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first version of modal analysis for natural frequencies

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This commit is contained in:
Jukka Aho
2016-06-17 02:10:17 +03:00
parent 74ed32a96c
commit 84bb370cea
14 changed files with 362 additions and 131 deletions
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src/elasticity.jl
+32 -33
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@@ -27,22 +27,14 @@ end
function assemble!(assembly::Assembly, problem::Problem{Elasticity}, element::Element, time=0.0)
props = problem.properties
gdofs = get_gdofs(problem, element)
if problem.properties.formulation in [:plane_stress, :plane_strain]
Kt, f = assemble(problem, element, time, Val{:plane})
add!(assembly.K, gdofs, gdofs, Kt)
add!(assembly.f, gdofs, f)
return
elseif problem.properties.formulation in [:continuum_buckling]
Km, Kg = assemble(problem, element, time, Val{:continuum_buckling})
add!(assembly.K, gdofs, gdofs, Km)
add!(assembly.Kg, gdofs, gdofs, Kg)
return
else
Kt, f = assemble(problem, element, time, Val{problem.properties.formulation})
add!(assembly.K, gdofs, gdofs, Kt)
add!(assembly.f, gdofs, f)
return
formulation = props.formulation
if formulation in [:plane_stress, :plane_strain]
formulation = :plane
end
Km, Kg, f = assemble(problem, element, time, Val{formulation})
add!(assembly.K, gdofs, gdofs, Km)
add!(assembly.Kg, gdofs, gdofs, Kg)
add!(assembly.f, gdofs, f)
end
""" Elasticity equations for 2d cases. """
@@ -53,7 +45,8 @@ function assemble{El<:Union{Tri3,Tri6,Quad4}}(problem::Problem{Elasticity}, elem
nnodes = length(element)
BL = zeros(3, dim*nnodes)
BNL = zeros(4, dim*nnodes)
Kt = zeros(dim*nnodes, dim*nnodes)
Km = zeros(dim*nnodes, dim*nnodes)
Kg = zeros(dim*nnodes, dim*nnodes)
f = zeros(dim*nnodes)
for ip in get_integration_points(element)
@@ -127,9 +120,9 @@ function assemble{El<:Union{Tri3,Tri6,Quad4}}(problem::Problem{Elasticity}, elem
S2[1,2] = S2[2,1] = stress_vec[3]
S2[3:4,3:4] = S2[1:2,1:2]
Kt += w*BL'*D*BL # material stiffness
Km += w*BL'*D*BL # material stiffness
if props.finite_strain # add geometric stiffness
Kt += w*BNL'*S2*BNL # geometric stiffness
Kg += w*BNL'*S2*BNL # geometric stiffness
end
if get_formulation_type(problem) == :incremental
@@ -150,7 +143,7 @@ function assemble{El<:Union{Tri3,Tri6,Quad4}}(problem::Problem{Elasticity}, elem
end
return Kt, f
return Km, Kg, f
end
function assemble{El<:Union{Seg2,Seg3}}(problem::Problem{Elasticity}, element::Element{El}, time::Real, ::Type{Val{:plane}})
@@ -158,7 +151,8 @@ function assemble{El<:Union{Seg2,Seg3}}(problem::Problem{Elasticity}, element::E
props = problem.properties
dim = get_unknown_field_dimension(problem)
nnodes = size(element, 2)
Kt = zeros(dim*nnodes, dim*nnodes)
Km = zeros(dim*nnodes, dim*nnodes)
Kg = zeros(dim*nnodes, dim*nnodes)
f = zeros(dim*nnodes)
for ip in get_integration_points(element)
@@ -189,7 +183,7 @@ function assemble{El<:Union{Seg2,Seg3}}(problem::Problem{Elasticity}, element::E
end
return Kt, f
return Km, Kg, f
end
""" Elasticity equations, 3d, linear. """
@@ -200,7 +194,8 @@ function assemble{El<:Union{Tet4, Tet10, Hex8}}(problem::Problem{Elasticity}, el
nnodes = length(element)
