GetFEM  5.4.2
plate.cc
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1 /*===========================================================================
2 
3  Copyright (C) 2002-2020 Yves Renard, Michel Salaün.
4 
5  This file is a part of GetFEM
6 
7  GetFEM is free software; you can redistribute it and/or modify it
8  under the terms of the GNU Lesser General Public License as published
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10  (at your option) any later version along with the GCC Runtime Library
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19 
20 ===========================================================================*/
21 
22 /**
23  @file plate.cc
24  @brief Linear Elastostatic plate problem.
25 
26  This program is used to check that getfem++ is working. This is
27  also a good example of use of GetFEM.
28 */
29 
30 #include "getfem/getfem_assembling.h" /* import assembly methods (and norms comp.) */
31 #include "getfem/getfem_linearized_plates.h"
32 #include "getfem/getfem_export.h" /* export functions (save solution in a file) */
33 #include "getfem/getfem_regular_meshes.h"
34 #include "getfem/getfem_model_solvers.h"
35 #include "gmm/gmm.h"
36 
37 using std::endl; using std::cout; using std::cerr;
38 using std::ends; using std::cin;
39 
40 /* some GetFEM types that we will be using */
41 using bgeot::base_small_vector; /* special class for small (dim<16) vectors */
42 using bgeot::base_node; /* geometrical nodes(derived from base_small_vector)*/
43 using bgeot::scalar_type; /* = double */
44 using bgeot::size_type; /* = unsigned long */
45 using bgeot::dim_type;
46 using bgeot::base_matrix; /* small dense matrix. */
47 
48 /* definition of some matrix/vector types. These ones are built
49  * using the predefined types in Gmm++
50  */
51 typedef getfem::modeling_standard_sparse_vector sparse_vector;
52 typedef getfem::modeling_standard_sparse_matrix sparse_matrix;
53 typedef getfem::modeling_standard_plain_vector plain_vector;
54 
55 /*
56  structure for the elastostatic problem
57 */
58 struct plate_problem {
59 
60  enum { SIMPLY_FIXED_BOUNDARY_NUM = 0 };
61  getfem::mesh mesh; /* the mesh */
62  getfem::mesh_im mim, mim_subint;
63  getfem::mesh_fem mf_ut;
64  getfem::mesh_fem mf_u3;
65  getfem::mesh_fem mf_theta;
66  getfem::mesh_fem mf_rhs; /* mesh_fem for the right hand side (f(x),..) */
67  getfem::mesh_fem mf_coef; /* mesh_fem used to represent pde coefficients */
68  scalar_type lambda, mu; /* Lamé coefficients. */
69  scalar_type E, nu; /* Lamé coefficients. */
70  scalar_type epsilon; /* thickness of the plate. */
71  scalar_type pressure;
72  scalar_type residual; /* max residual for the iterative solvers */
73  scalar_type LX , LY ; // default : LX = LY = 1
74  bool mitc;
75  int sol_ref; // sol_ref = 0 : simple support on the vertical edges
76  // sol_ref = 1 : homogeneous on the vertical edges
77  // sol_ref = 2 : homogeneous on the 4 vertical
78  // edges with solution u3 = sin²(x)*sin²(y)
79  scalar_type eta; // useful only if sol_ref == 2 :
80  // eta = 0 => Kirchhoff-Love
81  // eta = small => Mindlin
82  size_type N_Four ;
83  base_matrix theta1_Four, theta2_Four, u3_Four ;
84 
85  int study_flag; // if studyflag = 1, then the loadings applied are chosen
86  // in order to have a maximal vertical displacement equal to one.
87  // Nothing is done if study_flag has another value.
88 
89  std::string datafilename;
90  bgeot::md_param PARAM;
91 
92  base_small_vector theta_exact(base_node P);
93  scalar_type u3_exact(base_node P);
94 
95  bool solve(plain_vector &Ut, plain_vector &U3, plain_vector &THETA);
96  void init(void);
97  void compute_error(plain_vector &Ut, plain_vector &U3, plain_vector &THETA);
98  plate_problem(void) : mim(mesh), mim_subint(mesh), mf_ut(mesh), mf_u3(mesh),
99  mf_theta(mesh), mf_rhs(mesh), mf_coef(mesh) {}
100 };
101 
102 /* Read parameters from the .param file, build the mesh, set finite element
103  * and integration methods and selects the boundaries.
