mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-27 04:10:54 +00:00
Jukka Aho
297 lines
10 KiB
Julia
297 lines
10 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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using ForwardDiff
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""" Find segment from slave element corresponding to master element nodes.
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Parameters
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----------
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x1_, n1_
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slave element geometry and normal direction
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x2
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master element node to project onto slave
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Returns
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-------
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xi
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dimensionless coordinate on slave corresponding to
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projected master
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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, debug=false)
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x1(xi1) = vec(get_basis(slave_element, [xi1], time))*x1_
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dx1(xi1) = vec(get_dbasis(slave_element, [xi1], time))*x1_
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n1(xi1) = vec(get_basis(slave_element, [xi1], time))*n1_
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dn1(xi1) = vec(get_dbasis(slave_element, [xi1], time))*n1_
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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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xi1_next = 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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dxi1 = clamp(dxi1, -0.3, 0.3)
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xi1_next = clamp(xi1 + dxi1, -1.0, 1.0)
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if norm(xi1_next - xi1) < tol
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return xi1_next
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end
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if debug
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info("xi1 = $xi1")
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info("R(xi1) = $(R(xi1))")
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info("dR(xi1) = $(dR(xi1))")
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info("dxi1 = $dxi1")
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info("norm = $(norm(xi1_next - xi1))")
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info("xi1_next = $xi1_next")
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end
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xi1 = xi1_next
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end
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info("x1 = $x1_")
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info("n1 = $n1_")
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info("x2 = $x2")
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info("xi1 = $xi1, dxi1 = $dxi1")
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info("-R(xi1) = $(-R(xi1))")
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info("dR(xi1) = $(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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x2(xi2) = vec(get_basis(master_element, [xi2], time))*x2_
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dx2(xi2) = vec(get_dbasis(master_element, [xi2], time))*x2_
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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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"""
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Frictionless 2d finite sliding contact with forwarddiff.
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true/false flags: finite_sliding, friction, use_forwarddiff
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"""
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function assemble!(problem::Problem{Contact}, time::Float64,
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::Type{Val{1}}, ::Type{Val{true}},
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::Type{Val{false}}, ::Type{Val{true}})
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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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slave_elements = get_slave_elements(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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gap = zeros(u)
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C = zeros(la)
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S = Set{Int64}()
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# 1. update nodal normals for slave 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 slave_elements
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conn = get_connectivity(element)
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push!(S, conn...)
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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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#=
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for ip in get_integration_points(element, 3)
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dN = get_dbasis(element, ip, time)
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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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=#
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dN = get_dbasis(element, [0.0], time)
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t = sum([kron(dN[:,i], x_el[i]') for i=1:length(x_el)])
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n = Q*t'
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n /= norm(n)
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for c in conn
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normals[:,c] += n
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end
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end
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for i in 1:size(normals,2)
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normals[:,i] /= norm(normals[:,i])
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end
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# swap element normals in 2d if they point to inside of body
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if props.rotate_normals
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for i=1:size(normals,2)
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normals[:,i] = -normals[:,i]
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end
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end
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normals2 = Dict()
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for j in S
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normals2[j] = normals[:,j]
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end
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update!(slave_elements, "normal", time => normals2)
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# 2. loop all slave elements
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for slave_element in slave_elements
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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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x1 = X1 + u1
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la1 = Field(Vector[la[:,i] for i in slave_element_nodes])
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n1 = Field(Vector[normals[:,i] for i in slave_element_nodes])
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nnodes = size(slave_element, 2)
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# 3. loop all master elements
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for master_element in slave_element("master elements", time)
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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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#x1_midpoint = 1/2*(x1[1]+x1[2])
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#x2_midpoint = 1/2*(x2[1]+x2[2])
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#distance = ForwardDiff.get_value(norm(x2_midpoint - x1_midpoint))
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#distance > props.maximum_distance && continue
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# calculate segmentation: we care only about endpoints
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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[2])
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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, 3)
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# jacobian of slave element in deformed state
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dN = get_dbasis(slave_element, ip, time)
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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 = ip.coords[1]
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xi_s = dot([1/2*(1-xi); 1/2*(1+xi)], xi1)
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N1 = get_basis(slave_element, xi_s, time)
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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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# 4. loop integration points of segment
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for ip in get_integration_points(slave_element, 3)
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# jacobian of slave element in deformed state
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dN = get_dbasis(slave_element, ip, time)
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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 = ip.coords[1]
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xi_s = dot([1/2*(1-xi); 1/2*(1+xi)], xi1)
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N1 = vec(get_basis(slave_element, xi_s, time))
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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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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, time))
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x_m = N2*x2
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Phi = Ae*N1
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la_s = Phi*la1 # traction force in gauss point
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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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gap[1,slave_element_nodes] += w*gn*Phi
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#gap[1,slave_element_nodes] += w*gn*N1'
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end # done integrating segment
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end # master elements done
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end # slave elements done
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# at this point we have calculated contact force fc and gap for all slave elements.
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# next task is to find out are they in contact or not and remove inactive nodes
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#nzgap = sort(nonzeros(sparse(ForwardDiff.get_value(gap))))
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#info("gap: $nzgap")
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for (i, j) in enumerate(sort(collect(S)))
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# if j in props.always_inactive
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# info("special node $j always inactive")
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# C[:,j] = la[:,j]
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# continue
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# end
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n = normals[:,j]
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t = Q'*n
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lan = dot(n, la[:,j])
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lat = dot(t, la[:,j])
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if lan - gap[1, j] > 0
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# info("set node $j active, normal direction = $(ForwardDiff.get_value(n)), tangent plane = $(ForwardDiff.get_value(t))")
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C[1,j] += gap[1, j]
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C[2,j] += lat
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else
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C[:,j] = la[:,j]
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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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if length(x) == 0
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error("2d autodiff contact problem: initialize problem.assembly.u & la before solution")
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end
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A = ForwardDiff.jacobian(calculate_interface, x)
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b = calculate_interface(x)
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A = sparse(A)
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b = sparse(b)
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SparseArrays.droptol!(A, 1.0e-9)
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SparseArrays.droptol!(b, 1.0e-9)
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ndofs = round(Int, length(x)/2)
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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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empty!(problem.assembly)
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add!(problem.assembly.K, K)
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add!(problem.assembly.C1, C1)
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add!(problem.assembly.C2, C2)
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add!(problem.assembly.D, D)
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add!(problem.assembly.f, f)
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add!(problem.assembly.g, g)
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end
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