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Move contact mechanics to separate package (#196)
Development of auto-differentiated mortar contact mechanics in 2D is moved to own separate package, MortarContact2DAD. Other changes are similar to what is done with MortarContact2D: elements are added to problems using `add_slave_elements!` and `add_master_elements!` instead of `add_elements!`, to make interface more explicit. Also, problem name is `Contact2DAD`, so the dimension is now explicitly stated in problem name. (Also have `Mortar2DAD`, compare to the `Mortar2D` and `Contact2D` of `MortarContact2D.jl`.)
This commit is contained in:
Jukka Aho
+2
-2
@@ -47,10 +47,10 @@ export assemble!, postprocess!
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### Mortar methods ###
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@reexport using MortarContact2D
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@reexport using MortarContact2DAD
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include("problems_mortar.jl")
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include("problems_mortar_3d.jl")
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include("problems_mortar_2d_autodiff.jl")
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export calculate_normals, calculate_normals!, project_from_slave_to_master,
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project_from_master_to_slave, Mortar, get_slave_elements,
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get_polygon_clip
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@@ -67,7 +67,7 @@ include("solvers_modal.jl")
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export Modal
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include("problems_contact.jl")
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include("problems_contact_3d.jl")
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include("problems_contact_2d_autodiff.jl")
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#include("problems_contact_3d_autodiff.jl")
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export Contact
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# Preprocess module
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@@ -1,380 +0,0 @@
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# 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_ad{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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""" Multiply basis / dbasis at `xi` with field. """
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function mul(func, xi, field)
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B = func(slave_element, [xi], time)
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return sum(B[i]*field[i] for i=1:length(B))
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end
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x1(xi1) = mul(get_basis, xi1, x1_)
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dx1(xi1) = mul(get_dbasis, xi1, x1_)
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n1(xi1) = mul(get_basis, xi1, n1_)
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dn1(xi1) = mul(get_dbasis, xi1, 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_ad{E<:MortarElements2D}(
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master_element::Element{E}, x1, n1, x2_;
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tol=1.0e-10, max_iterations=20)
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x2(xi2) = interpolate(vec(get_basis(master_element, [xi2], time)), x2_)
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dx2(xi2) = interpolate(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(problem, element)
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X_el = element("geometry", time)
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x_el = tuple( (X_el[i] + u[:,j] for (i,j) in enumerate(conn))... )
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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 = ((u[:,i] for i in slave_element_nodes)...)
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x1 = ((Xi+ui for (Xi,ui) in zip(X1,u1))...)
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la1 = ((la[:,i] for i in slave_element_nodes)...)
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n1 = ((normals[:,i] for i in slave_element_nodes)...)
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nnodes = size(slave_element, 2)
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# construct dual basis
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De = zeros(nnodes, nnodes)
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Me = zeros(nnodes, nnodes)
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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 = ((u[:,i] for i in master_element_nodes)...)
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x2 = ((Xi+ui for (Xi,ui) in zip(X2,u2))...)
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# calculate segmentation: we care only about endpoints
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xi1a = project_from_master_to_slave_ad(slave_element, field(x1), field(n1), x2[1])
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xi1b = project_from_master_to_slave_ad(slave_element, field(x1), field(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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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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end
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Ae = De*inv(Me)
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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 = ((u[:,i] for i in master_element_nodes)...)
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x2 = ((Xi+ui for (Xi,ui) in zip(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_ad(slave_element, field(x1), field(n1), x2[1])
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xi1b = project_from_master_to_slave_ad(slave_element, field(x1), field(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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slave_dofs = get_gdofs(problem, slave_element)
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master_dofs = get_gdofs(problem, master_element)
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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 = interpolate(N1, x1) # coordinate in gauss point
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n_s = interpolate(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_ad(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 = interpolate(N2, x2)
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Phi = Ae*N1
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la_s = interpolate(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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state = problem.properties.contact_state_in_first_iteration
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if problem.properties.iteration == 1
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info("First contact iteration, initial contact state = $state")
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if state == :AUTO
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avg_gap = ForwardDiff.value(mean([gap[1, j] for j in S]))
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std_gap = ForwardDiff.value(std([gap[1, j] for j in S]))
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if (avg_gap < 1.0e-12) && (std_gap < 1.0e-12)
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state = :ACTIVE
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else
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state = :UNKNOWN
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end
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info("Average weighted gap = $avg_gap, std gap = $std_gap, automatically determined contact state = $state")
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end
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end
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is_active = Dict{Int, Bool}()
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condition = Dict()
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for j in S
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if j in props.always_in_contact
