mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-27 20:26:58 +00:00
Jukka Aho
257 lines
8.7 KiB
Julia
257 lines
8.7 KiB
Julia
# This file is a part of JuliaFEM.
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# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
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""" Find segment from slave element corresponding to master element nodes.
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x1_, n1_
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slave element geometry and normal direction
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x2_ master element nodes to project onto slave
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"""
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function project_from_master_to_slave{E<:MortarElements2D}(
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slave_element::Element{E}, x1_::DVTI, n1_::DVTI, x2::Vector;
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tol=1.0e-10, max_iterations=20)
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function x1(xi1)
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N = get_basis(E, xi1)
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return vec(N)*x1_
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end
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function dx1(xi1)
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dN = get_dbasis(E, xi1)
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return vec(dN)*x1_
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end
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function n1(xi1)
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N = get_basis(E, xi1)
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return vec(N)*n1_
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end
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function dn1(xi1)
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dN = get_dbasis(E, xi1)
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return vec(dN)*n1_
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end
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cross2(a, b) = cross([a; 0], [b; 0])[3]
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R(xi1) = cross2(x1(xi1)-x2, n1(xi1))
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dR(xi1) = cross2(dx1(xi1), n1(xi1)) + cross2(x1(xi1)-x2, dn1(xi1))
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xi1 = 0.0
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dxi1 = 0.0
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for i=1:max_iterations
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dxi1 = -R(xi1)/dR(xi1)
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xi1 += dxi1
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if norm(dxi1) < tol
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return xi1
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end
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end
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info("x1 = $(ForwardDiff.get_value(x1_.data))")
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info("n1 = $(ForwardDiff.get_value(n1_.data))")
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info("x2 = $(ForwardDiff.get_value(x2))")
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info("xi1 = $(ForwardDiff.get_value(xi1)), dxi1 = $(ForwardDiff.get_value(dxi1))")
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info("-R(xi1) = $(ForwardDiff.get_value(-R(xi1)))")
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info("dR(xi1) = $(ForwardDiff.get_value(dR(xi1)))")
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error("find projection from master to slave: did not converge")
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end
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function project_from_slave_to_master{E<:MortarElements2D}(
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master_element::Element{E}, x1::Vector, n1::Vector, x2_::DVTI;
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tol=1.0e-10, max_iterations=20)
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function x2(xi2)
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N = get_basis(E, xi2)
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return vec(N)*x2_
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end
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function dx2(xi2)
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dN = get_dbasis(E, xi2)
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return vec(dN)*x2_
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end
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cross2(a, b) = cross([a; 0], [b; 0])[3]
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R(xi2) = cross2(x2(xi2)-x1, n1)
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dR(xi2) = cross2(dx2(xi2), n1)
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xi2 = 0.0
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dxi2 = 0.0
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for i=1:max_iterations
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dxi2 = -R(xi2) / dR(xi2)
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xi2 += dxi2
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if norm(dxi2) < tol
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return xi2
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end
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end
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error("find projection from slave to master: did not converge, last val: $xi2 and $dxi2")
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end
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function assemble!{E<:MortarElements2D}(assembly::Assembly,
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problem::Problem{Mortar}, slave_element::Element{E},
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time::Real, ::Type{Val{:forwarddiff}})
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haskey(slave_element, "master elements") || return
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props = problem.properties
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field_dim = get_unknown_field_dimension(problem)
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field_name = get_parent_field_name(problem)
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function calculate_interface(x::Vector)
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ndofs = round(Int, length(x)/2)
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nnodes = round(Int, ndofs/field_dim)
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u = reshape(x[1:ndofs], field_dim, nnodes)
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la = reshape(x[ndofs+1:end], field_dim, nnodes)
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fc = zeros(u)
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C = zeros(la)
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slave_element_nodes = get_connectivity(slave_element)
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X1 = slave_element("geometry", time)
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u1 = Field(Vector[u[:,i] for i in slave_element_nodes])
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la1 = Field(Vector[la[:,i] for i in slave_element_nodes])
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x1 = X1 + u1
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# 1. update nodal normals for this element. average nodes from adjacent elements
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adjacent_elements = find_elements(get_elements(problem), slave_element_nodes)
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adjacent_nodes = get_nodes(adjacent_elements) # including also nodes from adjacent elements
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Q = [0.0 -1.0; 1.0 0.0]
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normals = zeros(u)
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for element in adjacent_elements
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conn = get_connectivity(element)
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gdofs = get_gdofs(element, field_dim)
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X_el = element("geometry", time)
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u_el = Field(Vector[u[:, i] for i in conn])
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x_el = X_el + u_el
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for ip in get_integration_points(element, Val{3})
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dN = get_dbasis(element, ip)
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N = element(ip, time)
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t = sum([kron(dN[:,i], x_el[i]') for i=1:length(x_el)])
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normals[:, conn] += ip.weight*Q*t'*N
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end
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end
