SIFEL/GEFEL/basefun.h File Reference

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Functions

void a_coeff (double *a, double *x, double *y)
void a_coeff_3d (double *a, double *x, double *y, double *z, double v)
void ac_bf_quad_3_2d (double *n, double *l)
void ac_dx_bf_quad_3_2d (double *n, double *b, double *l)
void ac_dy_bf_quad_3_2d (double *n, double *c, double *l)
void b_coeff (double *b, double *y)
void b_coeff_3d (double *b, double *y, double *z, double v)
void bf_cct (double *n, double *l, double *sx, double *sy)
void bf_lin_1d (double *n, double x)
void bf_lin_3_2d (double *n, double x, double y)
void bf_lin_4_2d (double *n, double x, double y)
void bf_lin_hex_3d (double *n, double x, double y, double z)
void bf_lin_tet (double *n, double x, double y, double z)
void bf_lin_wed_3d (double *n, double x, double y, double z)
void bf_quad_1d (double *n, double x)
void bf_quad_3_2d (double *n, double x, double y)
void bf_quad_4_2d (double *n, double x, double y)
void bf_quad_hex_3d (double *n, double x, double y, double z)
void bf_quad_hexrot_3d (double *n, double x, double y, double z)
void bf_quad_tet (double *n, double x, double y, double z)
void bf_quad_wed_3d (double *n, double x, double y, double z)
void bf_rot_3_2d (double *n, double *l, double *b, double *c)
void bf_rot_4_2d (double *n, double x, double y, double *nx, double *ny, double *l)
void c_coeff (double *c, double *x)
void c_coeff_3d (double *c, double *x, double *z, double v)
void d_coeff_3d (double *d, double *x, double *y, double v)
void defl2D_fun (double *n, double xi, double l, double kappa)
void der_defl2D_fun (double *n, double xi, double l, double kappa)
void der_dilat (double *n, double l)
void der_roty_fun (double *n, double xi, double l, double kappa)
void dilat (double *n, double xi)
void dx_bf_lin_1d (double *n)
void dx_bf_lin_3_2d (double *n)
void dx_bf_lin_4_2d (double *n, double y)
void dx_bf_lin_hex_3d (double *n, double y, double z)
void dx_bf_lin_tet (double *n)
void dx_bf_lin_wed_3d (double *n, double z)
void dx_bf_quad_1d (double *n, double x)
void dx_bf_quad_3_2d (double *n, double x, double y)
void dx_bf_quad_4_2d (double *n, double x, double y)
void dx_bf_quad_hex_3d (double *n, double x, double y, double z)
void dx_bf_quad_hexrot_3d (double *n, double x, double y, double z)
void dx_bf_quad_tet (double *n, double x, double y, double z)
void dx_bf_quad_wed_3d (double *n, double x, double y, double z)
void dx_bf_rot_3_2d (double *n, double *l, double *b, double *c)
void dx_bf_rot_4_2d (double *n, double x, double y, double *nx, double *ny, double *l)
void dx_cct (double *n, double *l, double *b, double *sx, double *sy)
void dy_bf_lin_3_2d (double *n)
void dy_bf_lin_4_2d (double *n, double x)
void dy_bf_lin_hex_3d (double *n, double x, double z)
void dy_bf_lin_tet (double *n)
void dy_bf_lin_wed_3d (double *n, double z)
void dy_bf_quad_3_2d (double *n, double x, double y)
void dy_bf_quad_4_2d (double *n, double x, double y)
void dy_bf_quad_hex_3d (double *n, double x, double y, double z)
void dy_bf_quad_hexrot_3d (double *n, double x, double y, double z)
void dy_bf_quad_tet (double *n, double x, double y, double z)
void dy_bf_quad_wed_3d (double *n, double x, double y, double z)
void dy_bf_rot_3_2d (double *n, double *l, double *b, double *c)
void dy_bf_rot_4_2d (double *n, double x, double y, double *nx, double *ny, double *l)
void dy_cct (double *n, double *l, double *c, double *sx, double *sy)
void dz_bf_lin_hex_3d (double *n, double x, double y)
void dz_bf_lin_tet (double *n)
void dz_bf_lin_wed_3d (double *n, double x, double y)
void dz_bf_quad_hex_3d (double *n, double x, double y, double z)
void dz_bf_quad_hexrot_3d (double *n, double x, double y, double z)
void dz_bf_quad_tet (double *n, double x, double y, double z)
void dz_bf_quad_wed_3d (double *n, double x, double y, double z)
void plsa (double *a, double *x, double *y, double det)
void plsb (double *b, double *y, double det)
void plsc (double *c, double *x, double det)
void roty_fun (double *n, double xi, double l, double kappa)
void vola_3d (double *a, double *x, double *y, double *z, double det)
void volb_3d (double *b, double *y, double *z, double det)
void volc_3d (double *c, double *x, double *z, double det)
void vold_3d (double *d, double *x, double *y, double det)

