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dual basis formulation
This commit is contained in:
Jukka Aho
+24
-150
@@ -648,35 +648,15 @@ node_csys
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coordinate system in node, normal + tangent + "binormal"
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in 3d 3x3 matrix, in 2d 2x2 matrix, respectively
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"""
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abstract MortarProblem <: AbstractProblem
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function MortarProblem(parent_field_name::ASCIIString, parent_field_dim::Int, dim::Int=1, elements=[])
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return BoundaryProblem{MortarProblem}("mortar problem", parent_field_name, parent_field_dim, dim, elements)
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end
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function MortarProblem(problem_name::ASCIIString, parent_field_name::ASCIIString, parent_field_dim::Int, dim::Int=1, elements=[])
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return BoundaryProblem{MortarProblem}(problem_name, parent_field_name, parent_field_dim, dim, elements)
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end
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abstract ContactProblem{T} <: AbstractProblem
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abstract AbstractContact
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abstract TieContact <: AbstractContact
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abstract SmallSlidingContact <: AbstractContact
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function ContactProblem(problem_name::ASCIIString, parent_field_name::ASCIIString, parent_field_dim::Int, dim::Int=1, elements=[]; contact_type=TieContact)
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return BoundaryProblem{ContactProblem{contact_type}}(
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problem_name,
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parent_field_name,
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parent_field_dim,
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dim, elements)
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end
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abstract MortarProblem{T} <: AbstractProblem
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# Mortar assembly 2d
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typealias MortarElements2D Union{Seg2, Seg3}
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function assemble!{E<:MortarElements2D}(assembly::BoundaryAssembly, problem::BoundaryProblem{MortarProblem}, slave_element::Element{E}, time::Real)
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function assemble!{E<:MortarElements2D}(assembly::BoundaryAssembly,
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problem::BoundaryProblem{MortarProblem},
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slave_element::Element{E}, time::Real)
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# slave element must have a set of master elements
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haskey(slave_element, "master elements") || return
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@@ -688,15 +668,28 @@ function assemble!{E<:MortarElements2D}(assembly::BoundaryAssembly, problem::Bou
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slave_dofs = get_gdofs(slave_element, field_dim)
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for master_element in slave_element["master elements"]
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master_dofs = get_gdofs(master_element, field_dim)
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xi1a = project_from_master_to_slave(slave_element, master_element, [-1.0])
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xi1b = project_from_master_to_slave(slave_element, master_element, [ 1.0])
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xi1 = clamp([xi1a xi1b], -1.0, 1.0)
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l = 1/2*(xi1[2]-xi1[1])
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if abs(l) < 1.0e-9
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#warn("No contribution")
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continue # no contribution
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abs(l) > 1.0e-9 || continue # no contribution
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# Construct dual basis
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nnodes = size(slave_element, 2)
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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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J = get_jacobian(slave_element, ip, time)
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w = ip.weight*norm(J)*l
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xi = 1/2*(1-ip.xi)*xi1[1] + 1/2*(1+ip.xi)*xi1[2]
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N = slave_element(xi, time)
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De += w*diagm(vec(N))
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Me += w*N'*N
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end
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master_dofs = get_gdofs(master_element, field_dim)
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# info("Dual basis: De = \n$De")
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Ae = De*inv(Me)
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for ip in get_integration_points(slave_element, Val{5})
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J = get_jacobian(slave_element, ip, time)
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w = ip.weight*norm(J)*l
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@@ -708,9 +701,10 @@ function assemble!{E<:MortarElements2D}(assembly::BoundaryAssembly, problem::Bou
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# add contribution
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N1 = slave_element(xi_gauss, time)
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Phi = (Ae*N1')'
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N2 = master_element(xi_projected, time)
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S = w*kron(N1', N1)
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M = w*kron(N1', N2)
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S = w*kron(Phi', N1)
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M = w*kron(Phi', N2)
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for i=1:field_dim
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sd = slave_dofs[i:field_dim:end]
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md = master_dofs[i:field_dim:end]
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@@ -724,126 +718,6 @@ function assemble!{E<:MortarElements2D}(assembly::BoundaryAssembly, problem::Bou
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end
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end
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""" Calculate bi-orthogonal basis transformation matrix Aₑ. """
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function get_biorthogonal_transformation_matrix(element::Element, time::Real)
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nnodes = size(element, 2)
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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(element, Val{5})
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w = ip.weight
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J = get_jacobian(element, ip, time)
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JT = transpose(J)
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if size(JT, 2) == 1 # plane problem
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w *= norm(JT)
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else
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w *= norm(cross(JT[:,1], JT[:,2]))
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end
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N = element(ip, time)
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De += w*diagm(vec(N))
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Me += w*N'*N
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end
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Ae = De*inv(Me)
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return Ae
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end
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"""
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Small strain theory, allow frictionless tangential sliding, keep bodies in contact.