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# --> slave side normals in deformed state
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n1 = Field(Vector[ForwardDiff.get_value(normals[:,i]/norm(normals[:,i])) for i in slave_element_nodes])
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nnodes = size(slave_element, 2)
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lan_tot = zeros(nnodes) # normal pressure
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gap_tot = zeros(nnodes) # weighted normal gap
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for master_element in slave_element["master elements"]
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master_element_nodes = get_connectivity(master_element)
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X2 = master_element("geometry", time)
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u2 = Field(Vector[u[:,i] for i in master_element_nodes])
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x2 = X2 + u2
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# calculate segmentation: we care only about endpoints
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# note: these are quadratic/cubic functions, analytical solution possible
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xi1a = project_from_master_to_slave(slave_element, x1, n1, x2[1])
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xi1b = project_from_master_to_slave(slave_element, x1, n1, x2[end])
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xi1 = clamp([xi1a; xi1b], -1.0, 1.0)
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l = 1/2*abs(xi1[2]-xi1[1])
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isapprox(l, 0.0) && continue # no contribution in this master element
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De = zeros(nnodes, nnodes)
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Me = zeros(nnodes, nnodes)
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for ip in get_integration_points(slave_element, Val{5})
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# jacobian of slave element in deformed state
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dN = get_dbasis(slave_element, ip)
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j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
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w = ip.weight*norm(j)*l
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xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
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N1 = get_basis(slave_element, xi_s)
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De += w*diagm(vec(N1))
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Me += w*N1'*N1
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end
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Ae = De*inv(Me)
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slave_dofs = get_gdofs(slave_element, field_dim)
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master_dofs = get_gdofs(master_element, field_dim)
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for ip in get_integration_points(slave_element, Val{5})
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# jacobian of slave element in deformed state
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dN = get_dbasis(slave_element, ip)
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j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
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w = ip.weight*norm(j)*l
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# project gauss point from slave element to master element
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xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
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N1 = vec(get_basis(slave_element, xi_s))
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x_s = N1*x1 # coordinate in gauss point
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n_s = N1*n1 # normal direction in gauss point
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t_s = Q'*n_s # tangent direction in gauss point
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R_s = [n_s t_s]
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xi_m = project_from_slave_to_master(master_element, x_s, n_s, x2)
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N2 = vec(get_basis(master_element, xi_m))
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x_m = N2*x2
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Phi = Ae*N1
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u_s = N1*u1
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u_m = N2*u2
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la_s = Phi*la1 # traction force in gauss point
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la_nt = R_s*la_s
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gn = -dot(n_s, x_s - x_m) # normal gap
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fc[:,slave_element_nodes] += w*la_s*N1'
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fc[:,master_element_nodes] -= w*la_s*N2'
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#C[1,slave_element_nodes] += w*gn*Phi'
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lan_tot += w*la_nt[1]*Phi
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gap_tot += w*gn*Phi
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end
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end # master elements done
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for (i, j) in enumerate(slave_element_nodes)
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n = n1[i]
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t = Q'*n
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R = [n t]
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la_nt = R*la[:,j]
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info("node $j, n=$(ForwardDiff.get_value(n)) lan = $(ForwardDiff.get_value(la_nt[1])) gap = $(ForwardDiff.get_value(gap_tot[i]))")
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# if -lan_tot[i] + gap_tot[i] < 0
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if -la_nt[1] + gap_tot[i] < 0
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info("set node $j active")
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C[1,j] += gap_tot[i]
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# C[1,j] += la_nt[1] - max(0, la_nt[1] - gap_tot[i])
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C[2,j] += la_nt[2]
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else
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info("set node $j inactive")
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C[1,j] += la1[i][1]
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C[2,j] += la1[i][2]
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end
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end
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return vec([fc C])
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end
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# x doesn't mean deformed configuration here
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x = [problem.assembly.u; problem.assembly.la]
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ndofs = round(Int, length(x)/2)
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A, allresults = ForwardDiff.jacobian(calculate_interface, x, ForwardDiff.AllResults)
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b = -ForwardDiff.value(allresults)
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#b = -calculate_interface(x)
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#info("PE = $(ForwardDiff.value(allresults))")
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A = sparse(A)
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b = sparse(b)
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SparseMatrix.droptol!(A, 1.0e-12)
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SparseMatrix.droptol!(b, 1.0e-12)
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#println(A)
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K = A[1:ndofs,1:ndofs]
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C1 = transpose(A[1:ndofs,ndofs+1:end])
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C2 = A[ndofs+1:end,1:ndofs]
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D = A[ndofs+1:end,ndofs+1:end]
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f = b[1:ndofs]
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g = b[ndofs+1:end]
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add!(assembly.K, K)
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add!(assembly.C1, C1)
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add!(assembly.C2, C2)
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add!(assembly.D, D)
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add!(assembly.f, f)
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add!(assembly.g, g)
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return
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end
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