gf_mdbrick

# Calling Sequence

    B = gf_mdbrick('constraint', mdbrick pb, string CTYPE[, int nfem])

    B = gf_mdbrick('dirichlet', mdbrick pb, int bnum, mesh_fem mf_m, string CTYPE[, int nfem])

    B = gf_mdbrick('dirichlet on normal component', mdbrick pb, int bnum, mesh_fem mf_m, string CTYPE[, int nfem])

    B = gf_mdbrick('dirichlet on normal derivative', mdbrick pb, int bnum, mesh_fem mf_m, string CTYPE[, int nfem])

    B = gf_mdbrick('generalized dirichlet', mdbrick pb, int bnum[, int nfem])

    B = gf_mdbrick('source term', mdbrick pb[, int bnum=-1[, int nfem]])

    B = gf_mdbrick('normal source term', mdbrick pb, int bnum[, int nfem])

    B = gf_mdbrick('normal derivative source term', mdbrick parent, int bnum[, int nfem])

    B = gf_mdbrick('neumann KirchhoffLove source term', mdbrick pb, int bnum[, int nfem])

    B = gf_mdbrick('qu term', mdbrick pb[, int bnum[, int nfem]])

    B = gf_mdbrick('mass matrix', mesh_im mim, mesh_fem mf_u[, 'real'|'complex'])

    B = gf_mdbrick('generic elliptic', mesh_im mim, mesh_fem mfu[, 'scalar'|'matrix'|'tensor'][, 'real'|'complex'])

    B = gf_mdbrick('helmholtz', mesh_im mim, mesh_fem mfu[, 'real'|'complex'])

    B = gf_mdbrick('isotropic linearized elasticity', mesh_im mim, mesh_fem mfu)

    B = gf_mdbrick('linear incompressibility term', mdbrick pb, mesh_fem mfp[, int nfem])

    B = gf_mdbrick('nonlinear elasticity', mesh_im mim, mesh_fem mfu, string law)

    B = gf_mdbrick('nonlinear elasticity incompressibility term', mdbrick pb, mesh_fem mfp[, int nfem])

    B = gf_mdbrick('small deformations plasticity', mesh_im mim, mesh_fem mfu, scalar THRESHOLD)

    B = gf_mdbrick('dynamic', mdbrick pb, scalar rho[, int numfem])

    B = gf_mdbrick('bilaplacian', mesh_im mim, mesh_fem mfu[, 'Kirchhoff-Love'])

    B = gf_mdbrick('navier stokes', mesh_im mim, mesh_fem mfu, mesh_fem mfp)

    B = gf_mdbrick('isotropic_linearized_plate', mesh_im mim, mesh_im mims, mesh_fem mfut, mesh_fem mfu3, mesh_fem mftheta, scalar eps)

    B = gf_mdbrick('mixed_isotropic_linearized_plate', mesh_im mim, mesh_fem mfut, mesh_fem mfu3, mesh_fem mftheta, scalar eps)

    B = gf_mdbrick('plate_source_term', mdbrick pb[, int bnum=-1[, int nfem]])

    B = gf_mdbrick('plate_simple_support', mdbrick pb, int bnum, string CTYPE[, int nfem])

    B = gf_mdbrick('plate_clamped_support', mdbrick pb, int bnum, string CTYPE[, int nfem])

    B = gf_mdbrick('plate_closing', mdbrick pb[, int nfem])

## Description

General constructor for mdbrick objects.

## Command list

- `B = gf_mdbrick('constraint', mdbrick pb, string CTYPE[, int nfem])`

  Build a generic constraint brick. It may be useful in some situations, such as the Stokes problem where the pressure is defined modulo a constant. In such a situation, this brick can be used to add an additional constraint on the pressure value. `CTYPE` has to be chosen among 'augmented', 'penalized', and 'eliminated'. The constraint can be specified with gf_mdbrick_set(mdbrick MDB, 'constraints'). Note that Dirichlet bricks (except the 'generalized Dirichlet' one) are also specializations of the 'constraint' brick.