104  */
105 void plate_problem::init(void) {
106  std::string MESH_FILE = PARAM.string_value("MESH_FILE");
107  std::string MESH_TYPE = PARAM.string_value("MESH_TYPE","Mesh type ");
108  std::string FEM_TYPE_UT = PARAM.string_value("FEM_TYPE_UT","FEM name");
109  std::string FEM_TYPE_U3 = PARAM.string_value("FEM_TYPE_U3","FEM name");
110  std::string FEM_TYPE_THETA = PARAM.string_value("FEM_TYPE_THETA","FEM name");
111  std::string INTEGRATION = PARAM.string_value("INTEGRATION",
112  "Name of integration method");
113  std::string INTEGRATION_CT = PARAM.string_value("INTEGRATION_CT",
114  "Name of integration method");
115  cout << "MESH_TYPE=" << MESH_TYPE << "\n";
116  cout << "FEM_TYPE_UT=" << FEM_TYPE_UT << "\n";
117  cout << "INTEGRATION=" << INTEGRATION << "\n";
118  cout << "INTEGRATION_CT=" << INTEGRATION_CT << "\n";
119 
120  /* First step : build the mesh */
121  size_type N;
122  bgeot::pgeometric_trans pgt =
123  bgeot::geometric_trans_descriptor(MESH_TYPE);
124  if (!MESH_FILE.empty()) {
125  cout << "MESH_FILE=" << MESH_FILE << "\n";
126  mesh.read_from_file(MESH_FILE);
127  MESH_TYPE = bgeot::name_of_geometric_trans
128  (mesh.trans_of_convex(mesh.convex_index().first_true()));
129  cout << "MESH_TYPE=" << MESH_TYPE << "\n";
130  N = mesh.dim();
131  } else {
132  N = pgt->dim();
133  GMM_ASSERT1(N == 2, "For a plate problem, N should be 2");
134  std::vector<size_type> nsubdiv(N);
135  std::fill(nsubdiv.begin(),nsubdiv.end(),
136  PARAM.int_value("NX", "Number of space steps "));
137  getfem::regular_unit_mesh(mesh, nsubdiv, pgt,
138  PARAM.int_value("MESH_NOISED") != 0);
139  }
140 
141  datafilename = PARAM.string_value("ROOTFILENAME","Base name of data files.");
142  residual = PARAM.real_value("RESIDUAL"); if (residual == 0.) residual = 1e-10;
143  mitc = (PARAM.int_value("MITC", "Mitc version ?") != 0);
144 
145 
146  cout << "MITC = " ;
147  if (mitc) cout << "true \n" ; else cout << "false \n" ;
148  sol_ref = int(PARAM.int_value("SOL_REF") ) ;
149  study_flag = int(PARAM.int_value("STUDY_FLAG") ) ;
150  eta = (PARAM.real_value("ETA") );
151  N_Four = (PARAM.int_value("N_Four") ) ;
152 
153 
154  LX = PARAM.real_value("LX");
155  LY = PARAM.real_value("LY");
156  mu = PARAM.real_value("MU", "Lamé coefficient mu");
157  lambda = PARAM.real_value("LAMBDA", "Lamé coefficient lambda");
158  epsilon = PARAM.real_value("EPSILON", "thickness of the plate");
159  pressure = PARAM.real_value("PRESSURE",
160  "pressure on the top surface of the plate.");
161 
162 
163  cout << "SOL_REF = " ;
164  if (sol_ref==0) cout << "appui simple aux 2 bords verticaux\n" ;
165  if (sol_ref==1) cout << "encastrement aux 2 bords verticaux\n" ;
166  if (sol_ref==2) {
167  cout << "encastrement aux 4 bords verticaux, solution en sin(x)^2*sin(y)^2\n" ;
168  cout << "eta = " << eta <<"\n";
169  }
170  if (sol_ref==4) {
171  cout << "bord en appuis simple\n" ;
172  cout << "nombre de terme pour calcul sol exacte : " << N_Four << " \n" ;
173  // Calcul des coeeficients de Fourier de la solution exacte :
174  // Cas où le chargement est seulement vertical (pas de moment appliqué)
175  gmm::resize( theta1_Four, N_Four, N_Four) ;
176  gmm::resize( theta2_Four, N_Four, N_Four) ;
177  gmm::resize( u3_Four, N_Four, N_Four) ;
178  base_matrix Jmn(3, 3) ;
179  base_small_vector Bmn(3), Xmn(3) ;
180  scalar_type /*det_Jmn, */ A, B, e2, Pmn ;
181  E = 4.*mu*(mu+lambda) / (2. * mu + lambda);
182  nu = lambda / (2. * mu + lambda);
183  e2 = epsilon * epsilon / 4. ;
184  for(size_type i = 0 ; i < N_Four ; i++) {
185  for(size_type j = 0 ; j < N_Four ; j++) {
186  A = scalar_type(j + 1) * M_PI / LX ;
187  B = scalar_type(i + 1) * M_PI / LY ;
188  Jmn(0, 0) = 2. * A * A / (1. - nu) + B * B + 3. / e2 ;
189  Jmn(0, 1) = A * B * (1. +nu) / (1. - nu) ;
190  Jmn(0, 2) = A * 3. / e2 ;
191  Jmn(1, 0) = A * B * (1. +nu) / (1. - nu) ;