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"""
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function assemble!{E<:MortarElements2D}(assembly::BoundaryAssembly, problem::BoundaryProblem{ContactProblem{SmallSlidingContact}}, slave_element::Element{E}, time::Real)
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# get dimension and name of PARENT field
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field_dim = problem.parent_field_dim
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field_name = problem.parent_field_name
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slave_dofs = get_gdofs(slave_element, field_dim)
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#info("slave dofs of element: $slave_dofs")
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for master_element in slave_element["master elements"]
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xi1a = project_from_master_to_slave(slave_element, master_element, [-1.0])
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xi1b = project_from_master_to_slave(slave_element, master_element, [ 1.0])
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xi1 = clamp([xi1a xi1b], -1.0, 1.0)
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l = 1/2*(xi1[2]-xi1[1])
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abs(l) > 1.0e-9 || continue
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# Ae = get_biorthogonal_transformation_matrix(slave_element, time)
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nnodes = size(slave_element, 2)
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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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xi_gauss = 1/2*(1-ip_.xi)*xi1[1] + 1/2*(1+ip_.xi)*xi1[2]
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ip = IntegrationPoint(xi_gauss, ip_.weight)
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J = get_jacobian(slave_element, ip, time)
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w = ip.weight*norm(J)
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N = slave_element(ip, time)
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De += w*diagm(vec(N))
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Me += w*N'*N
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end
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Ae = De*inv(Me)
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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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J = get_jacobian(slave_element, ip, time)
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w = ip.weight*norm(J)*l
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# integration point on slave side segment
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xi_gauss = 1/2*(1-ip.xi)*xi1[1] + 1/2*(1+ip.xi)*xi1[2]
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# projected integration point
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xi_projected = project_from_slave_to_master(slave_element, master_element, xi_gauss)
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# add contribution to C1
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N1 = slave_element(xi_gauss, time)
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Phi = (Ae*N1')'
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N2 = master_element(xi_projected, time)
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#S = w*Phi'*N1
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#M = w*Phi'*N2
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S = w*N1'*N1
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M = w*N1'*N2
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nt = slave_element("normal-tangential coordinates", ip, time)
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#println("normal tangential = ")
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#println(round(nt, 3))
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nt = [1 0; 0 1]
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ntS = nt'*S
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ntM = nt'*M
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for i=1:field_dim
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sd = slave_dofs[i:field_dim:end]
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md = master_dofs[i:field_dim:end]
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add!(assembly.C1, sd, sd, S)
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add!(assembly.C1, sd, md, -M)
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add!(assembly.C2, sd, sd, ntS)
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add!(assembly.C2, sd, md, -ntM)
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end
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# construct C2 & D
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# info("normal dofs: $(slave_dofs[1:2:end])")
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# info("tangent dofs: $(slave_dofs[2:2:end])")
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#=
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# contribution in normal direction
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for dof in slave_dofs[1:2:end]
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add!(assembly.C2, [dof], sd, ntS[1,:])
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add!(assembly.C2, [dof], md, -ntM[1,:])
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end
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# contribution in tangent direction
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for dof in slave_dofs[1:2:end]
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add!(assembly.C2, sd[2:2:end], sd, ntS[2,:])
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add!(assembly.C2, sd[2:2:end], md, -ntM[2,:])
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# set lagrange multipliers to zero in tangent direction
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tangent = nt[2, :]
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add!(assembly.D, sd[2:2:end], sd, tangent)
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end
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for nid in get_connectivity(slave_element)
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ndofs = [2*(nid-1)+1, 2*(nid-1)+2]
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add!(assembly.C2, [2*(nid-1)+1], ndofs, ntS[1,:])
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add!(assembly.C2, [2*(nid-1)+1], ndofs, -ntM[1,:])
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end
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=#
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end
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end
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end
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typealias MortarElements3D Union{Tri3, Quad4}
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""" Find master elements from list of potential master elements. """
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