Function Documentation

void a_coeff ( double *  a,
double *  x,
double *  y 
)

function computes a_i coefficients of area-coordinates on triangles L(x,y)_i = (a_i + b_i.x + c_i.y)/area/2

Parameters:
a - coefficients
x,y - node coordinates

Definition at line 162 of file basefun.cpp.

void a_coeff_3d ( double *  a,
double *  x,
double *  y,
double *  z,
double  v 
)

function computes coefficients a_i of volume coordinates L(x,y,z)_i = (a_i + b_i.x + c_i.y + d_i.z)/6/volume

Parameters:
a - array of coefficients
x,y,z - array of node coordinates
v - volume of element

Definition at line 774 of file basefun.cpp.

void ac_bf_quad_3_2d ( double *  n,
double *  l 
)

function computes quadratic base functions on triangle

Parameters:
n - array of base functions
l - areacoordinates

Definition at line 260 of file basefun.cpp.

void ac_dx_bf_quad_3_2d ( double *  n,
double *  b,
double *  l 
)

function computes derivatives of quadratic base functions on triangle with respect of x

Parameters:
n - array of derivatives of base functions
b - array of coefficients of area coordinates
l - areacoordinates

Definition at line 284 of file basefun.cpp.

void ac_dy_bf_quad_3_2d ( double *  n,
double *  c,
double *  l 
)

function computes derivatives of quadratic base functions on triangle with respect of y

Parameters:
n - array of derivatives of base functions
c - array of coefficients of area coordinates
l - areacoordinates

Definition at line 308 of file basefun.cpp.

void b_coeff ( double *  b,
double *  y 
)

function computes b_i coefficients of area-coordinates on triangles L(x,y)_i = (a_i + b_i.x + c_i.y)/area/2

Parameters:
b - coefficients
y - node coordinates

Definition at line 178 of file basefun.cpp.

Referenced by planeelemrotlt::load_matrix(), and planeelemrotlt::mass_matrix().

void b_coeff_3d ( double *  b,
double *  y,
double *  z,
double  v 
)

function computes coefficients b_i of volume coordinates L(x,y,z)_i = (a_i + b_i.x + c_i.y + d_i.z)/6/volume

Parameters:
b - array of coefficients
y,z - array of node coordinates
v - volume of element

Definition at line 807 of file basefun.cpp.

void bf_cct ( double *  n,
double *  l,
double *  sx,
double *  sy 
)

function computes base functions of constant curvature triangle (finite element for plate problems)

Parameters:
n - array of base functions
l - area coordinates
sx,sy - arrays of components

Definition at line 697 of file basefun.cpp.

Referenced by cctelem::bf_matrix(), cctelem::geom_matrix(), and cctelem::geom_matrix_block().

void bf_lin_1d ( double *  n,
double  x 
)

function computes linear base functions on bar element natural coordinate is from segment <-1;1>

Parameters:
n - array of base functions
x - natural coodinate

Definition at line 10 of file basefun.cpp.

Referenced by linbartax::approx(), linbart::approx(), plquadcontact::approx(), barel3d::approx(), barel2d::approx(), gtopology::approx_weights(), linbartax::bf_matrix(), and linbart::bf_matrix().

void bf_lin_3_2d ( double *  n,
double  x,
double  y 
)

function computes linear approximation functions on triangle

Parameters:
n - array containing approximation functions
x,y - natural coordinates

1.4.2002

Definition at line 332 of file basefun.cpp.

Referenced by gtopology::approx_weights(), planeelemlt::bf_matrix(), axisymlt::bf_matrix(), and give_valuesinpoints().

void bf_lin_4_2d ( double *  n,
double  x,
double  y 
)

function computes bi-linear base functions on quadrilateral

Parameters:
n - array of base functions
x,y - natural coodinates

Definition at line 429 of file basefun.cpp.

Referenced by quadlineart::approx(), quadlinaxisym::approx(), soilplateq::approx(), q4plate::approx(), planeelemrotlq::approx(), planeelemlq::approx(), axisymlq::approx(), gtopology::approx_weights(), quadlineart::bf_matrix(), quadlinaxisym::bf_matrix(), planeelemlq::bf_matrix(), axisymlq::bf_matrix(), quadlineart::compute_error(), planeelemlq::compute_error(), axisymlq::geom_matrix(), axisymlq::geom_matrix_block(), quadlinaxisym::give_approx_fun(), give_valuesinpoints(), patch_averaging::nsp_spcoord_maxcoord_assembling(), planeelemlq::ntdbr_vector(), planeelemlq::ntn_matrix(), and radius().

void bf_lin_hex_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes tri-linear base functions on hexahedron

Parameters:
n - array of base functions
x,y,z - natural coodinates

Definition at line 1284 of file basefun.cpp.

