mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-06 04:21:33 +00:00
new commit
This commit is contained in:
ovainola
+6
-6
@@ -20,15 +20,15 @@ The JuliaFEM project develops open-source software for reliable, scalable, distr
|
||||
.. image:: https://coveralls.io/repos/JuliaFEM/JuliaFEM.jl/badge.svg?branch=master
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:target: https://coveralls.io/r/JuliaFEM/JuliaFEM.jl?branch=master
|
||||
|
||||
.. image:: http://juliafem.kapsi.fi/_static/notebooks-status.svg?ts=1
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:target: http://juliafem.kapsi.fi/tutorials/index.html
|
||||
.. image:: http://juliafem.org/_static/notebooks-status.svg?ts=1
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||||
:target: http://juliafem.org/tutorials/index.html
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|
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.. image:: http://juliafem.kapsi.fi/_static/doctests-status.svg?ts=1
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.. image:: http://juliafem.org/_static/doctests-status.svg?ts=1
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||||
|
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.. image:: http://juliafem.kapsi.fi/_static/unittests-status.svg?ts=1
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||||
.. image:: http://juliafem.org/_static/unittests-status.svg?ts=1
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|
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.. image:: http://juliafem.kapsi.fi/_static/lint-status.svg?ts=1
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||||
:target: http://juliafem.kapsi.fi/quality/index.html#lint-report
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||||
.. image:: http://juliafem.org/_static/lint-status.svg?ts=1
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||||
:target: http://juliafem.org/quality/index.html#lint-report
|
||||
|
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.. image:: https://img.shields.io/github/issues/JuliaFEM/JuliaFEM.jl.svg
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:target: https://github.com/JuliaFEM/JuliaFEM.jl/issues
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Vendored
+3
@@ -0,0 +1,3 @@
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module ReST
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end
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@@ -0,0 +1,12 @@
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JuliaFEM.abaqus_reader
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======================
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|
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Internal
|
||||
--------
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||||
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.. function:: add_handler(section, function_name)
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|
||||
source:
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||||
-------
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||||
[JuliaFEM/src/abaqus_reader.jl:18](https://github.com/JuliaFEM/JuliaFEM.jl/tree/08077a783a6459336cf07b02e323df0e9977c74f/src/abaqus_reader.jl#L18)
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|
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@@ -0,0 +1,93 @@
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JuliaFEM.elasticity_solver
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==========================
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Internal
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||||
--------
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.. function:: assemble!(fe, eldofs_, I, V)
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Assemble global RHS to I,V ready for sparse format
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:param fe : local vector
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:param eldofs_ : Array
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:param I,V : Arrays for sparse matrix
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:notes: eldofs can also be node ids for convenience. In that case dimension
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is calculated and eldofs are "extended" to problem dimension.
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||||
source:
|
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-------
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[JuliaFEM/src/elasticity_solver.jl:171](https://github.com/JuliaFEM/JuliaFEM.jl/tree/08077a783a6459336cf07b02e323df0e9977c74f/src/elasticity_solver.jl#L171)
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|
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.. function:: assemble!(ke, eldofs_, I, J, V)
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Assemble global stiffness matrix to I,J,V ready for sparse format
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:param ke : local matrix
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:param eldofs_ : Array
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:param I,J,V : Arrays for sparse matrix
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:notes: eldofs can also be node ids for convenience. In that case dimension
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is calculated and eldofs are "extended" to problem dimension.
