added elasticity solver

src/JuliaFEM.jl

@@ -3,6 +3,10 @@ module JuliaFEM
 
 VERSION < v"0.4-" && using Docile
 
+# import solvers
+include("elasticity_solver.jl")
+#using elasticity_solver
+
 export Model, new_model, new_field, get_field, add_nodes, get_nodes, add_elements, get_elements
 
 

src/elasticity_solver.jl

@@ -0,0 +1,83 @@
+# This file is a part of JuliaFEM. License is MIT: https://github.com/ovainola/JuliaFEM/blob/master/README.md
+module elasticity_solver
+
+VERSION < v"0.4-" && using Docile
+
+export solve_elasticity_interface!
+
+@doc """
+This is generic interface that reads data from data model, solves elasticity
+problem and updates model.
+
+Parameters
+----------
+model : to be defined
+""" ->
+function solve_elasticity_interface!()
+  return 0
+end
+
+
+
+# Below this line is internal functions related to solver. They can be used
+# directly if needed or using general interface combining data model and
+# solver.
+
+@doc """
+Calculate local tangent stiffness matrix and residual force vector R = T - F
+""" ->
+function calc_local_matrices!(X, u, R, Kt, dNdξ, λ, μ, ipoints, iweights)
+  dim, N = size(X)
+  I = eye(dim)
+  R[:,:] = 0.0
+  Kt[:,:] = 0.0
+
+  dF = zeros(dim, dim)
+
+  for m = 1:length(iweights)
+        w = iweights[m]
+        ξ = ipoints[m, :]
+        Jᵀ = X*dNdξ(ξ)
+        detJ = det(Jᵀ)
+        ∇N = inv(Jᵀ)*dNdξ(ξ)'
+        ∇u = u*∇N'
+        F = I + ∇u  # Deformation gradient
+        E = 1/2*(∇u' + ∇u + ∇u'*∇u)  # Green-Lagrange strain tensor
+        S = λ*trace(E)*I + 2*μ*E  # PK2 stress tensor
+        P = F*S  # PK1 stress tensor
+        R[:,:] += w*P*∇N*detJ
+
+        for p = 1:N
+            for i = 1:dim
+                dF[:,:] = 0.0
+                dF[i,:] = ∇N[:,p]
+                dE = 1/2*(F'*dF + dF'*F)
+                dS = λ*trace(dE)*I + 2*μ*dE
+                dP = dF*S + F*dS
+                for q = 1:N
+                    for j = 1:dim
+                        Kt[dim*(p-1)+i,dim*(q-1)+j] += w*(dP[j,:]*∇N[:,q])[1]*detJ
+                    end
+                end
+            end
+        end
+
+    end
+end
+
+
+@doc """
+Solve one increment of elasticity problem
+""" ->
+function solve_elasticity_increment!(X, u, du, R, Kt, elmap, nodalloads,
+                                     dirichletbc, λ, μ, dNdξ, ipoints,
+                                     iweights)
+  calc_local_matrices!(X, u, R, Kt, dNdξ, λ, μ, ipoints, iweights)
+  # FIXME: boundary conditions
+  free_dofs = find(isnan(dirichletbc))
+  R -= nodalloads
+  du[free_dofs] = Kt[free_dofs, free_dofs] \ -reshape(R, 8)[free_dofs]
+end
+
+
+end