Referenced by linhext::approx(), linhexrot::approx(), linhex::approx(), gtopology::approx_weights(), linhext::bf_matrix(), linhexrot::bf_matrix(), linhex::bf_matrix(), and linhexrot::geom_matrix_shear().

void bf_lin_tet ( double *  n,
double  x,
double  y,
double  z 
)

function computes tri-linear base functions on tetrahedron

Parameters:
n - array of base functions
x,y,z - natural coodinates

Definition at line 949 of file basefun.cpp.

Referenced by gtopology::approx_weights().

void bf_lin_wed_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes linear base functions on wedge

Parameters:
n - array of basis functions
x,y,z - natural coordinates

JK, 9.5.2004

Definition at line 1095 of file basefun.cpp.

Referenced by linwedge::approx(), and linwedge::bf_matrix().

void bf_quad_1d ( double *  n,
double  x 
)

function computes quadratic approximation functions on bar element

Parameters:
n - array containing approximation functions
x - natural coordinate

Definition at line 33 of file basefun.cpp.

Referenced by quadbartax::approx(), quadbart::approx(), barelq3d::approx(), barelq2d::approx(), gtopology::approx_weights(), quadbartax::bf_matrix(), and quadbart::bf_matrix().

void bf_quad_3_2d ( double *  n,
double  x,
double  y 
)

function computes quadratic approximation functions on triangle

Parameters:
n - array containing approximation functions
x,y - natural coordinates

1.4.2002

Definition at line 375 of file basefun.cpp.

Referenced by planeelemsubqt::approx(), planeelemqt::approx(), gtopology::approx_weights(), planeelemsubqt::bf_matrix(), planeelemqt::bf_matrix(), planeelemqt::compute_error(), give_valuesinpoints(), least_square::nsp_spcoord_maxcoord_assembling(), patch_averaging::nsp_spcoord_maxcoord_assembling(), planeelemqt::ntdbr_vector(), and planeelemqt::ntn_matrix().

void bf_quad_4_2d ( double *  n,
double  x,
double  y 
)

function computes bi-quadratic base functions on quadrilateral

Parameters:
n - array of base functions
x,y - natural coodinates

Definition at line 477 of file basefun.cpp.

Referenced by quadquadrilattax::approx(), quadquadrilatt::approx(), planeelemqq::approx(), axisymqq::approx(), gtopology::approx_weights(), quadquadrilattax::bf_matrix(), quadquadrilatt::bf_matrix(), planeelemqq::bf_matrix(), axisymqq::bf_matrix(), planeelemqq::compute_error(), axisymqq::geom_matrix(), axisymqq::geom_matrix_block(), quadquadrilattax::give_approx_fun(), quadquadrilatt::give_approx_fun(), give_valuesinpoints(), least_square::nsp_spcoord_maxcoord_assembling(), patch_averaging::nsp_spcoord_maxcoord_assembling(), planeelemqq::ntdbr_vector(), and planeelemqq::ntn_matrix().

void bf_quad_hex_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes tri-quadratic base functions on hexahedron

Parameters:
n - array of derivatives of base functions
x,y,z - natural coodinates

Definition at line 1362 of file basefun.cpp.

Referenced by quadhext::approx(), quadhex::approx(), gtopology::approx_weights(), quadhext::bf_matrix(), and quadhex::bf_matrix().

void bf_quad_hexrot_3d ( double *  n,
double  x,
double  y,
double  z 
)

Definition at line 1497 of file basefun.cpp.

void bf_quad_tet ( double *  n,
double  x,
double  y,
double  z 
)

function computes tri-quadratic base functions on tetrahedron

Parameters:
n - array of base functions
x,y,z - natural coodinates TKo - 11.2008

Definition at line 996 of file basefun.cpp.

Referenced by quadtet::approx(), gtopology::approx_weights(), and quadtet::bf_matrix().

void bf_quad_wed_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes quadratic approximation functions on wedge

Parameters:
n - array of basis functions
x,y,z - natural coordinates

JK, 19.9.2004

Definition at line 1172 of file basefun.cpp.

Referenced by quadwedge::approx(), and quadwedge::bf_matrix().

void bf_rot_3_2d ( double *  n,
double *  l,
double *  b,
double *  c 
)

function computes modified base functions on triangle for element with rotational DOFs

Parameters:
n - array of base functions
l - area coordinates
b,c - coefficients of area coordinates

Definition at line 538 of file basefun.cpp.

Referenced by planeelemrotlt::addgeommat(), and planeelemrotlt::bf_matrix().

void bf_rot_4_2d ( double *  n,
double  x,
double  y,
double *  nx,
double *  ny,
double *  l 
)

function computes modified base functions on quadrilateral for element with rotational DOFs

Parameters:
n - array of base functions
x,y - natural coordinates
nx,ny - array of x and y components of outer normal vectors
l - array of lengths of element edges

Definition at line 611 of file basefun.cpp.