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source:
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-------
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[JuliaFEM/src/elasticity_solver.jl:130](https://github.com/JuliaFEM/JuliaFEM.jl/tree/08077a783a6459336cf07b02e323df0e9977c74f/src/elasticity_solver.jl#L130)
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.. function:: calc_local_matrices!(X, u, R, Kt, N, dNdchi, lambda_, mu_, ipoints, iweights)
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|
||||
source:
|
||||
-------
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||||
[JuliaFEM/src/elasticity_solver.jl:68](https://github.com/JuliaFEM/JuliaFEM.jl/tree/08077a783a6459336cf07b02e323df0e9977c74f/src/elasticity_solver.jl#L68)
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|
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.. function:: eliminate_boundary_conditions(dirichletbc, I, J, V)
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Eliminate Dirichlet boundary conditions from matrix
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|
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:param dirichletbc : array [dim x nnodes]
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:param I, J, V : sparse matrix arrays
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:returns: I, J, V : boundary conditions removed
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:notes: pros:
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- matrix assembly remains positive definite
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cons:
|
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- maybe inefficient because of extra sparse matrix operations. (It's hard to remove stuff from sparse matrix.)
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- if u != 0 in dirichlet boundary requires extra care
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:raises: Exception, if displacement boundary conditions given, i.e.
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DX=2 for some node, for example.
|
||||
source:
|
||||
-------
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||||
[JuliaFEM/src/elasticity_solver.jl:218](https://github.com/JuliaFEM/JuliaFEM.jl/tree/08077a783a6459336cf07b02e323df0e9977c74f/src/elasticity_solver.jl#L218)
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|
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.. function:: eliminate_boundary_conditions(dirichletbc, I, V)
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||||
|
||||
Eliminate Dirichlet boundary conditions from vector
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||||
|
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:param dirichletbc : array [dim x nnodes]
|
||||
:param I, V : sparse vector arrays
|
||||
:returns: I, V : boundary conditions removed
|
||||
:notes: pros:
|
||||
- matrix assembly remains positive definite
|
||||
cons:
|
||||
- maybe inefficient because of extra sparse matrix operations. (It's hard to remove stuff from sparse matrix.)
|
||||
- if u != 0 in dirichlet boundary requires extra care
|
||||
:raises: Exception, if displacement boundary conditions given, i.e.
|
||||
DX=2 for some node, for example.
|
||||
source:
|
||||
-------
|
||||
[JuliaFEM/src/elasticity_solver.jl:257](https://github.com/JuliaFEM/JuliaFEM.jl/tree/08077a783a6459336cf07b02e323df0e9977c74f/src/elasticity_solver.jl#L257)
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|
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.. function:: interpolate{T<:Real}(field::Array{T<:Real, 1}, basis::Function, ip)
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||||
|
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Interpolate field variable using basis functions f for point ip.
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||||
This function tries to be as general as possible and allows interpolating
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lot of different fields.
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|
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:param field : Array{Number, dim}
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:param basis : Function
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||||
:param ip : Array{Number, 1}
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||||
source:
|
||||
-------
|
||||
[JuliaFEM/src/elasticity_solver.jl:30](https://github.com/JuliaFEM/JuliaFEM.jl/tree/08077a783a6459336cf07b02e323df0e9977c74f/src/elasticity_solver.jl#L30)
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|
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.. function:: solve_elasticity_increment!(X, u, du, elmap, nodalloads, dirichletbc, lambda, mu, N, dNdchi, ipoints, iweights)
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||||
|
||||
source:
|
||||
-------
|
||||
[JuliaFEM/src/elasticity_solver.jl:278](https://github.com/JuliaFEM/JuliaFEM.jl/tree/08077a783a6459336cf07b02e323df0e9977c74f/src/elasticity_solver.jl#L278)
|
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|
||||
@@ -0,0 +1,16 @@
|
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JuliaFEM.interfaces
|
||||
===================
|
||||
|
||||
Exported
|
||||
--------
|
||||
|
||||
.. function:: solve_elasticity_interface!()
|
||||
|
||||
This is generic interface that reads data from data model, solves elasticity
|
||||
problem and updates model.
