Elastopy

• Introduction

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This package solves the linear elasticity assuming the plane stress constitutive model. The solution is obtained via the finite element method.

The program input is a mesh (=.geo= and =.msh= files), material properties and boundary conditions. The boundary conditions are create using python functions. The results obtained from the function =statics.solver()= are the nodal displacements and nodal stresses.

• How to download

#+BEGIN_SRC shell pip install elastopy #+END_SRC

• How to use it

In order to use you need the =.geo= and =.msh= from gmsh. See the test folder for an example.

• Example of usage

First we import the necessary classes and functions

#+BEGIN_SRC ipython :session :exports both :results output drawer import numpy as np from elastopy import gmsh, Build, Material, statics, plotter #+END_SRC

#+RESULTS: :RESULTS: :END:

Then we create the model by parsing the mesh file and instanciante the =Build= class.

#+BEGIN_SRC ipython :session :exports both :results output drawer mesh_file = 'test/patch' mesh = gmsh.Parse(mesh_file) model = Build(mesh)

plotter.model(model, ele=True, nodes_label=True, ele_label=True, edges_label=True) plotter.show() #+END_SRC

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Next we define material parameters using the =Material= class which takes as argument keyword dictionaries where the key is the surface label,

#+BEGIN_SRC ipython :session :exports both :results output drawer surf = list(model.surf.keys()) material = Material(E={surf[0]: 1000}, nu={surf[0]: 0.3}) #+END_SRC

#+RESULTS: :RESULTS: :END:

Then we define body forces and boundary conditions as functions,

#+BEGIN_SRC ipython :session :exports both :results output drawer def b_force(x1, x2, t=1): return np.array([0.0, 0.0])

def trac_bc(x1, x2, t=1): return { ('line', 3): [-1, 0], ('line', 1): [1, 0]}

def displ_bc(x1, x2): return {('node', 0): [0, 0], ('node', 1): ['free', 0]} #+END_SRC

#+RESULTS: :RESULTS: :END:

finally we call the statics solver

#+BEGIN_SRC ipython :session :exports both :results output drawer U, SIG = statics.solver(model, material, b_force, trac_bc, displ_bc) #+END_SRC

#+RESULTS: :RESULTS: Starting statics solver at 0.000h Solution completed! :END:

We then proceed to process the results

#+BEGIN_SRC ipython :session :exports both :results output drawer plotter.model_deformed(model, U, magf=100, ele=True) print(np.round(SIG[:, 0], 2)) # s11 on all nodes plotter.show() #+END_SRC

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