Referenced by planeelemrotlq::addgeommat(), and planeelemrotlq::bf_matrix().

void c_coeff ( double *  c,
double *  x 
)

function computes c_i coefficients of area-coordinates on triangles L(x,y)_i = (a_i + b_i.x + c_i.y)/area/2

Parameters:
c - coefficients
x - node coordinates

Definition at line 194 of file basefun.cpp.

Referenced by planeelemrotlt::load_matrix(), and planeelemrotlt::mass_matrix().

void c_coeff_3d ( double *  c,
double *  x,
double *  z,
double  v 
)

function computes coefficients c_i of volume coordinates L(x,y,z)_i = (a_i + b_i.x + c_i.y + d_i.z)/6/volume

Parameters:
c - array of coefficients
x,z - array of node coordinates
v - volume of element

Definition at line 832 of file basefun.cpp.

void d_coeff_3d ( double *  d,
double *  x,
double *  y,
double  v 
)

function computes coefficients d_i of volume coordinates L(x,y,z)_i = (a_i + b_i.x + c_i.y + d_i.z)/6/volume

Parameters:
d - array of coefficients
x,y - array of node coordinates
v - volume of element

Definition at line 857 of file basefun.cpp.

void defl2D_fun ( double *  n,
double  xi,
double  l,
double  kappa 
)

function computes approximation function of deflection of 2D beam element

Parameters:
n - array containing approximation functions
xi - natural coordinate from segment <0;1>
l - length of the beam
kappa - 6.0*E*I/k/G/A/l/l

20.2.2002

Definition at line 92 of file basefun.cpp.

Referenced by beamel2d::bf_matrix().

void der_defl2D_fun ( double *  n,
double  xi,
double  l,
double  kappa 
)

function computes derivative of deflection function with respect of x

Parameters:
n - array containing approximation functions
xi - natural coordinate from segment <0;1>
l - length of the beam
kappa - 6.0*E*I/k/G/A/l/l

20.2.2002

Definition at line 110 of file basefun.cpp.

Referenced by beamel2d::dbf_matrix(), and beamel2d::geom_matrix().

void der_dilat ( double *  n,
double  l 
)

function computes derivative of approximation function of dilatation of 2D beam element with respect of x

Parameters:
n - array containing approximation functions
l - length of the beam

20.2.2002

Definition at line 76 of file basefun.cpp.

Referenced by beamel2d::geom_matrix().

void der_roty_fun ( double *  n,
double  xi,
double  l,
double  kappa 
)

function computes derivative of function of rotation of 2D beam element with respect of x

Parameters:
n - array containing approximation functions
xi - natural coordinate from segment <0;1>
l - length of the beam
kappa - 6.0*E*I/k/G/A/l/l

20.2.2002

Definition at line 146 of file basefun.cpp.

Referenced by beamel2d::geom_matrix().

void dilat ( double *  n,
double  xi 
)

function computes approximation function of dilatation of 2D beam element

Parameters:
n - array containing approximation functions
xi - natural coordinate from segment <0;1>

20.2.2002

Definition at line 62 of file basefun.cpp.

Referenced by beamel2d::bf_matrix().

void dx_bf_lin_1d ( double *  n  ) 

function computes derivatives of linear base functions on bar element with respect of natural coordinate x

Parameters:
n - array of derivatives of base functions

Definition at line 21 of file basefun.cpp.

Referenced by derivatives_1d(), barel2d::geom_matrix(), linbartax::grad_matrix(), linbart::grad_matrix(), jac1d2d(), jac1d3d(), and jac_1d().

void dx_bf_lin_3_2d ( double *  n  ) 

function computes derivatives of linear approximation functions with respect to natural coordinate xi

Parameters:
n - array containing derivatives

1.4.2002

Definition at line 346 of file basefun.cpp.

Referenced by derivatives_2d(), jac2d3d(), and jac_2d().

void dx_bf_lin_4_2d ( double *  n,
double  y 
)

function computes derivatives of bi-linear base functions on quadrilateral with respect of natural coordinate x

Parameters:
n - array of derivatives of base functions
y - natural coodinate

Definition at line 445 of file basefun.cpp.

Referenced by planeelemlq::bvectors(), derivatives_2d(), planeelemlq::geom_matrix(), axisymlq::geom_matrix(), planeelemlq::geom_matrix_block(), axisymlq::geom_matrix_block(), quadlineart::grad_matrix(), quadlinaxisym::grad_matrix(), jac2d3d(), and jac_2d().

void dx_bf_lin_hex_3d ( double *  n,
double  y,
double  z 
)

function computes derivatives of tri-linear base functions on hexahedron with respect of natural coordinate x

Parameters:
n - array of derivatives of base functions
y,z - natural coodinates

Definition at line 1302 of file basefun.cpp.