- `B = gf_mdbrick('dirichlet', mdbrick pb, int bnum, mesh_fem mf_m, string CTYPE[, int nfem])`

  Build a Dirichlet condition brick which impose the value of a field along a mesh boundary. The `bnum` parameter selects on which mesh region the Dirichlet condition is imposed. `CTYPE` has to be chosen among 'augmented', 'penalized', and 'eliminated'. The `mf_m` may generally be taken as the mesh_fem of the unknown, but for 'augmented' Dirichlet conditions, you may have to respect the Inf-Sup condition and choose an adequate mesh_fem.

- `B = gf_mdbrick('dirichlet on normal component', mdbrick pb, int bnum, mesh_fem mf_m, string CTYPE[, int nfem])`

  Build a Dirichlet condition brick which imposes the value of the normal component of a vector field.

- `B = gf_mdbrick('dirichlet on normal derivative', mdbrick pb, int bnum, mesh_fem mf_m, string CTYPE[, int nfem])`

  Build a Dirichlet condition brick which imposes the value of the normal derivative of the unknown.

- `B = gf_mdbrick('generalized dirichlet', mdbrick pb, int bnum[, int nfem])`

  This is the "old" Dirichlet brick of getfem. This brick can be used to impose general Dirichlet conditions `h(x)u(x) = r(x)`, however it may have some issues with elaborated fem's (such as Argyris, etc). It should be avoided when possible.

- `B = gf_mdbrick('source term', mdbrick pb[, int bnum=-1[, int nfem]])`

  Add a boundary or volumic source term ( \int B.v ). If `bnum` is omitted (or set to -1) , the brick adds a volumic source term on the whole mesh. For `bnum` >= 0, the source term is imposed on the mesh region `bnum`. Use gf_mdbrick_set(mdbrick MDB, 'param','source term',mf,B) to set the source term field. The source term is expected as a vector field of size Q (with Q = qdim).

- `B = gf_mdbrick('normal source term', mdbrick pb, int bnum[, int nfem])`

  Add a boundary source term ( \int (Bn).v ). The source term is imposed on the mesh region `bnum` (which of course is not allowed to be a volumic region, only boundary regions are allowed). Use gf_mdbrick_set(mdbrick MDB, 'param','source term',mf,B) to set the source term field. The source term B is expected as tensor field of size QxN (with Q = qdim, N = mesh dim). For example, if you consider an elasticity problem, this brick may be used to impose a force on the boundary with B as the stress tensor.

- `B = gf_mdbrick('normal derivative source term', mdbrick parent, int bnum[, int nfem])`

  Add a boundary source term ( \int (\partial_n B).v ). The source term is imposed on the mesh region `bnum`. Use gf_mdbrick_set(mdbrick MDB, 'param','source term',mf,B) to set the source term field, which is expected as a vector field of size Q (with Q = qdim).

- `B = gf_mdbrick('neumann KirchhoffLove source term', mdbrick pb, int bnum[, int nfem])`

  Add a boundary source term for neumann Kirchhoff-Love plate problems. Should be used with the Kirchhoff-Love flavour of the bilaplacian brick.

- `B = gf_mdbrick('qu term', mdbrick pb[, int bnum[, int nfem]])`

  Update the tangent matrix with a \int (Qu).v term. The Q(x) parameter is a matrix field of size qdim x qdim. An example of use is for the "iku" part of Robin boundary conditions \partial_n u + iku = ...

- `B = gf_mdbrick('mass matrix', mesh_im mim, mesh_fem mf_u[, 'real'|'complex'])`

  Build a mass-matrix brick.

- `B = gf_mdbrick('generic elliptic', mesh_im mim, mesh_fem mfu[, 'scalar'|'matrix'|'tensor'][, 'real'|'complex'])`

  Setup a generic elliptic problem. a(x)*grad(U).grad(V) The brick parameter `a` may be a scalar field, a matrix field, or a tensor field (default is scalar).

- `B = gf_mdbrick('helmholtz', mesh_im mim, mesh_fem mfu[, 'real'|'complex'])`

  Setup a Helmholtz problem. The brick has one parameter, 'wave_number'.

- `B = gf_mdbrick('isotropic linearized elasticity', mesh_im mim, mesh_fem mfu)`

  Setup a linear elasticity problem. The brick has two scalar parameter, 'lambda' and 'mu' (the Lame coefficients).

- `B = gf_mdbrick('linear incompressibility term', mdbrick pb, mesh_fem mfp[, int nfem])`

  Add an incompressibily constraint (div u = 0).

