sfepy.terms.terms_piezo module¶

class sfepy.terms.terms_piezo.PiezoCouplingTerm(name, arg_str, integral, region, **kwargs)[source]¶

Piezoelectric coupling term. Can be evaluated.

Definition:

$\int_{\Omega} g_{kij}\ e_{ij}(\ul{v}) \nabla_k p\\ \int_{\Omega} g_{kij}\ e_{ij}(\ul{u}) \nabla_k q$

Call signature:

dw_piezo_coupling	`(material, virtual, state)`
	`(material, state, virtual)`
	`(material, parameter_v, parameter_s)`

Arguments 1:

material: $g_{kij}$
virtual/parameter_v: $\ul{v}$
state/parameter_s: $p$

Arguments 2:

material : $g_{kij}$
state : $\ul{u}$
virtual : $q$

arg_shapes = {'material': 'D, S', 'parameter_s': 1, 'parameter_v': 'D', 'state/div': 'D', 'state/grad': 1, 'virtual/div': (1, None), 'virtual/grad': ('D', None)}¶

arg_types = (('material', 'virtual', 'state'), ('material', 'state', 'virtual'), ('material', 'parameter_v', 'parameter_s'))¶

get_eval_shape(mat, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

modes = ('grad', 'div', 'eval')¶

name = 'dw_piezo_coupling'¶

set_arg_types()[source]¶

class sfepy.terms.terms_piezo.PiezoStrainTerm(name, arg_str, integral, region, **kwargs)[source]¶

Evaluate piezoelectric strain tensor.

It is given in the usual vector form exploiting symmetry: in 3D it has 6 components with the indices ordered as $[11, 22, 33, 12, 13, 23]$ , in 2D it has 3 components with the indices ordered as $[11, 22, 12]$ .

Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.

Definition:

$\int_{\Omega} g_{kij} e_{ij}(\ul{u})$

Call signature:

ev_piezo_strain

(material, parameter)

Arguments:

material : $g_{kij}$
parameter : $\ul{u}$

arg_shapes = {'material': 'D, S', 'parameter': 'D'}¶

get_eval_shape(mat, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'ev_piezo_strain'¶

class sfepy.terms.terms_piezo.PiezoStressTerm(name, arg_str, integral, region, **kwargs)[source]¶

Evaluate piezoelectric stress tensor.

It is given in the usual vector form exploiting symmetry: in 3D it has 6 components with the indices ordered as $[11, 22, 33, 12, 13, 23]$ , in 2D it has 3 components with the indices ordered as $[11, 22, 12]$ .

Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.

Definition:

$\int_{\Omega} g_{kij} \nabla_k p$

Call signature:

ev_piezo_stress

(material, parameter)

Arguments:

material : $g_{kij}$
parameter : $p$

arg_shapes = {'material': 'D, S', 'parameter': '1'}¶

arg_types = ('material', 'parameter')¶

static function(out, val_qp, vg, fmode)[source]¶

get_eval_shape(mat, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'ev_piezo_stress'¶

class sfepy.terms.terms_piezo.SDPiezoCouplingTerm(*args, **kwargs)[source]¶

Sensitivity (shape derivative) of the piezoelectric coupling term.

Definition:

$\int_{\Omega} \hat{g}_{kij}\ e_{ij}(\ul{u}) \nabla_k p$

$\hat{g}_{kij} = g_{kij}(\nabla \cdot \ul{\Vcal}) - g_{kil}{\partial \Vcal_j \over \partial x_l} - g_{lij}{\partial \Vcal_k \over \partial x_l}$

Call signature:

ev_sd_piezo_coupling

(material, parameter_u, parameter_p, parameter_mv)

Arguments:

material : $g_{kij}$
parameter_u : $\ul{u}$
parameter_p : $p$
parameter_mv : $\ul{\Vcal}$

arg_shapes = {'material': 'D, S', 'parameter_mv': 'D', 'parameter_p': 1, 'parameter_u': 'D'}¶

arg_types = ('material', 'parameter_u', 'parameter_p', 'parameter_mv')¶

geometries = ['2_3', '2_4', '3_4', '3_8']¶

get_function(mat, par_u, par_p, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'ev_sd_piezo_coupling'¶