Referenced by linhexrot::bvectors(), linhex::bvectors(), derivatives_3d(), linhexrot::geom_matrix(), linhex::geom_matrix(), linhex::geom_matrix_block(), linhexrot::geom_matrix_shear(), linhext::grad_matrix(), and jac_3d().

void dx_bf_lin_tet ( double *  n  ) 

Definition at line 959 of file basefun.cpp.

Referenced by derivatives_3d(), lintet::geom_matrix(), and jac_3d().

void dx_bf_lin_wed_3d ( double *  n,
double  z 
)

function computes derivatives of linear base functions on wedge with respect to x

Parameters:
n - array of basis functions
z - natural coordinate

JK, 9.5.2004

Definition at line 1113 of file basefun.cpp.

Referenced by derivatives_3d(), linwedge::geom_matrix(), and jac_3d().

void dx_bf_quad_1d ( double *  n,
double  x 
)

function computes derivatives of quadratic approximation functions with respect of x on bar element

Parameters:
n - array containing approximation functions
x - natural coordinate

Definition at line 47 of file basefun.cpp.

Referenced by derivatives_1d(), barelq3d::geom_matrix(), barelq2d::geom_matrix(), quadbartax::grad_matrix(), quadbart::grad_matrix(), jac1d2d(), jac1d3d(), and jac_1d().

void dx_bf_quad_3_2d ( double *  n,
double  x,
double  y 
)

function computes derivatives of quadratic approximation functions on triangle with respect to xi

Parameters:
n - array containing approximation functions
x,y - natural coordinates

1.4.2002

Definition at line 393 of file basefun.cpp.

Referenced by derivatives_2d(), planeelemsubqt::geom_matrix(), planeelemqt::geom_matrix(), planeelemsubqt::geom_matrix_block(), planeelemqt::geom_matrix_block(), jac2d3d(), and jac_2d().

void dx_bf_quad_4_2d ( double *  n,
double  x,
double  y 
)

function computes derivatives of bi-quadratic base functions on quadrilateral with respect of natural coordinate x

Parameters:
n - array of derivatives of base functions
x,y - natural coodinates

Definition at line 497 of file basefun.cpp.

Referenced by derivatives_2d(), planeelemqq::geom_matrix(), axisymqq::geom_matrix(), axisymqq::geom_matrix_block(), quadquadrilattax::grad_matrix(), quadquadrilatt::grad_matrix(), jac2d3d(), and jac_2d().

void dx_bf_quad_hex_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes derivatives of tri-quadratic base functions on hexahedron with respect of natural coordinate x

Parameters:
n - array of derivatives of base functions
x,y,z - natural coodinates

Definition at line 1398 of file basefun.cpp.

Referenced by derivatives_3d(), quadhex::geom_matrix(), quadhext::grad_matrix(), and jac_3d().

void dx_bf_quad_hexrot_3d ( double *  n,
double  x,
double  y,
double  z 
)

Definition at line 1516 of file basefun.cpp.

Referenced by linhexrot::geom_matrix(), and linhexrot::geom_matrix_shear().

void dx_bf_quad_tet ( double *  n,
double  x,
double  y,
double  z 
)

function computes derivatives of tri-quadratic base functions on tetrahedron with respect of natural coordinate x

Parameters:
n - array of derivatives of base functions
x,y,z - natural coodinates TKo - 11.2008

Definition at line 1019 of file basefun.cpp.

Referenced by derivatives_3d(), quadtet::geom_matrix(), and jac_3d().

void dx_bf_quad_wed_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes derivatives of linear approximation functions on wedge with respect to x

Parameters:
n - array of basis functions
x,y,z - natural coordinates

JK, 19.9.2004

Definition at line 1199 of file basefun.cpp.

Referenced by derivatives_3d(), quadwedge::geom_matrix(), and jac_3d().

void dx_bf_rot_3_2d ( double *  n,
double *  l,
double *  b,
double *  c 
)

function computes derivatives of modified base functions on triangle for element with rotational DOFs with respect of x

Parameters:
n - array of base functions
l - area coordinates
b,c - coefficients of area coordinates

Definition at line 562 of file basefun.cpp.

Referenced by planeelemrotlt::addgeommat(), planeelemrotlt::geom_matrix(), and planeelemrotlt::geom_matrix_block().

void dx_bf_rot_4_2d ( double *  n,
double  x,
double  y,
double *  nx,
double *  ny,
double *  l 
)

function computes derivatives of modified base functions on quadrilateral for element with rotational DOFs with respect of natural coordinate x

Parameters:
n - array of base functions
x,y - natural coordinates
nx,ny - array of x and y components of outer normal vectors
l - array of lengths of element edges

Definition at line 640 of file basefun.cpp.

