
end
end # master elements done
end # slave elements done, contact virtual work ready
C = gap
return vec([fc C])
end
# x doesn't mean deformed configuration here
x = [problem.assembly.u; problem.assembly.la]
ndofs = round(Int, length(x)/2)
A = ForwardDiff.jacobian(calculate_interface, x)
b = -calculate_interface(x)
A = sparse(A)
b = sparse(b)
SparseArrays.droptol!(A, 1.0e-12)
SparseArrays.droptol!(b, 1.0e-12)
K = A[1:ndofs,1:ndofs]
C1 = transpose(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]
empty!(problem.assembly)
problem.assembly.K = K
problem.assembly.C1 = C1
problem.assembly.C2 = C2
problem.assembly.D = D
problem.assembly.f = f
problem.assembly.g = g
end