192  Jmn(1, 1) = 2. * B * B / (1. - nu) + A * A + 3. / e2 ;
193  Jmn(1, 2) = B * 3. / e2 ;
194  Jmn(2, 0) = - A ;
195  Jmn(2, 1) = - B ;
196  Jmn(2, 2) = A * A + B * B ;
197  gmm::scale(Jmn, - E*(epsilon/2.) / (1. + nu) ) ;
198 
199  // calcul du développement de Fourrier du chargement :
200  if ( ( (i + 1) % 2 == 1 ) && ( (j + 1) % 2 == 1) ) {
201  Pmn = 16. * pressure / ( scalar_type(i + 1) * scalar_type(j + 1) * M_PI * M_PI) ; }
202  else {
203  Pmn = 0. ; }
204  Bmn[0] = 0. ;
205  Bmn[1] = 0. ;
206  Bmn[2] = Pmn ;
207  gmm::lu_solve(Jmn, Xmn, Bmn) ;
208  theta1_Four(i, j) = Xmn[0] ;
209  theta1_Four(i, j) = Xmn[1] ;
210  u3_Four(i, j) = Xmn[2] ;
211  }
212  }
213  }
214 
215  mf_ut.set_qdim(dim_type(N));
216  mf_theta.set_qdim(dim_type(N));
217 
218  /* set the finite element on the mf_u */
219  getfem::pfem pf_ut = getfem::fem_descriptor(FEM_TYPE_UT);
220  getfem::pfem pf_u3 = getfem::fem_descriptor(FEM_TYPE_U3);
221  getfem::pfem pf_theta = getfem::fem_descriptor(FEM_TYPE_THETA);
222 
223  getfem::pintegration_method ppi =
224  getfem::int_method_descriptor(INTEGRATION);
225  getfem::pintegration_method ppi_ct =
226  getfem::int_method_descriptor(INTEGRATION_CT);
227 
228  mim.set_integration_method(mesh.convex_index(), ppi);
229  mim_subint.set_integration_method(mesh.convex_index(), ppi_ct);
230  mf_ut.set_finite_element(mesh.convex_index(), pf_ut);
231  mf_u3.set_finite_element(mesh.convex_index(), pf_u3);
232  mf_theta.set_finite_element(mesh.convex_index(), pf_theta);
233 
234  /* set the finite element on mf_rhs (same as mf_u is DATA_FEM_TYPE is
235  not used in the .param file */
236  std::string data_fem_name = PARAM.string_value("DATA_FEM_TYPE");
237  if (data_fem_name.size() == 0) {
238  GMM_ASSERT1(pf_ut->is_lagrange(), "You are using a non-lagrange FEM. "
239  << "In that case you need to set "
240  << "DATA_FEM_TYPE in the .param file");
241  mf_rhs.set_finite_element(mesh.convex_index(), pf_ut);
242  } else {
243  mf_rhs.set_finite_element(mesh.convex_index(),
244  getfem::fem_descriptor(data_fem_name));
245  }
246 
247  /* set the finite element on mf_coef. Here we use a very simple element
248  * since the only function that need to be interpolated on the mesh_fem
249  * is f(x)=1 ... */
250  mf_coef.set_finite_element(mesh.convex_index(),
251  getfem::classical_fem(pgt,0));
252 
253  /* set boundary conditions
254  * (Neuman on the upper face, Dirichlet elsewhere) */
255  cout << "Selecting Neumann and Dirichlet boundaries\n";
256  getfem::mesh_region border_faces;
257  getfem::outer_faces_of_mesh(mesh, border_faces);
258  for (getfem::mr_visitor i(border_faces); !i.finished(); ++i) {
259  assert(i.is_face());
260  base_node un = mesh.normal_of_face_of_convex(i.cv(), i.f());
261  un /= gmm::vect_norm2(un);
262  switch(sol_ref){
263  case 0 :
264  if (gmm::abs(un[1]) <= 1.0E-7) // new Neumann face
265  mesh.region(SIMPLY_FIXED_BOUNDARY_NUM).add(i.cv(), i.f());
266  break ;
267  case 1 :
268  if (gmm::abs(un[1]) <= 1.0E-7) // new Neumann face
269  mesh.region(SIMPLY_FIXED_BOUNDARY_NUM).add(i.cv(), i.f());
270  break ;
271  case 2 :
272  if ( (gmm::abs(un[0]) <= 1.0E-7) || (gmm::abs(un[1]) <= 1.0E-7) )
273  mesh.region(SIMPLY_FIXED_BOUNDARY_NUM).add(i.cv(), i.f());
274  break ;
275  case 3 :
276  if (un[0] <= (- 1. + 1.0E-7)) // new Neumann face
277  mesh.region(SIMPLY_FIXED_BOUNDARY_NUM).add(i.cv(), i.f());
278  break ;
279  case 4 :
280  if ( (gmm::abs(un[0]) <= 1.0E-7) || (gmm::abs(un[1]) <= 1.0E-7) )
281  mesh.region(SIMPLY_FIXED_BOUNDARY_NUM).add(i.cv(), i.f());
282  break ;
283  default :
284  GMM_ASSERT1(false, "SOL_REF parameter is undefined");
285  break ;
286  }
287  }
288 }
289 
290 base_small_vector plate_problem::theta_exact(base_node P) {
291  base_small_vector theta(2);
292  if (sol_ref == 0) { // appui simple aux 2 bords
293  theta[0] = - (-pressure / (32. * mu * epsilon * epsilon * epsilon / 8.))
