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https://github.com/JuliaFEM/JuliaFEM.jl.git
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Preallocate matrices in Elasticity problem
Now style is to assemble all same kind/dimension elements at same time in one function call, so it's possible to allocate all necessary matrices only one time.
This commit is contained in:
Jukka Aho
+139
-104
@@ -62,13 +62,10 @@ Function groups elements to arrays by their type and assembles one element type
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at time. This makes it possible to pre-allocate matrices common to same type
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of elements.
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"""
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function assemble!(assembly::Assembly, problem::Problem{Elasticity}, elements::Vector{Element}, time)
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function assemble!(assembly::Assembly, problem::Problem{Elasticity},
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elements::Vector{Element}, time)
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formulation = Val{problem.properties.formulation}
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element_types = unique(map(get_element_type, elements))
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for element_type in element_types
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elements_subset = filter_by_element_type(element_type, elements)
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elements_subset = [element for element in elements_subset]
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nelements = length(elements_subset)
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for (element_type, elements_subset) in group_by_element_type(elements)
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assemble!(assembly, problem, elements_subset, time, formulation)
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end
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end
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@@ -101,13 +98,6 @@ function initialize_internal_params!(params, ip, type_) #::Type{Val{:type_2d}})
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end
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end
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function get_keys(element)
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all_keys = element.fields.keys
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idx = filter(x->isassigned(all_keys, x), collect(1:length(all_keys)))
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map(x -> all_keys[x], idx)
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end
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""" Assemble 3d continuum elements in general solid mechanics problem. """
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function assemble!{El<:Elasticity3DVolumeElements}(assembly::Assembly,
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problem::Problem{Elasticity},
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@@ -116,16 +106,34 @@ function assemble!{El<:Elasticity3DVolumeElements}(assembly::Assembly,
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props = problem.properties
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dim = get_unknown_field_dimension(problem)
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nnodes = length(El)
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ndofs = dim*nnodes
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BL = zeros(6, ndofs)
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BNL = zeros(9, ndofs)
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Km = zeros(ndofs, ndofs)
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Kg = zeros(ndofs, ndofs)
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f_int = zeros(ndofs)
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f_ext = zeros(ndofs)
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bi = BasisInfo(El)
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gradu = zeros(dim, dim)
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strain = zeros(dim, dim)
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strain_vec = zeros(6)
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stress_vec = zeros(6)
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F = zeros(dim, dim)
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D = zeros(6, 6)
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Dtan = zeros(6, 6)
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Bt_mul_D = zeros(ndofs, 6)
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Bt_mul_D_mul_B = zeros(ndofs, ndofs)
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Bt_mul_S = zeros(ndofs)
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for element in elements
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nnodes = length(element)
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ndofs = dim*nnodes
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BL = zeros(6, ndofs)
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BNL = zeros(9, ndofs)
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Km = zeros(ndofs, ndofs)
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Kg = zeros(ndofs, ndofs)
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f = zeros(ndofs)
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bi = BasisInfo(El)
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u = element("displacement", time)
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fill!(Km, 0.0)
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fill!(Kg, 0.0)
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fill!(f_int, 0.0)
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fill!(f_ext, 0.0)
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for ip in get_integration_points(element)
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X = element("geometry", time)
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@@ -135,104 +143,121 @@ function assemble!{El<:Elasticity3DVolumeElements}(assembly::Assembly,
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dN = bi.grad