|
||||
|
||||
:param model : to be defined
|
||||
source:
|
||||
-------
|
||||
[JuliaFEM/src/interfaces.jl:22](https://github.com/JuliaFEM/JuliaFEM.jl/tree/08077a783a6459336cf07b02e323df0e9977c74f/src/interfaces.jl#L22)
|
||||
|
||||
@@ -0,0 +1,3 @@
|
||||
JuliaFEM
|
||||
========
|
||||
|
||||
@@ -0,0 +1,3 @@
|
||||
JuliaFEM.xdmf
|
||||
=============
|
||||
|
||||
+7
-27
@@ -41,6 +41,7 @@ const modules = append_list
|
||||
# run(`cp $main_folder/$file_ $this_folder`)
|
||||
|
||||
cd(dirname(@__FILE__)) do
|
||||
<<<<<<< HEAD
|
||||
# Run the doctests *before* we start to generate *any* documentation.
|
||||
# for m in modules
|
||||
# failures = failed(doctest(m))
|
||||
@@ -50,11 +51,14 @@ cd(dirname(@__FILE__)) do
|
||||
# exit(1) # Bail when doctests fail.
|
||||
# end
|
||||
# end
|
||||
=======
|
||||
>>>>>>> origin/master
|
||||
# Generate and save the contents of docstrings as markdown files.
|
||||
index = Index()
|
||||
for mod in modules
|
||||
Lexicon.update!(index, save(joinpath(api_directory, "$(mod).rst"), mod))
|
||||
end
|
||||
<<<<<<< HEAD
|
||||
#save(joinpath(api_directory, "index.rst"))
|
||||
|
||||
# Add a reminder not to edit the generated files.
|
||||
@@ -64,35 +68,11 @@ cd(dirname(@__FILE__)) do
|
||||
# all changes to the originating docstrings/files rather than these ones.
|
||||
# """)
|
||||
# end
|
||||
=======
|
||||
# save(joinpath(api_directory, "index.rst"), index; md_subheader = :category)
|
||||
>>>>>>> origin/master
|
||||
|
||||
# info("Adding all documentation changes in $(api_directory) to this commit.")
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||||
# success(`git add $(api_directory)`) || exit(1)
|
||||
|
||||
end
|
||||
|
||||
# point of this?
|
||||
#cd(dirname(dirname(@__FILE__))) do
|
||||
# yaml = """
|
||||
# # This is automatically generated by docs/build.jl. Edit that file if you
|
||||
# # wish to make any permenant changes.
|
||||
# site_name: JuliaFEM.jl
|
||||
# site_description: JuliaFEM.jl, open-source software for reliable, scalable, distributed Finite Element Method.
|
||||
# repo_name: GitHub
|
||||
# # docs_dir: 'docs'
|
||||
# # site_dir: 'site'
|
||||
# repo_url: https://github.com/JuliaFEM/JuliaFEM.jl
|
||||
# pages:
|
||||
# - Home: 'index.md'
|
||||
# #- API Docs:
|
||||
# - JuliaFEM: 'api/JuliaFEM.md'
|
||||
# - JuliaFEM.elasticity_solver: 'api/JuliaFEM.elasticity_solver.md'
|
||||
# theme: readthedocs
|
||||
# """
|
||||
#
|
||||
# # TODO: add the solutions if I figure out how to get them to render properly
|
||||
#
|
||||
# open("mkdocs.yml", "w") do f
|
||||
# write(f, yaml)
|
||||
# end
|
||||
#end
|
||||
|
||||
|
||||
@@ -0,0 +1,6 @@
|
||||
src
|
||||
===
|
||||
|
||||
.. toctree::
|
||||
:maxdepth: 4
|
||||
|
||||
@@ -27,7 +27,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"execution_count": 1,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -38,7 +38,7 @@
|
||||
"Logger(root,DEBUG,Pipe(open, 0 bytes waiting),root)"
|
||||
]
|
||||
},
|
||||
"execution_count": 8,
|
||||
"execution_count": 1,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -63,7 +63,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -74,7 +74,7 @@
|
||||
"calc_local_matrices! (generic function with 1 method)"
|
||||
]
|
||||
},
|
||||
"execution_count": 9,
|
||||
"execution_count": 2,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -159,12 +159,12 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"*Design principle 6*: we test our code. We use FactCheck in testing."
