# linear_elasticity/linear_elastic_interactive.py¶

Description

Linear elasticity example using the imperative API.

`source code`

```#!/usr/bin/env python
"""
Linear elasticity example using the imperative API.
"""
from argparse import ArgumentParser
import numpy as nm

import sys
sys.path.append('.')

from sfepy.base.base import IndexedStruct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.mechanics.matcoefs import stiffness_from_lame

def shift_u_fun(ts, coors, bc=None, problem=None, shift=0.0):
"""
Define a displacement depending on the y coordinate.
"""
val = shift * coors[:,1]**2

return val

def main():
from sfepy import data_dir

parser = ArgumentParser()
options = parser.parse_args()

mesh = Mesh.from_file(data_dir + '/meshes/2d/rectangle_tri.mesh')
domain = FEDomain('domain', mesh)

min_x, max_x = domain.get_mesh_bounding_box()[:,0]
eps = 1e-8 * (max_x - min_x)
omega = domain.create_region('Omega', 'all')
gamma1 = domain.create_region('Gamma1',
'vertices in x < %.10f' % (min_x + eps),
'facet')
gamma2 = domain.create_region('Gamma2',
'vertices in x > %.10f' % (max_x - eps),
'facet')

field = Field.from_args('fu', nm.float64, 'vector', omega,
approx_order=2)

u = FieldVariable('u', 'unknown', field)
v = FieldVariable('v', 'test', field, primary_var_name='u')

m = Material('m', D=stiffness_from_lame(dim=2, lam=1.0, mu=1.0))
f = Material('f', val=[[0.02], [0.01]])

integral = Integral('i', order=3)

t1 = Term.new('dw_lin_elastic(m.D, v, u)',
integral, omega, m=m, v=v, u=u)
t2 = Term.new('dw_volume_lvf(f.val, v)', integral, omega, f=f, v=v)
eq = Equation('balance', t1 + t2)
eqs = Equations([eq])

fix_u = EssentialBC('fix_u', gamma1, {'u.all' : 0.0})

bc_fun = Function('shift_u_fun', shift_u_fun,
extra_args={'shift' : 0.01})
shift_u = EssentialBC('shift_u', gamma2, {'u.0' : bc_fun})

ls = ScipyDirect({})

nls_status = IndexedStruct()
nls = Newton({}, lin_solver=ls, status=nls_status)

pb = Problem('elasticity', equations=eqs)
pb.save_regions_as_groups('regions')

pb.set_bcs(ebcs=Conditions([fix_u, shift_u]))

pb.set_solver(nls)

status = IndexedStruct()
variables = pb.solve(status=status)

print('Nonlinear solver status:\n', nls_status)
print('Stationary solver status:\n', status)

pb.save_state('linear_elasticity.vtk', variables)

if __name__ == '__main__':
main()
```