Referenced by planeelemrotlq::addgeommat(), planeelemrotlq::geom_matrix(), and planeelemrotlq::geom_matrix_block().

void dx_cct ( double *  n,
double *  l,
double *  b,
double *  sx,
double *  sy 
)

function computes derivates of base functions of constant curvature triangle with respect of x (finite element for plate problems)

Parameters:
n - array of base functions
l - area coordinates
b - array of coefficients of area coordinates
sx,sy - arrays of components

Definition at line 723 of file basefun.cpp.

Referenced by cctelem::geom_matrix(), and cctelem::geom_matrix_block().

void dy_bf_lin_3_2d ( double *  n  ) 

function computes derivatives of linear approximation functions with respect to natural coordinate eta

Parameters:
n - array containing derivatives

1.4.2002

Definition at line 360 of file basefun.cpp.

Referenced by derivatives_2d(), jac2d3d(), and jac_2d().

void dy_bf_lin_4_2d ( double *  n,
double  x 
)

function computes derivatives of bi-linear base functions on quadrilateral with respect of natural coordinate y

Parameters:
n - array of derivatives of base functions
x - natural coodinate

Definition at line 461 of file basefun.cpp.

Referenced by planeelemlq::bvectors(), derivatives_2d(), planeelemlq::geom_matrix(), axisymlq::geom_matrix(), planeelemlq::geom_matrix_block(), axisymlq::geom_matrix_block(), quadlineart::grad_matrix(), quadlinaxisym::grad_matrix(), jac2d3d(), and jac_2d().

void dy_bf_lin_hex_3d ( double *  n,
double  x,
double  z 
)

function computes derivatives of tri-linear base functions on hexahedron with respect of natural coordinate y

Parameters:
n - array of derivatives of base functions
x,z - natural coodinates

Definition at line 1322 of file basefun.cpp.

Referenced by linhexrot::bvectors(), linhex::bvectors(), derivatives_3d(), linhexrot::geom_matrix(), linhex::geom_matrix(), linhex::geom_matrix_block(), linhexrot::geom_matrix_shear(), linhext::grad_matrix(), and jac_3d().

void dy_bf_lin_tet ( double *  n  ) 

Definition at line 969 of file basefun.cpp.

Referenced by derivatives_3d(), lintet::geom_matrix(), and jac_3d().

void dy_bf_lin_wed_3d ( double *  n,
double  z 
)

function computes derivatives of linear base functions on wedge with respect to y

Parameters:
n - array of basis functions
z - natural coordinate

JK, 9.5.2004

Definition at line 1131 of file basefun.cpp.

Referenced by derivatives_3d(), linwedge::geom_matrix(), and jac_3d().

void dy_bf_quad_3_2d ( double *  n,
double  x,
double  y 
)

function computes derivatives of quadratic approximation functions on triangle with respect to eta

Parameters:
n - array containing approximation functions
x,y - natural coordinates

1.4.2002

Definition at line 411 of file basefun.cpp.

Referenced by derivatives_2d(), planeelemsubqt::geom_matrix(), planeelemqt::geom_matrix(), planeelemsubqt::geom_matrix_block(), planeelemqt::geom_matrix_block(), jac2d3d(), and jac_2d().

void dy_bf_quad_4_2d ( double *  n,
double  x,
double  y 
)

function computes derivatives of bi-quadratic base functions on quadrilateral with respect of natural coordinate y

Parameters:
n - array of derivatives of base functions
x,y - natural coodinates

Definition at line 517 of file basefun.cpp.

Referenced by derivatives_2d(), planeelemqq::geom_matrix(), axisymqq::geom_matrix(), axisymqq::geom_matrix_block(), quadquadrilattax::grad_matrix(), quadquadrilatt::grad_matrix(), jac2d3d(), and jac_2d().

void dy_bf_quad_hex_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes derivatives of tri-quadratic base functions on hexahedron with respect of natural coordinate y

Parameters:
n - array of derivatives of base functions
x,y,z - natural coodinates

Definition at line 1434 of file basefun.cpp.

Referenced by derivatives_3d(), quadhex::geom_matrix(), quadhext::grad_matrix(), and jac_3d().

void dy_bf_quad_hexrot_3d ( double *  n,
double  x,
double  y,
double  z 
)

Definition at line 1535 of file basefun.cpp.

Referenced by linhexrot::geom_matrix(), and linhexrot::geom_matrix_shear().

void dy_bf_quad_tet ( double *  n,
double  x,
double  y,
double  z 
)

function computes derivatives of tri-quadratic base functions on tetrahedron with respect of natural coordinate y

Parameters:
n - array of derivatives of base functions
x,y,z - natural coodinates TKo - 11.2008

Definition at line 1044 of file basefun.cpp.