|
||||
"*Design principle 6*: we test our code. We use FactCheck for testing."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"execution_count": 3,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
@@ -175,7 +175,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -191,16 +191,23 @@
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"28-Jul 22:15:35:DEBUG:root:Converged in 6 iterations.\n",
|
||||
"28-Jul 22:15:35:DEBUG:root:solution vector: \n",
|
||||
"29-Jul 23:12:24:DEBUG:root:Converged in 6 iterations.\n",
|
||||
"29-Jul 23:12:24:DEBUG:root:solution vector: \n",
|
||||
" [0.0 -0.39914506095474317 -0.07228582695592449 0.0\n",
|
||||
" 0.0 -2.1779892317073504 -2.222244754401764 0.0]\n",
|
||||
"28-Jul 22:15:35:DEBUG:root:norm of u: 3.1292483947150043\n",
|
||||
"28-Jul 22:15:35:DEBUG:root:Converged in 6 iterations.\n",
|
||||
"28-Jul 22:15:35:DEBUG:root:solution vector: \n",
|
||||
"29-Jul 23:12:24:DEBUG:root:norm of u: 3.1292483947150043\n",
|
||||
"29-Jul 23:12:25:DEBUG:root:Converged in 6 iterations.\n",
|
||||
"29-Jul 23:12:25:DEBUG:root:solution vector: \n",
|
||||
" [0.0 0.7433248532717793 1.0485210147234858 0.0\n",
|
||||
" 0.0 -2.085766534304891 -1.9606633242166027 0.0]\n",
|
||||
"28-Jul 22:15:35:DEBUG:root:norm of u: 3.129248394715006\n"
|
||||
"29-Jul 23:12:25:DEBUG:root:norm of u: 3.129248394715006\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"2 facts verified.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -209,7 +216,7 @@
|
||||
"delayed_handler (generic function with 4 methods)"
|
||||
]
|
||||
},
|
||||
"execution_count": 11,
|
||||
"execution_count": 4,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -289,56 +296,63 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"One element solutions are not particularly interesting so next step is to create function that assembles global matrix from local matrices."
|
||||
"One element solutions are not particularly interesting so next step is to create function that assembles global matrix from local matrices. Some data types:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"execution_count": 5,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"2 facts verified.\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"type Node\n",
|
||||
" id :: Int\n",
|
||||
" coordinates :: Array{Float64, 1}\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"type Element\n",
|
||||
" id :: Int\n",
|
||||
" nodes :: Array{Node, 1}\n",
|
||||
" attributes :: Dict{ASCIIString, Any}\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"type FunctionSpace\n",
|
||||
" family :: String\n",
|
||||
" order :: Int\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"type IntegrationScheme\n",
|
||||
" points :: Array{Float64, 2}\n",
|
||||
" weights :: Array{Float64, 1}\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"type IJVMatrix\n",
|
||||
" I :: Array{Int64, 1}\n",
|
||||
" J :: Array{Int64, 1}\n",
|
||||
" V :: Array{Float64, 1}\n",
|
||||
" elements :: Array{Int64, 1}\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 105,
|
||||
"execution_count": 6,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"type Element\n",
|
||||
" id :: Int\n",
|
||||
" nodes :: Array{Int64, 1}\n",
|
||||
" coordinates :: Array{Float64, 2}\n",
|
||||
" attributes :: Dict{ASCIIString, Any}\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"type Assembly\n",
|
||||
" # LHS\n",
|