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is_active[j] = true
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continue
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end
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lan = dot(normals[:,j], la[:,j])
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condition[j] = ForwardDiff.value(lan - gap[1, j])
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is_active[j] = condition[j] > 0
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end
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if problem.properties.iteration == 1 && state == :ACTIVE
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for j in S
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is_active[j] = true
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end
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end
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if problem.properties.iteration == 1 && state == :INACTIVE
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for j in S
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is_active[j] = false
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end
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end
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if Logging._root.level == DEBUG
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debug("Summary of nodes")
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for j in sort(collect(keys(is_active)))
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n = map(ForwardDiff.value, normals[:,j])
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debug("$j, c=$(condition[j]), s=$(is_active[j]), n=$n")
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end
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end
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for j in S
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if is_active[j]
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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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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 = 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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f += C1*problem.assembly.la
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g += D*problem.assembly.la
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#=
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if !haskey(problem, "contact force")
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problem.fields["contact force"] = Field(time => f)
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else
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update!(problem.fields["contact force"], time => f)
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end
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fc = problem.fields["contact force"]
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if length(fc) > 1
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# kick in generalized alpha rule for time integration
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alpha = 0.5
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info("Applying Generalized alpha time integration")
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K = (1-alpha)*K
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C1 = (1-alpha)*C1
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f = alpha*fc[end-1].data
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end
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=#
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problem.assembly.K = K
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problem.assembly.C1 = transpose(C1)
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problem.assembly.C2 = C2
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problem.assembly.D = D
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problem.assembly.f = sparse(f)
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problem.assembly.g = sparse(g)
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end
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@@ -1,247 +0,0 @@
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# 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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const MortarElements2D = Union{Seg2,Seg3}
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# forwarddiff version of mesh tying in 2d
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function project_from_master_to_slave_ad{E<:MortarElements2D}(
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slave_element::Element{E}, x1_, n1_, x2, time;
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tol=1.0e-10, max_iterations=20)
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x1(xi1) = interpolate(vec(get_basis(slave_element, [xi1], time)), x1_)
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dx1(xi1) = interpolate(vec(get_dbasis(slave_element, [xi1], time)), x1_)
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n1(xi1) = interpolate(vec(get_basis(slave_element, [xi1], time)), n1_)
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dn1(xi1) = interpolate(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))
|
||||
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 = $(ForwardDiff.get_value(x1_.data))")
|
||||
info("n1 = $(ForwardDiff.get_value(n1_.data))")
|
||||
info("x2 = $(ForwardDiff.get_value(x2))")
|
||||
info("xi1 = $(ForwardDiff.get_value(xi1)), dxi1 = $(ForwardDiff.get_value(dxi1))")
|
||||
info("-R(xi1) = $(ForwardDiff.get_value(-R(xi1)))")
|
||||
info("dR(xi1) = $(ForwardDiff.get_value(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_, time;
|
||||
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
|
||||
|
||||
""" 2d mesh tie using ForwardDiff.
|
||||
|
||||
Construct .. + fc*la and C(d,la)=0
|
||||
|
||||
"""
|
||||
function assemble!(problem::Problem{Mortar}, time::Float64, ::Type{Val{1}}, ::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)
|
||||
if field_name != "displacement"
|
||||
error("mortar forwarddiff assembly: only displacement field with adjust=yes supported")
|
||||
end
|
||||
|
||||
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
|
||||
|
||||
if props.rotate_normals
|
||||
for j in S
|
||||
normals[:,j] = -normals[:,j]
|
||||
end
|
||||
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 slave_element("master elements", time)
|
||||
|
||||
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
|
||||
|
||||
# 3.2. bi-orthogonal basis
|
||||
De = zeros(nsl, nsl)
|
||||
Me = zeros(nsl, nsl)
|
||||
Ae = zeros(nsl, nsl)
|
||||
if props.dual_basis
|
||||
for ip in get_integration_points(slave_element, 3)
|
||||
detJ = slave_element(ip, time, Val{:detJ})
|
||||
w = ip.weight*detJ*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))
|
||||
De += w*diagm(N1)
|
||||
Me += w*N1*N1'
|
||||
end
|
||||
Ae = De*inv(Me)
|
||||
else
|
||||
Ae = eye(nsl)
|
||||
end
|
||||
|
||||
# 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 = Ae*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
|
||||
@@ -33,9 +33,9 @@ function Modal(nev=10, which=:SM)
|
||||
end
|
||||
|
||||
""" Eliminate Dirichlet boundary condition from matrices K, M. """
|
||||
function eliminate_boundary_conditions!(K_red::SparseMatrixCSC,
|
||||
M_red::SparseMatrixCSC,
|
||||
problem::Problem{Dirichlet}, ndim::Int)
|
||||
function FEMBase.eliminate_boundary_conditions!(K_red::SparseMatrixCSC,
|
||||
M_red::SparseMatrixCSC,
|
||||
problem::Problem{Dirichlet}, ndim::Int)
|
||||
K = sparse(problem.assembly.K, ndim, ndim)
|
||||
C1 = sparse(problem.assembly.C1, ndim, ndim)
|
||||
C2 = sparse(problem.assembly.C2, ndim, ndim)
|
||||
@@ -100,10 +100,10 @@ end
|
||||
|
||||
|
||||
""" Eliminate mesh tie constraints from matrices K, M. """
|
||||
function eliminate_boundary_conditions!(K_red::SparseMatrixCSC,
|
||||
M_red::SparseMatrixCSC,
|
||||
problem::Union{Problem{Mortar}, Problem{Mortar2D}},
|
||||
ndim::Int)
|
||||
function FEMBase.eliminate_boundary_conditions!(K_red::SparseMatrixCSC,
|
||||
M_red::SparseMatrixCSC,
|
||||
problem::Union{Problem{Mortar}, Problem{Mortar2D}},
|
||||
ndim::Int)
|
||||
|
||||
C1 = sparse(problem.assembly.C1, ndim, ndim)
|
||||
C2 = sparse(problem.assembly.C2, ndim, ndim)
|
||||
|
||||
Reference in New Issue
Block a user