mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-09-27 20:26:58 +00:00
Jukka Aho
9ad66be08b
* running v0.6 conversion code proposed by @ovainola in #108. * change travis so that build is done using 0.6 * documentation is build from 0.6 * fix most of deprecation warnings * fix test to pass 0.6
246 lines
8.6 KiB
Julia
246 lines
8.6 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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# forwarddiff version of mesh tying in 2d
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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, time::Float64;
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tol=1.0e-10, max_iterations=20)
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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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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, time::Float64;
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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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""" 2d mesh tie using ForwardDiff.
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Construct .. + fc*la and C(d,la)=0
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"""
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function assemble!(problem::Problem{Mortar}, time::Float64, ::Type{Val{1}}, ::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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if field_name != "displacement"
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error("mortar forwarddiff assembly: only displacement field with adjust=yes supported")
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end
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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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tangents = 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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X1 = element("geometry", time)
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u1 = Field([u[:,i] for i in conn])
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x1 = X1 + u1
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dN = get_dbasis(element, [0.0], time)
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tangent = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
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for nid in conn
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tangents[:,nid] += tangent[:]
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end
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end
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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 j in S
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tangents[:,j] /= norm(tangents[:,j])
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normals[:,j] = Q*tangents[:,j]
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end
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if props.rotate_normals
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for j in S
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normals[:,j] = -normals[:,j]
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end
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end
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#update!(slave_elements, "normal", time => Dict(j => normals[:,j] for j in S))
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#update!(slave_elements, "tangent", time => Dict(j => tangents[:,j] for j in S))
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# 2. loop all slave elements
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for slave_element in slave_elements
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nsl = length(slave_element)
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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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# 3. loop all master elements
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for master_element in slave_element("master elements", time)
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nm = length(master_element)
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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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# 3.1 calculate segmentation
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xi1a = project_from_master_to_slave(slave_element, x1, n1, x2[1], time)
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xi1b = project_from_master_to_slave(slave_element, x1, n1, x2[2], time)
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# xi1a = project_from_master_to_slave(slave_element, X2[1], time)
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# xi1b = project_from_master_to_slave(slave_element, X2[2], time)
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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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# 3.2. bi-orthogonal basis
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De = zeros(nsl, nsl)
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Me = zeros(nsl, nsl)
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Ae = zeros(nsl, nsl)
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if props.dual_basis
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for ip in get_integration_points(slave_element, 3)
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detJ = slave_element(ip, time, Val{:detJ})
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w = ip.weight*detJ*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 = vec(get_basis(slave_element, xi_s, time))
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De += w*diagm(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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else
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Ae = eye(nsl)
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end
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# 3.3. loop integration points of one integration segment and calculate
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# local mortar matrices
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for ip in get_integration_points(slave_element, 3)
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detJ = slave_element(ip, time, Val{:detJ})
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w = ip.weight*detJ*l
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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 = vec(get_basis(slave_element, xi_s, time))
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Phi = Ae*N1
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# project gauss point from slave element to master element in direction n_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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#xi_m = project_from_slave_to_master(master_element, X_s, n_s, time)
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xi_m = project_from_slave_to_master(master_element, x_s, n_s, x2, time)
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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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la_s = Phi*la1
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gn = dot(n_s, x_s-x_m)
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u_s = N1*u1
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u_m = N2*u2
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X_s = N1*X1
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X_m = N2*X2
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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[:,slave_element_nodes] += w*(u_s-u_m)*Phi'
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if props.adjust
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G = w*(X_s-X_m)*Phi'
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gap[:,slave_element_nodes] += G
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end
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end
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end # master elements done
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end # slave elements done, contact virtual work ready
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C = gap
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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 = 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-12)
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SparseArrays.droptol!(b, 1.0e-12)
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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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problem.assembly.K = K
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problem.assembly.C1 = C1
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problem.assembly.C2 = C2
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problem.assembly.D = D
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problem.assembly.f = f
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problem.assembly.g = g
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end
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