2d mortar

src/mortar_elements.jl

@@ -0,0 +1,84 @@
+# 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
+