- `B = gf_mdbrick('nonlinear elasticity', mesh_im mim, mesh_fem mfu, string law)`

  Setup a nonlinear elasticity (large deformations) problem. The material `law` can be chosen among: - 'SaintVenant Kirchhoff' : Linearized material law. - 'Mooney Rivlin' : Can be preceded with the words 'compressible' or 'incompressible' to force a specific version. By default, the incompressible version is considered, which has to be used with the nonlinear incompressibily term. The compressible version requires one additional material coefficient. - 'neo Hookean' : A special case of the 'Mooney Rivlin' law that requires one material coefficient less. By default, its compressible version is used. - 'Ciarlet Geymonat'

- `B = gf_mdbrick('nonlinear elasticity incompressibility term', mdbrick pb, mesh_fem mfp[, int nfem])`

  Add an incompressibily constraint to a large strain elasticity problem.

- `B = gf_mdbrick('small deformations plasticity', mesh_im mim, mesh_fem mfu, scalar THRESHOLD)`

  Setup a plasticity problem (with small deformations). The `THRESHOLD` parameter is the maximum value of the Von Mises stress before 'plastification' of the material.

- `B = gf_mdbrick('dynamic', mdbrick pb, scalar rho[, int numfem])`

  Dynamic brick. This brick is not fully working.

- `B = gf_mdbrick('bilaplacian', mesh_im mim, mesh_fem mfu[, 'Kirchhoff-Love'])`

  Setup a bilaplacian problem. If the 'Kirchhoff-Love' option is specified, the Kirchhoff-Love plate model is used.

- `B = gf_mdbrick('navier stokes', mesh_im mim, mesh_fem mfu, mesh_fem mfp)`

  Setup a Navier-Stokes problem (this brick is not ready, do not use it).

- `B = gf_mdbrick('isotropic_linearized_plate', mesh_im mim, mesh_im mims, mesh_fem mfut, mesh_fem mfu3, mesh_fem mftheta, scalar eps)`

  Setup a linear plate model brick. For moderately thick plates, using the Reissner-Mindlin model. `eps` is the plate thinkness, the mesh_fem `mfut` and `mfu3` are used respectively for the membrane displacement and the transverse displacement of the plate. The mesh_fem `mftheta` is the rotation of the normal ("section rotations"). The second integration method `mims` can be chosen equal to `mim`, or different if you want to perform sub-integration on the transverse shear term (mitc4 projection). This brick has two parameters "lambda" and "mu" (the Lame coefficients)

- `B = gf_mdbrick('mixed_isotropic_linearized_plate', mesh_im mim, mesh_fem mfut, mesh_fem mfu3, mesh_fem mftheta, scalar eps)`

  Setup a mixed linear plate model brick. For thin plates, using Kirchhoff-Love model. For a non-mixed version, use the bilaplacian brick.

- `B = gf_mdbrick('plate_source_term', mdbrick pb[, int bnum=-1[, int nfem]])`

  Add a boundary or a volumic source term to a plate problem. This brick has two parameters: "B" is the displacement (ut and u3) source term, "M" is the moment source term (i.e. the source term on the rotation of the normal).

- `B = gf_mdbrick('plate_simple_support', mdbrick pb, int bnum, string CTYPE[, int nfem])`

  Add a "simple support" boundary condition to a plate problem. Homogeneous Dirichlet condition on the displacement, free rotation. `CTYPE` specifies how the constraint is enforced ('penalized', 'augmented' or 'eliminated').

- `B = gf_mdbrick('plate_clamped_support', mdbrick pb, int bnum, string CTYPE[, int nfem])`

  Add a "clamped support" boundary condition to a plate problem. Homogeneous Dirichlet condition on the displacement and on the rotation. `CTYPE` specifies how the constraint is enforced ('penalized', 'augmented' or 'eliminated').

- `B = gf_mdbrick('plate_closing', mdbrick pb[, int nfem])`

  Add a free edges condition for the mixed plate model brick. This brick is required when the mixed linearized plate brick is used. It must be inserted after all other boundary conditions (the reason is that the brick has to inspect all other boundary conditions to determine the number of disconnected boundary parts which are free edges).

## See Also

- getfem types

## Authors

Y. Collette