ndofs = dim*nnodes
BL = zeros(6, ndofs)
Kt = zeros(ndofs, ndofs)
Km = zeros(ndofs, ndofs)
Kg = zeros(ndofs, ndofs)
f = zeros(ndofs)
for ip in get_integration_points(element)
@@ -233,7 +228,7 @@ function assemble{El<:Union{Tet4, Tet10, Hex8}}(problem::Problem{Elasticity}, el
0.0 0.0 0.0 0.0 0.5-nu 0.0
0.0 0.0 0.0 0.0 0.0 0.5-nu]
Kt += w*BL'*D*BL
Km += w*BL'*D*BL
if haskey(element, "displacement load")
T = element("displacement load", ip, time)
@@ -255,7 +250,7 @@ function assemble{El<:Union{Tet4, Tet10, Hex8}}(problem::Problem{Elasticity}, el
end
end
return Kt, f
return Km, Kg, f
end
""" Material and geometric stiffness for linear buckling analysis. """
@@ -269,6 +264,7 @@ function assemble{El<:Union{Tet4, Tet10, Hex8}}(problem::Problem{Elasticity}, el
BNL = zeros(9, ndofs)
Km = zeros(ndofs, ndofs)
Kg = zeros(ndofs, ndofs)
f = zeros(ndofs)
for ip in get_integration_points(element)
detJ = element(ip, time, Val{:detJ})
@@ -332,7 +328,7 @@ function assemble{El<:Union{Tet4, Tet10, Hex8}}(problem::Problem{Elasticity}, el
end
return Km, Kg
return Km, Kg, f
end
""" Elasticity equations, 3d nonlinear. """
@@ -344,7 +340,8 @@ function assemble{El<:Union{Tet4, Tet10, Hex8}}(problem::Problem{Elasticity}, el
ndofs = dim*nnodes
BL = zeros(6, ndofs)
BNL = zeros(9, ndofs)
Kt = zeros(ndofs, ndofs)
Km = zeros(ndofs, ndofs)
Kg = zeros(ndofs, ndofs)
f = zeros(ndofs)
for ip in get_integration_points(element)
@@ -410,7 +407,7 @@ function assemble{El<:Union{Tet4, Tet10, Hex8}}(problem::Problem{Elasticity}, el
update!(ip, "strain", time => strain_vec)
update!(ip, "stress", time => stress_vec)
Kt += w*BL'*D*BL
Km += w*BL'*D*BL
if get_formulation_type(problem) == :incremental
f -= w*BL'*stress_vec
@@ -442,7 +439,7 @@ function assemble{El<:Union{Tet4, Tet10, Hex8}}(problem::Problem{Elasticity}, el
S3[4:6,4:6] = S3[7:9,7:9] = S3[1:3,1:3]
if props.finite_strain
Kt += w*BNL'*S3*BNL
Kg += w*BNL'*S3*BNL
end
# geometric stiffness end
@@ -464,7 +461,7 @@ function assemble{El<:Union{Tet4, Tet10, Hex8}}(problem::Problem{Elasticity}, el
end
return Kt, f
return Km, Kg, f
end
""" Elasticity equations, surface traction for continuum formulation. """
@@ -473,7 +470,8 @@ function assemble{El<:Union{Tri3, Tri6, Quad4}}(problem::Problem{Elasticity}, el
props = problem.properties
dim = get_unknown_field_dimension(problem)
nnodes = size(element, 2)
Kt = zeros(dim*nnodes, dim*nnodes)
Km = zeros(dim*nnodes, dim*nnodes)
Kg = zeros(dim*nnodes, dim*nnodes)
f = zeros(dim*nnodes)
for ip in get_integration_points(element)
@@ -498,7 +496,7 @@ function assemble{El<:Union{Tri3, Tri6, Quad4}}(problem::Problem{Elasticity}, el
f += w*p*vec(n*N)
end
end
return Kt, f
return Km, Kg, f
end
function assemble{El<:Union{Tri3, Tri6, Quad4}}(problem::Problem{Elasticity}, element::Element{El}, time::Real, ::Type{Val{:continuum_linear}})
@@ -604,10 +602,11 @@ function assemble(problem::Problem{Elasticity}, element::Element, time::Real, ::
end
field = element("displacement", time)
Kt, allresults = ForwardDiff.jacobian(get_residual_vector, vec(field),
Km, allresults = ForwardDiff.jacobian(get_residual_vector, vec(field),
AllResults, cache=autodiffcache)
Kg = zeros(Km)
f = -ForwardDiff.value(allresults)
return Kt, f
return Km, Kg, f
end