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w = ip.weight*detJ
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# kinematics; calculate deformation gradient and strain
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gradu = zeros(dim, dim)
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if haskey(element, "displacement")
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gradu += element("displacement", ip, time, Val{:Grad})
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# calculate displacement gradient
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fill!(gradu, 0.0)
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for i=1:dim
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for j=1:dim
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for k=1:nnodes
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gradu[i,j] += bi.grad[j,k]*u[k][i]
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end
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end
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end
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strain = 1/2*(gradu' + gradu)
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F = eye(dim)
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# calculate strain tensor and deformation gradient
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fill!(strain, 0.0)
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fill!(F, 0.0)
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F[:,:] += I
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if props.finite_strain
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F += gradu
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strain += 1/2*gradu'*gradu
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strain[:,:] = 1/2 * (gradu + gradu' + gradu'*gradu)
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F[:,:] += gradu
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else
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strain[:,:] = 1/2 * (gradu + gradu')
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end
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strain_vec[1] = strain[1,1]
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strain_vec[2] = strain[2,2]
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strain_vec[3] = strain[3,3]
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strain_vec[4] = 2.0*strain[1,2]
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strain_vec[5] = 2.0*strain[2,3]
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strain_vec[6] = 2.0*strain[1,3]
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# material stiffness start
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fill!(BL, 0.0)
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for i=1:nnodes
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BL[1, 3*(i-1)+1] = F[1,1]*dN[1,i]
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BL[1, 3*(i-1)+2] = F[2,1]*dN[1,i]
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BL[1, 3*(i-1)+3] = F[3,1]*dN[1,i]
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BL[2, 3*(i-1)+1] = F[1,2]*dN[2,i]
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BL[2, 3*(i-1)+2] = F[2,2]*dN[2,i]
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BL[2, 3*(i-1)+3] = F[3,2]*dN[2,i]
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BL[3, 3*(i-1)+1] = F[1,3]*dN[3,i]
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BL[3, 3*(i-1)+2] = F[2,3]*dN[3,i]
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BL[3, 3*(i-1)+3] = F[3,3]*dN[3,i]
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BL[4, 3*(i-1)+1] = F[1,1]*dN[2,i] + F[1,2]*dN[1,i]
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BL[4, 3*(i-1)+2] = F[2,1]*dN[2,i] + F[2,2]*dN[1,i]
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BL[4, 3*(i-1)+3] = F[3,1]*dN[2,i] + F[3,2]*dN[1,i]
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BL[5, 3*(i-1)+1] = F[1,2]*dN[3,i] + F[1,3]*dN[2,i]
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BL[5, 3*(i-1)+2] = F[2,2]*dN[3,i] + F[2,3]*dN[2,i]
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BL[5, 3*(i-1)+3] = F[3,2]*dN[3,i] + F[3,3]*dN[2,i]
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BL[6, 3*(i-1)+1] = F[1,3]*dN[1,i] + F[1,1]*dN[3,i]
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BL[6, 3*(i-1)+2] = F[2,3]*dN[1,i] + F[2,1]*dN[3,i]
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BL[6, 3*(i-1)+3] = F[3,3]*dN[1,i] + F[3,1]*dN[3,i]
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if props.finite_strain
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for i=1:nnodes
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BL[1, 3*(i-1)+1] = F[1,1]*dN[1,i]
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BL[1, 3*(i-1)+2] = F[2,1]*dN[1,i]
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BL[1, 3*(i-1)+3] = F[3,1]*dN[1,i]
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BL[2, 3*(i-1)+1] = F[1,2]*dN[2,i]
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BL[2, 3*(i-1)+2] = F[2,2]*dN[2,i]
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BL[2, 3*(i-1)+3] = F[3,2]*dN[2,i]
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BL[3, 3*(i-1)+1] = F[1,3]*dN[3,i]
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BL[3, 3*(i-1)+2] = F[2,3]*dN[3,i]
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BL[3, 3*(i-1)+3] = F[3,3]*dN[3,i]
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BL[4, 3*(i-1)+1] = F[1,1]*dN[2,i] + F[1,2]*dN[1,i]
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BL[4, 3*(i-1)+2] = F[2,1]*dN[2,i] + F[2,2]*dN[1,i]
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BL[4, 3*(i-1)+3] = F[3,1]*dN[2,i] + F[3,2]*dN[1,i]
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BL[5, 3*(i-1)+1] = F[1,2]*dN[3,i] + F[1,3]*dN[2,i]
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BL[5, 3*(i-1)+2] = F[2,2]*dN[3,i] + F[2,3]*dN[2,i]
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BL[5, 3*(i-1)+3] = F[3,2]*dN[3,i] + F[3,3]*dN[2,i]
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BL[6, 3*(i-1)+1] = F[1,3]*dN[1,i] + F[1,1]*dN[3,i]
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BL[6, 3*(i-1)+2] = F[2,3]*dN[1,i] + F[2,1]*dN[3,i]