Referenced by derivatives_3d(), quadtet::geom_matrix(), and jac_3d().

void dy_bf_quad_wed_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes derivatives of quadratic approximation functions on wedge with respect to y

Parameters:
n - array of basis functions
x,y,z - natural coordinates

JK, 19.9.2004

Definition at line 1226 of file basefun.cpp.

Referenced by derivatives_3d(), quadwedge::geom_matrix(), and jac_3d().

void dy_bf_rot_3_2d ( double *  n,
double *  l,
double *  b,
double *  c 
)

function computes derivatives of modified base functions on triangle for element with rotational DOFs with respect of y

Parameters:
n - array of base functions
l - area coordinates
b,c - coefficients of area coordinates

Definition at line 586 of file basefun.cpp.

Referenced by planeelemrotlt::addgeommat(), planeelemrotlt::geom_matrix(), and planeelemrotlt::geom_matrix_block().

void dy_bf_rot_4_2d ( double *  n,
double  x,
double  y,
double *  nx,
double *  ny,
double *  l 
)

function computes derivatives of modified base functions on quadrilateral for element with rotational DOFs with respect of natural coordinate y

Parameters:
n - array of base functions
x,y - natural coordinates
nx,ny - array of x and y components of outer normal vectors
l - array of lengths of element edges

Definition at line 669 of file basefun.cpp.

Referenced by planeelemrotlq::addgeommat(), planeelemrotlq::geom_matrix(), and planeelemrotlq::geom_matrix_block().

void dy_cct ( double *  n,
double *  l,
double *  c,
double *  sx,
double *  sy 
)

function computes derivates of base functions of constant curvature triangle with respect of y (finite element for plate problems)

Parameters:
n - array of base functions
l - area coordinates
b - array of coefficients of area coordinates
sx,sy - arrays of components

Definition at line 749 of file basefun.cpp.

Referenced by cctelem::geom_matrix(), and cctelem::geom_matrix_block().

void dz_bf_lin_hex_3d ( double *  n,
double  x,
double  y 
)

function computes derivatives of tri-linear base functions on hexahedron with respect of natural coordinate z

Parameters:
n - array of derivatives of base functions
x,y - natural coodinates

Definition at line 1342 of file basefun.cpp.

Referenced by linhexrot::bvectors(), linhex::bvectors(), derivatives_3d(), linhexrot::geom_matrix(), linhex::geom_matrix(), linhex::geom_matrix_block(), linhexrot::geom_matrix_shear(), linhext::grad_matrix(), and jac_3d().

void dz_bf_lin_tet ( double *  n  ) 

Definition at line 979 of file basefun.cpp.

Referenced by derivatives_3d(), lintet::geom_matrix(), and jac_3d().

void dz_bf_lin_wed_3d ( double *  n,
double  x,
double  y 
)

function computes derivatives of linear base functions on wedge with respect to z

Parameters:
n - array of basis functions
x,y - natural coordinates

JK, 9.5.2004

Definition at line 1149 of file basefun.cpp.

Referenced by derivatives_3d(), linwedge::geom_matrix(), and jac_3d().

void dz_bf_quad_hex_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes derivatives of tri-quadratic base functions on hexahedron with respect of natural coordinate z

Parameters:
n - array of derivatives of base functions
x,y,z - natural coodinates

Definition at line 1468 of file basefun.cpp.

Referenced by derivatives_3d(), quadhex::geom_matrix(), quadhext::grad_matrix(), and jac_3d().

void dz_bf_quad_hexrot_3d ( double *  n,
double  x,
double  y,
double  z 
)

Definition at line 1555 of file basefun.cpp.

Referenced by linhexrot::geom_matrix(), and linhexrot::geom_matrix_shear().

void dz_bf_quad_tet ( double *  n,
double  x,
double  y,
double  z 
)

function computes derivatives of tri-quadratic base functions on tetrahedron with respect of natural coordinate z

Parameters:
n - array of derivatives of base functions
x,y,z - natural coodinates TKo - 11.2008

Definition at line 1069 of file basefun.cpp.

Referenced by derivatives_3d(), quadtet::geom_matrix(), and jac_3d().

void dz_bf_quad_wed_3d ( double *  n,
double  x,
double  y,
double  z 
)

function computes derivatives of quadratic approximation functions on wedge with respect to z

Parameters:
n - array of basis functions
x,y,z - natural coordinates

JK, 19.9.2004

Definition at line 1253 of file basefun.cpp.