294  * (4. * pow(P[0] - .5, 3.) - 3 * (P[0] - .5));
295  theta[1] = 0.;
296  }
297  if (sol_ref == 1) { // encastrement aux 2 bords
298  theta[0] = - (-pressure / (16. * mu * epsilon * epsilon * epsilon / 8.))
299  * P[0] * ( 2.*P[0]*P[0] - 3.* P[0] + 1. ) ;
300  theta[1] = 0.;
301  }
302  if (sol_ref == 2) { // encastrement aux 4 bords et sols vraiment 2D, non polynomiale
303  theta[0] = (1. + eta) * M_PI * sin(2.*M_PI*P[0]) * sin(M_PI*P[1])* sin(M_PI*P[1]) ;
304  theta[1] = (1. + eta) * M_PI * sin(2.*M_PI*P[1]) * sin(M_PI*P[0])* sin(M_PI*P[0]) ;
305  }
306  if (sol_ref == 3) { // plaque cantilever
307  theta[0] = - (- 3. * pressure / (8. * mu * epsilon * epsilon * epsilon / 8.))
308  * P[0] * ( 0.25 * P[0] * P[0] - P[0] + 1. ) ;
309  theta[1] = 0.;
310  }
311  if (sol_ref == 4) { // bord entier en appui simple
312  theta[0] = 0. ;
313  theta[1] = 0. ;
314  for(size_type i = 0 ; i < N_Four ; i ++) {
315  for(size_type j = 0 ; j < N_Four ; j ++) {
316  theta[0] -= theta1_Four(i, j) * cos( scalar_type(j + 1) * M_PI * P[0] / LX ) * sin( scalar_type(i + 1) * M_PI * P[1] / LY ) ;
317  theta[0] -= theta2_Four(i, j) * sin( scalar_type(j + 1) * M_PI * P[0] / LX ) * cos( scalar_type(i + 1) * M_PI * P[1] / LY ) ;
318  }
319  }
320  }
321  return theta;
322 }
323 
324 scalar_type plate_problem::u3_exact(base_node P) {
325  switch(sol_ref) {
326  case 0 : return (pressure / (32. * mu * epsilon * epsilon * epsilon / 8.))
327  * P[0] * (P[0] - 1.)
328  * (gmm::sqr(P[0] - .5) -1.25-(8.* epsilon*epsilon / 4.));
329  break ;
330  case 1 : return (pressure /(32.* mu * epsilon * epsilon * epsilon / 8.))
331  * P[0] * (P[0] - 1.)
332  * ( P[0] * P[0] - P[0] - 8. * epsilon *epsilon / 4.) ;
333  break ;
334  case 2 : return gmm::sqr(sin(M_PI*P[0])) * gmm::sqr(sin(M_PI*P[1]));
335  break ;
336  case 3 : return (3. * pressure / (4. * mu * epsilon * epsilon * epsilon / 8. ))
337  * P[0] * ( P[0] * P[0] * P[0] / 24. - P[0] * P[0] / 6. + P[0] / 4.
338  - (epsilon * epsilon / 4.) * P[0] / 3.