||||
" I :: Array{Int64, 1}\n",
|
||||
" J :: Array{Int64, 1}\n",
|
||||
" A :: Array{Float64, 1}\n",
|
||||
" # RHS\n",
|
||||
" i :: Array{Int64, 1}\n",
|
||||
" b :: Array{Float64, 1}\n",
|
||||
" # global dofs for each element\n",
|
||||
" gdofs :: Dict{Int64, Array{Int64, 1}}\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 19,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -346,17 +360,29 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Element2(1,[Node2(1,[1.0,2.0,3.0])],Dict(\"Young's modulus\"=>2.1e11,\"Poisson's ration\"=>0.3),\"Lagrange(1,2)\",\"FPG4\")"
|
||||
"get_shape_functions (generic function with 1 method)"
|
||||
]
|
||||
},
|
||||
"execution_count": 105,
|
||||
"execution_count": 19,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"function get_shape_functions(fs::FunctionSpace)\n",
|
||||
" if (fs.family == \"Lagrange\") & (fs.order == 1)\n",
|
||||
"\"\"\"\n",
|
||||
"Return shape functions and their derivatives for a element.\n",
|
||||
"\n",
|
||||
"Parameters\n",
|
||||
"----------\n",
|
||||
"element::Element\n",
|
||||
"\n",
|
||||
"Returns\n",
|
||||
"-------\n",
|
||||
"tuple (basis, dbasis)\n",
|
||||
"\"\"\"\n",
|
||||
"function get_shape_functions(el::Element)\n",
|
||||
" ndim, nnodes = size(el.coordinates)\n",
|
||||
" if (nnodes == 4) & (ndim == 2)\n",
|
||||
" basis(xi) = [\n",
|
||||
" (1-xi[1])*(1-xi[2])/4\n",
|
||||
" (1+xi[1])*(1-xi[2])/4\n",
|
||||
@@ -369,36 +395,12 @@
|
||||
" return basis, dbasis\n",
|
||||
" end\n",
|
||||
" throw(\"Unknown function space\")\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"function get_integration_scheme(is::IntegrationScheme)\n",
|
||||
" if is.\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"function assemble!(IJV::IJVMatrix, element::Element, gdofs, fs::FunctionSpace, is::IntegrationScheme)\n",
|
||||
" nnodes = length(element.nodes)\n",
|
||||
" ndim = length(elements.nodes[1].coordinates)\n",
|
||||
"\n",
|
||||
" # Material properties\n",
|
||||
" E = element.attributes[\"Young\"]\n",
|
||||
" nu = element.attributes[\"Poisson\"]\n",
|
||||
" mu = E/(2*(1+nu))\n",
|
||||
" la = E*nu/((1+nu)*(1-2*nu))\n",
|
||||
" la = 2*la*mu/(la + 2*mu)\n",
|
||||
"\n",
|
||||
" R = zeros(ndim, nnodes)\n",
|
||||
" K = zeros(ndim*nnodes, ndim*nnodes)\n",
|
||||
"\n",
|
||||
" basis, dbasis = get_shape_functions(fs)\n",
|
||||
"\n",
|
||||
" calc_local_matrices!(X, u, R, K, basis, dbasis, la, mu, ipoints, iweights)\n",
|
||||
"\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"execution_count": 20,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -406,25 +408,30 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"IntegrationScheme(4x2 Array{Float64,2}:\n",
|
||||
" -0.57735 -0.57735\n",
|
||||
" 0.57735 -0.57735\n",
|
||||
" 0.57735 0.57735\n",
|
||||
" -0.57735 0.57735,[1.0,1.0,1.0,1.0])"
|
||||
"get_integration_scheme (generic function with 2 methods)"
|
||||
]
|
||||
},
|
||||
"execution_count": 13,
|
||||
"execution_count": 20,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"is = IntegrationScheme(1/sqrt(3)*[-1 -1; 1 -1; 1 1; -1 1], [1, 1, 1, 1])\n"
|
||||
"\"\"\"\n",
|
||||
"\"\"\"\n",
|
||||
"function get_integration_scheme(el::Element, order=2)\n",
|
||||
" ndim, nnodes = size(el.coordinates)\n",
|
||||
" if (nnodes == 4) & (order == 2)\n",
|
||||
" ipoints = 1/sqrt(3)*[-1 -1; 1 -1; 1 1; -1 1]\n",
|
||||
" iweights = [1, 1, 1, 1]\n",
|