Referenced by derivatives_3d(), quadwedge::geom_matrix(), and jac_3d().

void plsa ( double *  a,
double *  x,
double *  y,
double  det 
)

function computes a_i coefficients of area-coordinates on triangles L(x,y)_i = a_i + b_i.x + c_i.y

Parameters:
a - coefficients
x,y - node coordinates
det - determinant=2*area

Definition at line 211 of file basefun.cpp.

void plsb ( double *  b,
double *  y,
double  det 
)

function computes b_i coefficients of area-coordinates on triangles L(x,y)_i = a_i + b_i.x + c_i.y

Parameters:
b - coefficients
y - node coordinates
det - determinant=2*area

Definition at line 228 of file basefun.cpp.

Referenced by planeelemrotlt::addgeommat(), trlineart::conductivity_matrix(), trlinaxisym::conductivity_matrix(), planeelemrotlt::geom_matrix(), planeelemlt::geom_matrix(), cctelem::geom_matrix(), axisymlt::geom_matrix(), planeelemrotlt::geom_matrix_block(), cctelem::geom_matrix_block(), axisymlt::geom_matrix_block(), trlineart::internal_fluxes(), trlinaxisym::internal_fluxes(), trlineart::intpointgrad(), trlinaxisym::intpointgrad(), trlineart::l_matrix(), and trlineart::l_t_matrix().

void plsc ( double *  c,
double *  x,
double  det 
)

function computes c_i coefficients of area-coordinates on triangles L(x,y)_i = a_i + b_i.x + c_i.y

Parameters:
c - coefficients
x - node coordinates
det - determinant=2*area

Definition at line 245 of file basefun.cpp.

Referenced by planeelemrotlt::addgeommat(), trlineart::conductivity_matrix(), trlinaxisym::conductivity_matrix(), planeelemrotlt::geom_matrix(), planeelemlt::geom_matrix(), cctelem::geom_matrix(), axisymlt::geom_matrix(), planeelemrotlt::geom_matrix_block(), cctelem::geom_matrix_block(), axisymlt::geom_matrix_block(), trlineart::internal_fluxes(), trlinaxisym::internal_fluxes(), trlineart::intpointgrad(), trlinaxisym::intpointgrad(), trlineart::l_matrix(), and trlineart::l_t_matrix().

void roty_fun ( double *  n,
double  xi,
double  l,
double  kappa 
)

function computes approximation function of rotation of 2D beam element

Parameters:
n - array containing approximation functions
xi - natural coordinate from segment <0;1>
l - length of the beam
kappa - 6.0*E*I/k/G/A/l/l

20.2.2002

Definition at line 128 of file basefun.cpp.

Referenced by beamel2d::bf_matrix(), and beamel2d::geom_matrix().

void vola_3d ( double *  a,
double *  x,
double *  y,
double *  z,
double  det 
)

function computes coefficients a_i of volume coordinates L(x,y,z)_i = a_i + b_i.x + c_i.y + d_i.z

Parameters:
a - array of coefficients
x,y,z - array of node coordinates
det - determinat=6*volume

Definition at line 881 of file basefun.cpp.

void volb_3d ( double *  b,
double *  y,
double *  z,
double  det 
)

function computes coefficients b_i of volume coordinates L(x,y,z)_i = a_i + b_i.x + c_i.y + d_i.z

Parameters:
b - array of coefficients
y,z - array of node coordinates
det - determinat=6*volume

Definition at line 899 of file basefun.cpp.

Referenced by lintett::conductivity_matrix(), lintetrot::geom_matrix(), lintet::geom_matrix_old(), lintetrot::geom_matrix_shear(), lintett::internal_fluxes(), lintett::intpointgrad(), lintett::l_matrix(), and lintett::l_t_matrix().

void volc_3d ( double *  c,
double *  x,
double *  z,
double  det 
)

function computes coefficients c_i of volume coordinates L(x,y,z)_i = a_i + b_i.x + c_i.y + d_i.z

Parameters:
c - array of coefficients
x,z - array of node coordinates
det - determinat=6*volume

Definition at line 917 of file basefun.cpp.

Referenced by lintett::conductivity_matrix(), lintetrot::geom_matrix(), lintet::geom_matrix_old(), lintetrot::geom_matrix_shear(), lintett::internal_fluxes(), lintett::intpointgrad(), lintett::l_matrix(), and lintett::l_t_matrix().

void vold_3d ( double *  d,
double *  x,
double *  y,
double  det 
)

function computes coefficients d_i of volume coordinates L(x,y,z)_i = a_i + b_i.x + c_i.y + d_i.z

Parameters:
d - array of coefficients
x,y - array of node coordinates
det - determinat=6*volume

Definition at line 933 of file basefun.cpp.

Referenced by lintett::conductivity_matrix(), lintetrot::geom_matrix(), lintet::geom_matrix_old(), lintetrot::geom_matrix_shear(), lintett::internal_fluxes(), lintett::intpointgrad(), lintett::l_matrix(), and lintett::l_t_matrix().

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