339  + 2. * (epsilon * epsilon / 4.) / 3.) ;
340  break ;
341  case 4 :
342  scalar_type u3_local ;
343  u3_local = 0. ;
344  for(size_type i = 0 ; i < N_Four ; i ++) {
345  for(size_type j = 0 ; j < N_Four ; j ++)
346  u3_local += u3_Four(i, j) * sin( scalar_type(j + 1) * M_PI * P[0] / LX ) * sin( scalar_type(i + 1) * M_PI * P[1] / LY ) ;
347  }
348  return (u3_local) ;
349  break ;
350  default : GMM_ASSERT1(false, "indice de solution de référence incorrect");
351  }
352 }
353 
354 
355 /* compute the error with respect to the exact solution */
356 void plate_problem::compute_error(plain_vector &Ut, plain_vector &U3, plain_vector &THETA) {
357  cout.precision(16);
358  if (PARAM.int_value("SOL_EXACTE") == 1) {
359  gmm::clear(Ut); gmm::clear(U3); gmm::clear(THETA);
360  }
361 
362  std::vector<scalar_type> V(mf_rhs.nb_dof()*2);
363 
364  getfem::interpolation(mf_ut, mf_rhs, Ut, V);
365  mf_rhs.set_qdim(2);
366  scalar_type l2 = gmm::sqr(getfem::asm_L2_norm(mim, mf_rhs, V));
367  scalar_type h1 = gmm::sqr(getfem::asm_H1_norm(mim, mf_rhs, V));
368  scalar_type linf = gmm::vect_norminf(V);
369  mf_rhs.set_qdim(1);
370  cout << "L2 error = " << sqrt(l2) << endl
371  << "H1 error = " << sqrt(h1) << endl
372  << "Linfty error = " << linf << endl;
373 
374  getfem::interpolation(mf_theta, mf_rhs, THETA, V);
375  GMM_ASSERT1(!mf_rhs.is_reduced(),
376  "To be adapted, use interpolation_function");
377  for (size_type i = 0; i < mf_rhs.nb_dof(); ++i) {
378  gmm::add(gmm::scaled(theta_exact(mf_rhs.point_of_basic_dof(i)), -1.0),
379  gmm::sub_vector(V, gmm::sub_interval(i*2, 2)));
380  }
381  mf_rhs.set_qdim(2);
382  l2 += gmm::sqr(getfem::asm_L2_norm(mim, mf_rhs, V));
383  h1 += gmm::sqr(getfem::asm_H1_semi_norm(mim, mf_rhs, V));
384  linf = std::max(linf, gmm::vect_norminf(V));
385  mf_rhs.set_qdim(1);
386  cout << "L2 error theta:" << sqrt(l2) << endl
387  << "H1 error theta:" << sqrt(h1) << endl
388  << "Linfty error = " << linf << endl;
389 
390  gmm::resize(V, mf_rhs.nb_dof());
391  getfem::interpolation(mf_u3, mf_rhs, U3, V);
392 
393  for (size_type i = 0; i < mf_rhs.nb_dof(); ++i)
394  V[i] -= u3_exact(mf_rhs.point_of_basic_dof(i));
395 
396  l2 = gmm::sqr(getfem::asm_L2_norm(mim, mf_rhs, V));
397  h1 = gmm::sqr(getfem::asm_H1_semi_norm(mim, mf_rhs, V));
398  linf = std::max(linf, gmm::vect_norminf(V));
399 
400  cout.precision(16);
401  cout << "L2 error u3:" << sqrt(l2) << endl
402  << "H1 error u3:" << sqrt(h1) << endl
403  << "Linfty error = " << linf << endl;
404 
405  // stockage de l'erreur H1 :
406  if (PARAM.int_value("SAUV")){
407  std::ofstream f_out("errH1.don");
408  if (!f_out) throw std :: runtime_error("Impossible to open file") ;
409  f_out << sqrt(h1) << "\n" ;
410  }
411 
412 
413 }
414 
415 /**************************************************************************/
416 /* Model. */
417 /**************************************************************************/
418 
419 bool plate_problem::solve(plain_vector &Ut, plain_vector &U3, plain_vector &THETA) {
420  size_type nb_dof_rhs = mf_rhs.nb_dof();
421 
422  cout << "Number of dof for ut: " << mf_ut.nb_dof() << endl;
423  cout << "Number of dof for u3: " << mf_u3.nb_dof() << endl;
424  cout << "Number of dof for theta: " << mf_theta.nb_dof() << endl;
425 
426  E = 4.*mu*(mu+lambda) / (2. * mu + lambda);
427  nu = lambda / (2. * mu + lambda);
428  scalar_type kappa = 5./6.;
429 
430  getfem::model md;
431  md.add_fem_variable("ut", mf_ut);
432  md.add_fem_variable("u3", mf_u3);
433  md.add_fem_variable("theta", mf_theta);
434 
435  // Linearized plate brick.
436  md.add_initialized_scalar_data("E", E);
437  md.add_initialized_scalar_data("nu", nu);
438  md.add_initialized_scalar_data("lambda", lambda);
439  md.add_initialized_scalar_data("mu", mu);
440  md.add_initialized_scalar_data("epsilon", epsilon);
441  md.add_initialized_scalar_data("kappa", kappa);
442  getfem::add_Mindlin_Reissner_plate_brick(md, mim, mim_subint, "u3", "theta",
443  "E", "nu", "epsilon", "kappa",
444  (mitc) ? 2 : 1);
445  getfem::add_isotropic_linearized_elasticity_brick(md, mim, "ut", "lambda", "mu");
446 
447  // Defining the surface source term.
