fixed problems with surface loads. det(element, ip, time) should be avoided.

src/elasticity.jl

@@ -70,20 +70,20 @@ https://en.wikipedia.org/wiki/Hooke's_law
 """
 function get_residual_vector{P<:ElasticityProblem}(problem::Problem{P}, element::Element, ip::IntegrationPoint, time::Number; variation=nothing)
 
-
-    # u = element("displacement", ip, time, variation)
-
     r = zeros(Float64, problem.dim, length(element))
 
+    J = get_jacobian(element, ip, time)
+
     # internal forces
     if haskey(element, "youngs modulus") && haskey(element, "poissons ratio")
         u = element("displacement", time, variation)
         grad = element(ip, time, Val{:grad})
         gradu = grad*u
 
-        F = I + gradu # deformation gradient
-#       info("gradu = \n$(ForwardDiff.get_value(gradu))")
+        # deformation gradient
+        F = I + gradu
 
+        # material
         young = element("youngs modulus", ip, time)
         poisson = element("poissons ratio", ip, time)
         mu = young/(2*(1+poisson))
@@ -91,29 +91,30 @@ function get_residual_vector{P<:ElasticityProblem}(problem::Problem{P}, element:
         if P == PlaneStressElasticityProblem
             lambda = 2*lambda*mu/(lambda + 2*mu)  # <- correction for 2d problems
         end
-        E = 1/2*(F'*F - I)  # strain
+
+        # strain
+        E = 1/2*(F'*F - I)
+
+        # stress
         S = lambda*trace(E)*I + 2*mu*E
 
-        #J = det(element, ip, time)
-        #T = J^-1*F*S*F'
-        #ip["cauchy stress"] = T
-        #ip["gl strain"] = E
-
-        r += F*S*grad
+        r += F*S*grad*det(J)
     end
 
     # external forces - volume load
     if haskey(element, "displacement load")
         basis = element(ip, time)
         b = element("displacement load", ip, time)
-        r -= b*basis
+        r -= b*basis*det(J)
     end
 
     # external forces - surface traction force
     if haskey(element, "displacement traction force")
         basis = element(ip, time)
         T = element("displacement traction force", ip, time)
-        r -= T*basis
+        JT = transpose(J)
+        s = size(JT, 2) == 1 ? JT : cross(JT[:,1], JT[:,2])
+        r -= T*basis*norm(s)
     end
 
     return vec(r)