||||
" return ipoints, iweights\n",
|
||||
" end\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 111,
|
||||
"execution_count": 48,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -432,45 +439,183 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"Node2(2,[3.0,2.0,3.0])"
|
||||
"assemble_element! (generic function with 2 methods)"
|
||||
]
|
||||
},
|
||||
"execution_count": 111,
|
||||
"execution_count": 48,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"e2 = Element2(2, [n1], Dict(\"Young's modulus\" => 90.0e9, \"Poisson's ration\" => 0.3), \"Lagrange(1,2)\", \"FPG4\")\n",
|
||||
"e2.nodes[1]"
|
||||
"function assemble_element!(ass::Assembly, el::Element, io=2)\n",
|
||||
"\n",
|
||||
" # Material properties\n",
|
||||
" E = el.attributes[\"Young\"]\n",
|
||||
" nu = el.attributes[\"Poisson\"]\n",
|
||||
" mu = E/(2*(1+nu))\n",
|
||||
" la = E*nu/((1+nu)*(1-2*nu))\n",
|
||||
" la = 2*la*mu/(la + 2*mu)\n",
|
||||
"\n",
|
||||
" dofs = prod(size(el.coordinates))\n",
|
||||
" X = el.coordinates\n",
|
||||
" u = el.attributes[\"displacement\"]\n",
|
||||
" R = el.attributes[\"displacement nodal force\"]\n",
|
||||
" K = el.attributes[\"displacement tangent stiffness\"]\n",
|
||||
"\n",
|
||||
" gdofs = ass.gdofs[el.id]\n",
|
||||
" basis, dbasis = get_shape_functions(el)\n",
|
||||
" ipoints, iweights = get_integration_scheme(el, io)\n",
|
||||
" calc_local_matrices!(X, u, R, K, basis, dbasis, la, mu, ipoints, iweights)\n",
|
||||
"\n",
|
||||
" for i=1:dofs\n",
|
||||
" for j=1:dofs\n",
|
||||
" push!(ass.I, gdofs[i])\n",
|
||||
" push!(ass.J, gdofs[j])\n",
|
||||
" push!(ass.A, K[i,j])\n",
|
||||
" end\n",
|
||||
" push!(ass.i, gdofs[i])\n",
|
||||
" push!(ass.b, R[i])\n",
|
||||
" end\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Time to test again. From last test we know that correct solution is\n",
|
||||
"\n",
|
||||
" [0.0 -0.39914506095474317 -0.07228582695592449 0.0\n",
|
||||
" 0.0 -2.1779892317073504 -2.222244754401764 0.0]\n",
|
||||
"\n",
|
||||
"This time we assemble global stiffness matrix in different order, 2 3 4 1"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 49,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"one element assembly\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"30-Jul 00:08:18:DEBUG:root:Creating nodes\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Creating elements\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 1\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 3.0814821107320176\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 2\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 0.32007464366194766\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 3\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 0.040279810888447135\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 4\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 0.000925649536063315\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 5\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 1.5582555024825817e-7\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Starting iteration 6\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Assembling\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solving\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Solution norm = 1.0317166868587156e-14\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Converged in 6 iterations.\n",