448  if (study_flag == 1 ){
449  cout << "Attention : l'intensité de la pression verticale " ;
450  cout << "a été choisie pour que le déplacement maximal soit unitaire." ;
451  cout << "Pour annuler cette option, faire STUDY_FLAG = 0\n" ;
452  switch(sol_ref) {
453  case 0 :
454  pressure = 128. * mu * epsilon * epsilon * epsilon / 8. ;
455  pressure /= 1.25 + 8. * epsilon * epsilon / 4. ;
456  break ;
457  case 1 :
458  pressure = 128. * mu * epsilon * epsilon * epsilon / 8. ;
459  pressure /= 0.25 + 8. * epsilon * epsilon / 4. ;
460  break ;
461  case 3 :
462  pressure = 32. * mu * epsilon * epsilon * epsilon / 8.;
463  pressure /= 3. + 8. * epsilon * epsilon / 4.;
464  default :
465  break ;
466  }
467  }
468  plain_vector F(nb_dof_rhs);
469  plain_vector M(nb_dof_rhs * 2);
470  if (sol_ref == 2) {
471  base_small_vector P(2) ;
472  scalar_type sx, sy, cx, cy, s2x, s2y, c2x, c2y ;
473  E = 4.*mu*(mu+lambda) / (2. * mu + lambda);
474  nu = lambda / (2. * mu + lambda);
475  for (size_type i = 0; i < nb_dof_rhs; ++i) {
476  P = mf_rhs.point_of_basic_dof(i);
477  sx = sin(M_PI*P[0]) ;
478  cx = cos(M_PI*P[0]) ;
479  sy = sin(M_PI*P[1]) ;
480  cy = cos(M_PI*P[1]) ;
481  c2x = cos(2.*M_PI*P[0]) ;
482  c2y = cos(2.*M_PI*P[1]) ;
483  s2x = sin(2.*M_PI*P[0]) ;
484  s2y = sin(2.*M_PI*P[1]) ;
485  F[i] = 2. * (epsilon / 2.) * E * M_PI * M_PI * eta *
486  ( sy * sy * c2x + sx * sx * c2y ) / ( 1. + nu ) ;
487  M[2*i] = -((epsilon * epsilon * epsilon / 8.) * E * M_PI * s2x / 3. / (1. + nu))
488  * ( (4. * M_PI * M_PI * (1. + eta) * (2. * c2y - 1.) / (1.- nu))
489  - 3. * eta * sy * sy / (epsilon/2.) / (epsilon/2.) ) ;
490  M[2*i+1] = -((epsilon * epsilon * epsilon/8.) * E * M_PI * s2y / 3. / (1. + nu))
491  * ( (4. * M_PI * M_PI * (1. + eta) * (2. * c2x - 1.) / (1.- nu))
492  - 3. * eta * sx * sx / (epsilon/2.) / (epsilon/2.) ) ;
493  }
494  }
495  else // sol_ref = 0 ou 1 ou 3 ou 4: pression verticale uniforme
496  for (size_type i = 0; i < nb_dof_rhs; ++i) {
497  F[i] = pressure;
498  }
499 
500  md.add_initialized_fem_data("VF", mf_rhs, F);
501  getfem::add_source_term_brick(md, mim, "u3", "VF");
502  md.add_initialized_fem_data("VM", mf_rhs, M);
503  getfem::add_source_term_brick(md, mim, "theta", "VM");
504 
505  getfem::add_Dirichlet_condition_with_multipliers
506  (md, mim, "u3", mf_u3, SIMPLY_FIXED_BOUNDARY_NUM);
507  getfem::add_Dirichlet_condition_with_multipliers
508  (md, mim, "ut", mf_ut, SIMPLY_FIXED_BOUNDARY_NUM);
509 
510  if (sol_ref == 1 || sol_ref == 2 || sol_ref == 3)
511  getfem::add_Dirichlet_condition_with_multipliers
512  (md, mim, "theta", mf_ut, SIMPLY_FIXED_BOUNDARY_NUM);
513 
514 
515  // Generic solve.