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BL[6, 3*(i-1)+3] = F[3,3]*dN[1,i] + F[3,1]*dN[3,i]
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end
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else
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for i=1:nnodes
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BL[1, 3*(i-1)+1] = dN[1,i]
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BL[2, 3*(i-1)+2] = dN[2,i]
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BL[3, 3*(i-1)+3] = dN[3,i]
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BL[4, 3*(i-1)+1] = dN[2,i]
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BL[4, 3*(i-1)+2] = dN[1,i]
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BL[5, 3*(i-1)+2] = dN[3,i]
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BL[5, 3*(i-1)+3] = dN[2,i]
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BL[6, 3*(i-1)+1] = dN[3,i]
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BL[6, 3*(i-1)+3] = dN[1,i]
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end
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end
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strain_vec = [strain[1,1]; strain[2,2]; strain[3,3]; strain[1,2]; strain[2,3]; strain[1,3]]
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# calculate stress
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fill!(D, 0.0)
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E = element("youngs modulus", ip, time)
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nu = element("poissons ratio", ip, time)
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D = E/((1.0+nu)*(1.0-2.0*nu)) * [
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1.0-nu nu nu 0.0 0.0 0.0
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nu 1.0-nu nu 0.0 0.0 0.0
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nu nu 1.0-nu 0.0 0.0 0.0
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0.0 0.0 0.0 0.5-nu 0.0 0.0
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0.0 0.0 0.0 0.0 0.5-nu 0.0
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0.0 0.0 0.0 0.0 0.0 0.5-nu]
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la = E*nu/((1.0+nu)*(1.0-2.0*nu))
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mu = E/(2.0*(1.0+nu))
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D[1,1] = D[2,2] = D[3,3] = 2*mu + la
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D[4,4] = D[5,5] = D[6,6] = mu
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D[1,2] = D[2,1] = D[2,3] = D[3,2] = D[1,3] = D[3,1] = la
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element_keys = get_keys(element)
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# determine material model
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if "plasticity" in element_keys
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plastic_def = element("plasticity")[ip.id]
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material_model = :linear_elasticity
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if haskey(element, "plasticity")
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material_model = :ideal_plasticity
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end
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calculate_stress! = plastic_def["type"]
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yield_surface_ = plastic_def["yield_surface"]
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params = plastic_def["params"]
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# calculate stress vector based on material model
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initialize_internal_params!(params, ip, Val{:type_3d})
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if material_model == :linear_elasticity
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Dtan[:,:] = D[:,:]
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stress_vec[:] = Dtan * strain_vec
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end
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if time == 0.0
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error("Given step time = $(time). Please select time > 0.0")
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end
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if material_model == :ideal_plasticity
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plastic_def = element("plasticity")[ip.id]
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t_last = ip("prev_time", time)
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update!(ip, "prev_time", time => t_last)
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calculate_stress! = plastic_def["type"]
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yield_surface_ = plastic_def["yield_surface"]
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params = plastic_def["params"]
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dt = time - t_last
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initialize_internal_params!(params, ip, Val{:type_3d})
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stress_last = ip("stress", t_last)
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strain_last = ip("strain", t_last)
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if time == 0.0
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error("Given step time = $(time). Please select time > 0.0")
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end
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dstrain_vec = strain_vec - strain_last
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stress_vec = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
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plastic_strain = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
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Dtan = [0.0 0.0 0.0 0.0 0.0 0.0;
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0.0 0.0 0.0 0.0 0.0 0.0;
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0.0 0.0 0.0 0.0 0.0 0.0
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0.0 0.0 0.0 0.0 0.0 0.0;
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0.0 0.0 0.0 0.0 0.0 0.0;
