Flexural Subsidence


Functions

void subside_grid_load (Eh_dbl_grid w, Eh_dbl_grid v_0, double eet, double y)
void subside_point_load (Eh_dbl_grid g, double load, double h, double E, int i_load, int j_load)
 Solve the flexure equation for a point load.
void subside_half_plane_load (Eh_dbl_grid g, double load, double h, double E)
 Solve the flexure equation for a half-plane load.
double get_flexure_parameter (double h, double E, gssize n_dim)
 Calculate the flexure parameter.

Function Documentation

double get_flexure_parameter ( double  h,
double  E,
gssize  n_dim 
)

Calculate the flexure parameter.

The flexure parameter is defined as,

\[ \lambda \equiv \cases{ \root 4 \of { \rho_m g \over 4 D },&$n=1$\cr \root 4 \of { \rho_m g \over D },&$n=2$\cr} \]

Parameters:
h The effective elastic thickness
E Young's modulus
n_dim The number of spatial dimensions (1 or 2)

Definition at line 213 of file subside.c.

References eh_require, sed_gravity(), and sed_rho_mantle().

void subside_grid_load ( Eh_dbl_grid  w,
Eh_dbl_grid  v_0,
double  eet,
double  y 
)

Definition at line 52 of file subside.c.

References Subside_data::eet, eh_dbl_grid_add(), eh_dbl_grid_data(), eh_dbl_grid_set(), eh_dbl_grid_val(), eh_free, eh_grid_destroy(), eh_grid_dup(), eh_grid_n_el(), eh_grid_n_x(), eh_grid_n_y(), eh_new, eh_require, Subside_data::id, N_THREADS, subside_helper(), subside_point_load(), Subside_data::v_0, and Subside_data::y.

Referenced by run_isostasy().

void subside_half_plane_load ( Eh_dbl_grid  g,
double  load,
double  h,
double  E 
)

Solve the flexure equation for a half-plane load.

The solution for a half-plane load is,

\[ w(r) = {q \over \rho_m g } e^{ -\lambda r } \cos (\lambda r) \]

where $ r $ is the distance from the edge of the load.

The load is assumed to begin on the right-hand edge of the grid and continue to infinity.

Note:
Currently this function only operates on 1D grids. If a 2D grid is used, this function silently does nothing.
Parameters:
g The grid to subside
load The load
h The effective elastic thickness
E Young's modulus
Todo:
This needs to be extended to 2D.

Definition at line 180 of file subside.c.

References eh_dbl_grid_data(), eh_grid_n_x(), eh_grid_n_y(), eh_grid_y(), eh_require, get_flexure_parameter(), sed_gravity(), and sed_rho_mantle().

void subside_point_load ( Eh_dbl_grid  g,
double  load,
double  h,
double  E,
int  i_load,
int  j_load 
)

Solve the flexure equation for a point load.

\[ w(x) = {q \lambda \over 2 \rho_m g} e^{ -\lambda x } \left( \cos (\lambda x) + \sin (\lambda x) \right) \]

Parameters:
g The grid to subside
load The load
h The effective elastic thickness
E Young's modulus
i_load The x-index of the point load
j_load The y-index of the point load

Definition at line 136 of file subside.c.

References eh_dbl_grid_data(), eh_grid_n_x(), eh_grid_n_y(), eh_grid_x(), eh_grid_y(), eh_kei_0(), get_flexure_parameter(), M_PI, sed_gravity(), and sed_rho_mantle().


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