516  gmm::iteration iter(residual, 1, 40000);
517  getfem::standard_solve(md, iter);
518 
519 
520  gmm::resize(Ut, mf_ut.nb_dof());
521  gmm::copy(md.real_variable("ut"), Ut);
522  gmm::resize(U3, mf_u3.nb_dof());
523  gmm::copy(md.real_variable("u3"), U3);
524  gmm::resize(THETA, mf_theta.nb_dof());
525  gmm::copy(md.real_variable("theta"), THETA);
526 
527  if (PARAM.int_value("VTK_EXPORT")) {
528  cout << "export to " << datafilename + ".vtk" << "..\n";
529  getfem::vtk_export exp(datafilename + ".vtk",
530  PARAM.int_value("VTK_EXPORT")==1);
531  exp.exporting(mf_u3);
532  exp.write_point_data(mf_u3, U3, "plate_normal_displacement");
533  cout << "export done, you can view the data file with (for example)\n"
534  "mayavi2 -d " << datafilename << ".vtk -f "
535  "WarpScalar -m Surface -m Outline\n";
536 // cout << "export done, you can view the data file with (for example)\n"
537 // "mayavi -d " << datafilename << ".vtk -f ExtractVectorNorm -f "
538 // "WarpVector -m BandedSurfaceMap -m Outline\n";
539  }
540  if (PARAM.int_value("DX_EXPORT")) {
541  cout << "export to " << datafilename + ".dx" << ".\n";
542  getfem::dx_export exp(datafilename + ".dx",
543  PARAM.int_value("DX_EXPORT")==1);
544  exp.exporting(mf_u3);
545  exp.write_point_data(mf_u3, U3, "plate_normal_displacement");
546  }
547 
548 
549  return (iter.converged());
550 }
551 
552 /**************************************************************************/
553 /* main program. */
554 /**************************************************************************/
555 
556 int main(int argc, char *argv[]) {
557 
558  GETFEM_MPI_INIT(argc, argv);
559  GMM_SET_EXCEPTION_DEBUG; // Exceptions make a memory fault, to debug.
560  FE_ENABLE_EXCEPT; // Enable floating point exception for Nan.
561 
562  try {
563  plate_problem p;
564  p.PARAM.read_command_line(argc, argv);
565  p.init();
566  if ((p.study_flag != 1)&&((p.sol_ref == 0) || (p.sol_ref ==1)))
567  p.pressure *= p.epsilon * p.epsilon * p.epsilon / 8.;
568  p.mesh.write_to_file(p.datafilename + ".mesh");
569  plain_vector Ut, U3, THETA;
570  bool ok = p.solve(Ut, U3, THETA);
571  p.compute_error(Ut, U3, THETA);
572  GMM_ASSERT1(ok, "Solve has failed");
573 
574  }
575  GMM_STANDARD_CATCH_ERROR;
576 
577  GETFEM_MPI_FINALIZE;
578 
579  return 0;
580 }
getfem_export.h
Export solutions to various formats.
getfem_model_solvers.h
Standard solvers for model bricks.
getfem::add_Mindlin_Reissner_plate_brick
size_type add_Mindlin_Reissner_plate_brick(model &md, const mesh_im &mim, const mesh_im &mim_reduced, const std::string &u3, const std::string &Theta, const std::string &param_E, const std::string &param_nu, const std::string &param_epsilon, const std::string &param_kappa, size_type variant=size_type(2), size_type region=size_type(-1))
Add a term corresponding to the classical Reissner-Mindlin plate model for which u3 is the transverse...
Definition: getfem_linearized_plates.cc:28
bgeot::name_of_geometric_trans
std::string name_of_geometric_trans(pgeometric_trans p)
Get the string name of a geometric transformation.
Definition: bgeot_geometric_trans.cc:1173
getfem::asm_H1_norm
scalar_type asm_H1_norm(const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
compute the H1 norm of U.
Definition: getfem_assembling.h:302
gmm::resize
void resize(M &v, size_type m, size_type n)
*â€/
Definition: gmm_blas.h:231
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:49
getfem::int_method_descriptor
pintegration_method int_method_descriptor(std::string name, bool throw_if_not_found=true)
Get an integration method from its name .
Definition: getfem_integration.cc:1130
getfem_regular_meshes.h
Build regular meshes.
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:59
getfem::mesh_im
Describe an integration method linked to a mesh.
Definition: getfem_mesh_im.h:47
getfem::add_Dirichlet_condition_with_multipliers
size_type APIDECL add_Dirichlet_condition_with_multipliers(model &md, const mesh_im &mim, const std::string &varname, const std::string &multname, size_type region, const std::string &dataname=std::string())
Add a Dirichlet condition on the variable varname and the mesh region region.
Definition: getfem_models.cc:4671
getfem::model::add_initialized_fem_data
void add_initialized_fem_data(const std::string &name, const mesh_fem &mf, const VECT &v)
Add an initialized fixed size data to the model, assumed to be a vector field if the size of the vect...
Definition: getfem_models.h:835
bgeot::geometric_trans_descriptor
pgeometric_trans geometric_trans_descriptor(std::string name)
Get the geometric transformation from its string name.
Definition: bgeot_geometric_trans.cc:1163
getfem::classical_fem
pfem classical_fem(bgeot::pgeometric_trans pgt, short_type k, bool complete=false)
Give a pointer on the structures describing the classical polynomial fem of degree k on a given conve...
Definition: getfem_fem.cc:4141
getfem::mesh_fem
Describe a finite element method linked to a mesh.