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0.0 0.0 0.0 0.0 0.0 0.0]
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calculate_stress!(stress_vec, stress_last, dstrain_vec, plastic_strain, D, params, Dtan, yield_surface_, time, dt, Val{:type_3d})
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t_last = ip("prev_time", time)
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update!(ip, "prev_time", time => t_last)
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dt = time - t_last
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stress_last = ip("stress", t_last)
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strain_last = ip("strain", t_last)
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dstrain_vec = strain_vec - strain_last
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fill!(stress_vec, 0.0)
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fill!(Dtan, 0.0)
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plastic_strain = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
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calculate_stress!(stress_vec, stress_last, dstrain_vec, plastic_strain, D, params, Dtan, yield_surface_, time, dt, Val{:type_3d})
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# plastic_def = element.dev["plasticity"]
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# calculate_stress! = plastic_def["stress"]
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# params = plastic_def["params"]
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# yield_surface_ = plastic_def["yield_surface"]
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# (stress_last, strain_last) = get_internal_params(element.dev, ip.id, Val{:type_3d})
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# dstrain_vec = strain_vec - strain_last
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# calculate_stress!(stress_vec, stress_last, dstrain_vec, D, params, Dtan, yield_surface_, Val{:type_3d})
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else
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stress_vec = D * ([1.0, 1.0, 1.0, 2.0, 2.0, 2.0].*strain_vec)
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Dtan = D
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end
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:strain in props.store_fields && update!(ip, "strain", time => strain_vec)
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@@ -245,7 +270,14 @@ function assemble!{El<:Elasticity3DVolumeElements}(assembly::Assembly,
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:stress13 in props.store_fields && update!(ip, "stress13", time => stress_vec[6])
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:plastic_strain in props.store_fields && update!(ip, "plastic_strain", time => plastic_strain)
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Km += w*BL'*Dtan*BL
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#Km += w*BL'*Dtan*BL
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At_mul_B!(Bt_mul_D, BL, Dtan)
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A_mul_B!(Bt_mul_D_mul_B, Bt_mul_D, BL)
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scale!(Bt_mul_D_mul_B, w)
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for i=1:ndofs^2
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@inbounds Km[i] += Bt_mul_D_mul_B[i]
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end
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# material stiffness end
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if props.geometric_stiffness
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@@ -278,26 +310,29 @@ function assemble!{El<:Elasticity3DVolumeElements}(assembly::Assembly,
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end
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# internal load
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At_mul_B!(Bt_mul_S, BL, stress_vec)
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scale!(Bt_mul_S, w)
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for i=1:ndofs
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@inbounds f_int[i] += Bt_mul_S[i]
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end
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# external load start
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if haskey(element, "displacement load")
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T = element("displacement load", ip, time)
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f += w*vec(T*N)
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f_ext += w*vec(T*N)
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end
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for i=1:dim
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if haskey(element, "displacement load $i")
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b = element("displacement load $i", ip, time)
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f[i:dim:end] += w*vec(b*N)
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f_ext[i:dim:end] += w*vec(b*N)
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end
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end
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# external load end
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if get_formulation_type(problem) == :incremental
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f -= w*BL'*stress_vec
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end
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end
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gdofs = get_gdofs(problem, element)
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@@ -309,7 +344,7 @@ function assemble!{El<:Elasticity3DVolumeElements}(assembly::Assembly,
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add!(assembly.Kg, gdofs, gdofs, Kg)
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end
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add!(assembly.f, gdofs, f)
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add!(assembly.f, gdofs, f_ext - f_int)
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end
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