The local frictional contact problem defined by. More...

#include <fclib.h>

Collaboration diagram for fclib_local:

Public Attributes
struct fclib_matrix *	W
	the matrix W (see mathematical description below) More...

struct fclib_matrix *	V
	the matrix V (see mathematical description below) More...

struct fclib_matrix *	R
	the matrix R (see mathematical description below) More...

double *	mu
	the vector \(\mu\) of coefficient of friction (see mathematical description below) More...

double *	q
	the vector q (see mathematical description below) More...

double *	s
	the vector s (see mathematical description below) More...

int	spacedim
	the dimension , 2 or 3, of the local space at contact (2d or 3d friction contact laws) More...

struct fclib_info *	info
	info on the problem More...

Detailed Description

The local frictional contact problem defined by.

given

a positive semi–definite matrix \({W} \in {\mathrm{I\!R}}^{m \times m}\)
a matrix \({V} \in {\mathrm{I\!R}}^{m \times p}\)
a matrix \({R} \in {\mathrm{I\!R}}^{p \times p}\)
a vector \(q \in {\mathrm{I\!R}}^{m}\),
a vector \(s \in {\mathrm{I\!R}}^{p}\),
a vector of coefficients of friction \(\mu \in {\mathrm{I\!R}}^{n_c}\)

the Mixed 3DFC problem is to find three vectors \(u\in{\mathrm{I\!R}}^m\), \(r\in {\mathrm{I\!R}}^m\) and \(\lambda \in {\mathrm{I\!R}}^p\) denoted by \(\mathrm{M3DFC}(R,V,W,q,s,\mu)\) such that

\begin{eqnarray*}\label{eq:lcp1} *\begin{cases} V^T {r} + R \lambda + s = 0 \\ \ \ \hat u = W {r} + V\lambda + q +\left[ \left[\begin{array}{c} \mu^\alpha \|u^\alpha_T\|\ \ 0 \ \ 0 \end{array}\right]^T, \alpha = 1 \ldots n_c \right]^T \\ \ \ C^\star_{\mu} \ni {\hat u} \perp r \in C_{\mu} \end{cases} \end{eqnarray*}

where the Coulomb friction cone for a contact \(\alpha\) is defined by

\begin{eqnarray*} \label{eq:CCC} C_{\mu^\alpha}^{\alpha} = \{r^\alpha, \|r^\alpha_T \| \leq \mu^\alpha |r^\alpha_N| \} \end{eqnarray*}

and the set \(C^{\alpha,\star}_{\mu^\alpha}\) is its dual.

Definition at line 249 of file fclib.h.