mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-20 04:03:45 +00:00
Jukka Aho
85 lines
2.6 KiB
Julia
85 lines
2.6 KiB
Julia
# This file is a part of JuliaFEM.
|
|
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
|
|
|
|
# Mortar elements
|
|
|
|
# slave element = non-mortar element where integration happens
|
|
# master element = mortar element projected to non-mortar side
|
|
|
|
abstract MortarElement <: Element
|
|
|
|
type MSeg2 <: MortarElement
|
|
connectivity :: Vector{Int}
|
|
basis :: Basis
|
|
fields :: FieldSet
|
|
master_elements :: Vector{MortarElement}
|
|
end
|
|
|
|
function MSeg2(connectivity, master_elements=[], biorthogonal=false)
|
|
basis(xi) = [(1-xi[1])/2 (1+xi[1])/2]
|
|
dbasisdxi(xi) = [-1/2 1/2]
|
|
return MSeg2(connectivity, Basis(basis, dbasisdxi), FieldSet(), master_elements)
|
|
end
|
|
|
|
""" Find projection from slave nodes to master element, i.e. find xi2 from
|
|
master element corresponding to the xi1.
|
|
"""
|
|
function project_from_slave_to_master(slave::MortarElement, master::MortarElement, xi1::Vector, time::Float64=0.0; max_iterations=5, tol=1.0e-9)
|
|
slave_basis = get_basis(slave)
|
|
master_basis = get_basis(master)
|
|
|
|
# slave side geometry and normal direction at xi1
|
|
X1 = slave_basis("geometry", xi1, time)
|
|
N1 = slave_basis("nodal ntsys", xi1, time)[:,1]
|
|
|
|
# master side geometry at xi2
|
|
X2(xi2) = master_basis("geometry", [xi2], time)
|
|
# dX2(xi2) = dmaster_basis("geometry", xi2, time)
|
|
|
|
# equation to solve
|
|
R(xi2) = det([X2(xi2)-X1 N1]')
|
|
# dR(xi2) = det([dX2(xi2) N1]')
|
|
dR = ForwardDiff.derivative(R)
|
|
|
|
# go!
|
|
xi2 = 0.0
|
|
for i=1:max_iterations
|
|
dxi2 = -R(xi2) / dR(xi2)
|
|
xi2 += dxi2
|
|
if norm(dxi2) < tol
|
|
return Float64[xi2]
|
|
end
|
|
end
|
|
error("find projection from slave to master: did not converge")
|
|
end
|
|
|
|
""" Find projection from master surface to slave point, i.e. find xi1 from slave element corresponding to the xi2. """
|
|
function project_from_master_to_slave(slave::MortarElement, master::MortarElement, xi2::Vector, time::Float64=0.0; max_iterations=5, tol=1.0e-9)
|
|
slave_basis = get_basis(slave)
|
|
master_basis = get_basis(master)
|
|
|
|
# slave side geometry and normal direction at xi1
|
|
X1(xi1) = slave_basis("geometry", [xi1], time)
|
|
N1(xi1) = slave_basis("nodal ntsys", [xi1], time)[:,1]
|
|
|
|
# master side geometry at xi2
|
|
X2 = master_basis("geometry", xi2, time)
|
|
|
|
# equation to solve
|
|
R(xi1) = det([X1(xi1)-X2 N1(xi1)]')
|
|
# dR(xi1) = det([dX1(xi1) N1(xi1)]') + det([X1(xi1)-X2 dN1(xi1)]')
|
|
dR = ForwardDiff.derivative(R)
|
|
|
|
# go!
|
|
xi1 = 0.0
|
|
for i=1:max_iterations
|
|
dxi1 = -R(xi1) / dR(xi1)
|
|
xi1 += dxi1
|
|
if norm(dxi1) < tol
|
|
return Float64[xi1]
|
|
end
|
|
end
|
|
error("find projection from master to slave: did not converge")
|
|
end
|
|
|