Definition: getfem_mesh_fem.h:148
getfem::interpolation
void interpolation(const mesh_fem &mf_source, const mesh_fem &mf_target, const VECTU &U, VECTV &V, int extrapolation=0, double EPS=1E-10, mesh_region rg_source=mesh_region::all_convexes(), mesh_region rg_target=mesh_region::all_convexes())
interpolation/extrapolation of (mf_source, U) on mf_target.
Definition: getfem_interpolation.h:693
getfem::model
`‘Model’' variables store the variables, the data and the description of a model.
Definition: getfem_models.h:114
gmm::iteration
The Iteration object calculates whether the solution has reached the desired accuracy,...
Definition: gmm_iter.h:53
getfem::mesh_region::visitor
"iterator" class for regions.
Definition: getfem_mesh_region.h:237
getfem::model::add_fem_variable
void add_fem_variable(const std::string &name, const mesh_fem &mf, size_type niter=1)
Add a variable being the dofs of a finite element method to the model.
Definition: getfem_models.cc:834
gmm::vect_norm2
number_traits< typename linalg_traits< V >::value_type >::magnitude_type vect_norm2(const V &v)
Euclidean norm of a vector.
Definition: gmm_blas.h:557
getfem_linearized_plates.h
Reissner-Mindlin plate model brick.
getfem::pfem
std::shared_ptr< const getfem::virtual_fem > pfem
type of pointer on a fem description
Definition: getfem_fem.h:244
bgeot::small_vector
container for small vectors of POD (Plain Old Data) types.
Definition: bgeot_small_vector.h:205
getfem::asm_L2_norm
scalar_type asm_L2_norm(const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
compute , U might be real or complex
Definition: getfem_assembling.h:56
gmm::rsvector
sparse vector built upon std::vector.
Definition: gmm_def.h:488
getfem::model::add_initialized_scalar_data
void add_initialized_scalar_data(const std::string &name, T e)
Add a scalar data (i.e.
Definition: getfem_models.h:782
getfem::mesh
Describe a mesh (collection of convexes (elements) and points).
Definition: getfem_mesh.h:95
bgeot::pgeometric_trans
std::shared_ptr< const bgeot::geometric_trans > pgeometric_trans
pointer type for a geometric transformation
Definition: bgeot_geometric_trans.h:186
gmm.h
Include common gmm files.
getfem::mesh_region
structure used to hold a set of convexes and/or convex faces.
Definition: getfem_mesh_region.h:55
getfem::regular_unit_mesh
void regular_unit_mesh(mesh &m, std::vector< size_type > nsubdiv, bgeot::pgeometric_trans pgt, bool noised=false)
Build a regular mesh of the unit square/cube/, etc.
Definition: getfem_regular_meshes.cc:238
getfem::add_source_term_brick
size_type APIDECL add_source_term_brick(model &md, const mesh_im &mim, const std::string &varname, const std::string &dataexpr, size_type region=size_type(-1), const std::string &directdataname=std::string())
Add a source term on the variable varname.
Definition: getfem_models.cc:4127
getfem::add_isotropic_linearized_elasticity_brick
size_type APIDECL add_isotropic_linearized_elasticity_brick(model &md, const mesh_im &mim, const std::string &varname, const std::string &dataname_lambda, const std::string &dataname_mu, size_type region=size_type(-1), const std::string &dataname_preconstraint=std::string())
Linear elasticity brick ( ).
Definition: getfem_models.cc:6106
getfem::outer_faces_of_mesh
void APIDECL outer_faces_of_mesh(const mesh &m, const dal::bit_vector &cvlst, convex_face_ct &flist)
returns a list of "exterior" faces of a mesh (i.e.
Definition: getfem_mesh.cc:822
gmm::vect_norminf
number_traits< typename linalg_traits< V >::value_type >::magnitude_type vect_norminf(const V &v)
Infinity norm of a vector.
Definition: gmm_blas.h:693
getfem::standard_solve
void standard_solve(model &md, gmm::iteration &iter, rmodel_plsolver_type lsolver, abstract_newton_line_search &ls)
A default solver for the model brick system.
Definition: getfem_model_solvers.cc:410
getfem::asm_H1_semi_norm
scalar_type asm_H1_semi_norm(const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
compute , U might be real or complex
Definition: getfem_assembling.h:179
getfem::dx_export
A (quite large) class for exportation of data to IBM OpenDX.
Definition: getfem_export.h:318
getfem::fem_descriptor
pfem fem_descriptor(const std::string &name)
get a fem descriptor from its string name.
Definition: getfem_fem.cc:4232
getfem::model::real_variable
const model_real_plain_vector & real_variable(const std::string &name, size_type niter) const
Gives the access to the vector value of a variable.
Definition: getfem_models.cc:2959
getfem_assembling.h
Miscelleanous assembly routines for common terms. Use the low-level generic assembly....
getfem::vtk_export
VTK/VTU export.
Definition: getfem_export.h:68

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