|
||||
"30-Jul 00:08:18:DEBUG:root:Displacement of element = \n",
|
||||
"[-0.39914506095474334 -0.07228582695592464 0.0 0.0\n",
|
||||
" -2.1779892317073504 -2.222244754401764 0.0 0.0]\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"delayed_handler (generic function with 4 methods)"
|
||||
]
|
||||
},
|
||||
"execution_count": 49,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"1 fact verified.\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"n1 = new_node()\n",
|
||||
"set_node_id(n1, 1)\n",
|
||||
"set_node_coords(n1, [0.0, 0.0])\n",
|
||||
"facts(\"one element assembly\") do\n",
|
||||
" Logging.debug(\"Creating nodes\")\n",
|
||||
" n1 = Node(1, Int64[])\n",
|
||||
" n2 = Node(2, Int64[])\n",
|
||||
" n3 = Node(3, Int64[])\n",
|
||||
" n4 = Node(4, Int64[])\n",
|
||||
" nodes = [n1.id, n2.id, n3.id, n4.id]\n",
|
||||
" coordinates = [10.0 0.0; 10.0 1.0; 0.0 1.0; 0.0 0.0]'\n",
|
||||
" attributes = Dict(\n",
|
||||
" \"Young\" => 90, \"Poisson\" => 0.25,\n",
|
||||
" \"displacement\" => zeros(2, 4),\n",
|
||||
" \"displacement nodal force\" => zeros(2, 4),\n",
|
||||
" \"displacement tangent stiffness\" => zeros(8, 8))\n",
|
||||
" Logging.debug(\"Creating elements\")\n",
|
||||
" el = Element(1, nodes, coordinates, attributes)\n",
|
||||
" for i=1:10\n",
|
||||
" Logging.debug(\"Starting iteration $i\")\n",
|
||||
" ass = Assembly(Int64[], Int64[], Float64[], Int64[], Float64[], Dict{Int64,Array{Int64,1}}())\n",
|
||||
" ass.gdofs[el.id] = [1, 2, 3, 4, 5, 6, 7, 8]\n",
|
||||
" Logging.debug(\"Assembling\")\n",
|
||||
" assemble_element!(ass, el)\n",
|
||||
" Logging.debug(\"Solving\")\n",
|
||||
" du = zeros(2, 4) # must be determined from ass\n",
|
||||
" F = [0 0; 0 -2; 0 0; 0 0]'\n",
|
||||
" free_dofs = [1, 2, 3, 4]\n",
|
||||
"\n",
|
||||
"n2 = new_node()\n",
|
||||
"set_node_id(n2, 2)\n",
|
||||
"set_node_coords(n2, [10.0, 0.0])\n",
|
||||
" # solution\n",
|
||||
" K = sparse(ass.I, ass.J, ass.A)\n",
|
||||
" R = full(sparsevec(ass.i, ass.b))\n",
|
||||
" R = reshape(R, (2, round(Int, length(R)/2)))\n",
|
||||
" du[free_dofs] = K[free_dofs, free_dofs] \\ -(R - F)[free_dofs]\n",
|
||||
"\n",
|
||||
"n3 = new_node()\n",
|
||||
"set_node_id(n3, 3)\n",
|
||||
"set_node_coords(n3, [10.0, 1.0])\n",
|
||||
" Logging.debug(\"Solution norm = $(norm(du))\")\n",
|
||||
" #Logging.debug(\"Solution increment = \\n$du\")\n",
|
||||
"\n",
|
||||
"n4 = new_node()\n",
|
||||
"set_node_id(n4, 4)\n",
|
||||
"set_node_coords(n4, [0.0, 1.0])\n",
|
||||
"\n",
|
||||
"nodes = [n1, n2, n3, n4]\n",
|
||||
"add_nodes(m, \"NALL\", nodes)"
|
||||
" # update solution back to elements\n",
|
||||
" eldu = du[ass.gdofs[el.id]]\n",
|
||||
" eldu = reshape(eldu, (2, round(Int, length(eldu)/2)))\n",
|
||||
" el.attributes[\"displacement\"] += eldu\n",
|
||||
" if norm(du) < 1.0e-9\n",
|
||||
" Logging.debug(\"Converged in $i iterations.\")\n",
|
||||
" break\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" disp = el.attributes[\"displacement\"]\n",
|
||||
" Logging.debug(\"Displacement of element = \\n$disp\")\n",
|
||||
" @fact norm(disp) => roughly(3.1292483947150043)\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Seems to be working. But we still need to handle boundary conditions more \"cleverly\" and generalize assembly to several elements (which is not problem)."
|
||||
]
|
||||
},
|
||||
{
|
||||
|
||||
Reference in New Issue
Block a user