siconos.fclib

Module documentation

class siconos.fclib.fclib_info

Bases: object

This structure allows the user to enter a problem information as a title, a short description and known mathematical properties of the problem

property title

title of the problem

property description

short decription of the problem

property math_info

known properties of the problem (existence, uniqueness, …)

class siconos.fclib.fclib_matrix_info

Bases: object

This structure allows the user to enter a description for a given matrix (comment, conditionning, determinant, rank.) if they are known.

property comment

comment on the matrix properties

property conditioning

property determinant

property rank

class siconos.fclib.fclib_matrix

Bases: object

matrix in compressed row/column or triplet form

property nzmax

maximum number of entries

property m

number of rows

property n

number of columns

property p

row indices (size nz)

Type:

compressed

Type:

row (size m+1) or column (size n+1) pointers; triplet

property i

column indices (size nz)

Type:

compressed

Type:

column or row indices, size nzmax; triplet

property x

numerical values, size nzmax

property nz

# of entries in triplet matrix, -1 for compressed columns, -2 for compressed rows

property info

info for this matrix

class siconos.fclib.fclib_global

Bases: object

The global frictional contact problem defined by

Given

• a symmetric positive definite matrix \({M} \in {\mathrm{I\!R}}^{n \times n}\)

• a vector \({f} \in {\mathrm{I\!R}}^n\),

• a matrix \({H} \in {\mathrm{I\!R}}^{n \times m}\)

• a matrix \({G} \in {\mathrm{I\!R}}^{n \times p}\)

• a vector \(w \in {\mathrm{I\!R}}^{m}\),

• a vector \(b \in {\mathrm{I\!R}}^{p}\),

• a vector of coefficients of friction \(\mu \in {\mathrm{I\!R}}^{n_c}\)

the Global Mixed 3DFC problem is to find four vectors \({v} \in {\mathrm{I\!R}}^n\), \(u\in{\mathrm{I\!R}}^m\), \(r\in {\mathrm{I\!R}}^m\) and \(\lambda \in {\mathrm{I\!R}}^p\) denoted by \(\mathrm{GM3DFC}(M,H,G,w,b,\mu)\) such that

\[\begin{split}\begin{cases} M v = {H} {r} + G\lambda + {f} \\ \\ G^T v +b =0 \\ \ \hat u = H^T v + w +\left[ \left[\begin{array}{c} \mu \|u^\alpha_T\| \\ 0 \\ 0 \end{array}\right]^T, \alpha = 1 \ldots n_c \right]^T \\ \\ C^\star_{\mu} \ni {\hat u} \perp r \in C_{\mu} \end{cases}\end{split}\]

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

\[C_{\mu^\alpha}^{\alpha} = \{r^\alpha, \|r^\alpha_T \| \leq \mu^\alpha |r^\alpha_N| \}\]

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

property M

the matrix M (see mathematical description below)

property H

the matrix M (see mathematical description below)

property G

the matrix M (see mathematical description below)

property mu

the vector \(\mu\) of coefficient of friction (see mathematical description below)

property f

the vector f (see mathematical description below)

property b

the vector b (see mathematical description below)

property w

the vector w (see mathematical description below)

property spacedim

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

property info

info on the problem

class siconos.fclib.fclib_global_rolling

Bases: object

The global rolling frictional contact problem defined by

Given

• a symmetric positive definite matrix \({M} \in {\mathrm{I\!R}}^{n \times n}\)-

• a vector \({f} \in {\mathrm{I\!R}}^n\) ,

• a matrix \({H} \in {\mathrm{I\!R}}^{n \times m}\)

• a matrix \({G} \in {\mathrm{I\!R}}^{n \times p}\)

• a vector \(w \in {\mathrm{I\!R}}^{m}\) ,

• a vector \(b \in {\mathrm{I\!R}}^{p}\) ,

• a vector of coefficients of friction \(\mu \in {\mathrm{I\!R}}^{n_c}\)

• a vector of coefficients of rolling friction \(\mu_r \in {\mathrm{I\!R}}^{n_c}\)

the Global Mixed 3DFC problem is to find four vectors \({v} \in {\mathrm{I\!R}}^n\), \(u\in{\mathrm{I\!R}}^m\) , \(r\in {\mathrm{I\!R}}^m\) and \(\lambda \in {\mathrm{I\!R}}^p\) denoted by \(\mathrm{GM3DFC}(M,H,G,w,b,\mu)\) such that

\[\begin{split}\begin{cases} M v = {H} {r} + G\lambda + {f} \\ \\ G^T v +b =0 \\ \\ \hat u = H^T v + w +\left[ \left[\begin{array}{c} \mu \|u^\alpha_T\|\\ 0 \\ 0 \end{array}\right]^T, \alpha = 1 \ldots n_c \right]^T \\ \\ C^\star_{\mu,\mu_r} \ni {\hat u} \perp r \in C_{\mu,\mu_r} \end{cases}\end{split}\]

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

\[C_{\mu^\alpha}^{\alpha} = \{r^\alpha, \|r^\alpha_T \| \leq \mu^\alpha |r^\alpha_N| \}\]

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

property M

the matrix M (see mathematical description below)

property H

the matrix M (see mathematical description below)

property G

the matrix M (see mathematical description below)

property mu

the vector \(\mu\) of coefficient of friction (see mathematical description below)

property mu_r

the vector \(\mu\) of rolling coefficient of friction (see mathematical description below)

property f

the vector f (see mathematical description below)

property b

the vector b (see mathematical description below)

property w

the vector w (see mathematical description below)

property spacedim

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

property info

info on the problem

class siconos.fclib.fclib_local

Bases: object

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

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

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

\[C_{\mu^\alpha}^{\alpha} = \{r^\alpha, \|r^\alpha_T \| \leq \mu^\alpha |r^\alpha_N| \}\]

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

property W

the matrix W (see mathematical description below)

property V

the matrix V (see mathematical description below)

property R

the matrix R (see mathematical description below)

property mu

the vector \(\mu\) of coefficient of friction (see mathematical description below)

property q

the vector q (see mathematical description below)

property s

the vector s (see mathematical description below)

property spacedim

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

property info

info on the problem

class siconos.fclib.fclib_solution

Bases: object

A solution or a guess for the frictional contact problem.

This structure allows to store a solution vector of a guess vector for the various frictional contact problems.

property v

global velocity (or position/displacement for quasi-static problems) solution vector

property u

local velocity (or position/displacement for quasi-static problems) solution vector

property r

local contact forces (or impulses) solution vector

property l

multiplier for equlity constraints ( \(\lambda\) ) solution vector

siconos.fclib.fclib_write_global(problem, path)

write global problem

Return type:

int

Returns:

1 on success, 0 on failure

siconos.fclib.fclib_write_local(problem, path)

write local problem

Return type:

int

Returns:

1 on success, 0 on failure

siconos.fclib.fclib_write_global_rolling(problem, path)

write global rolling problem

Return type:

int

Returns:

1 on success, 0 on failure

siconos.fclib.fclib_write_solution(solution, path)

write solution

Return type:

int

Returns:

1 on success, 0 on failure

siconos.fclib.fclib_write_guesses(number_of_guesses, guesses, path)

write initial guesses

Return type:

int

Returns:

1 on success, 0 on failure

siconos.fclib.fclib_read_global(path)

read global problem

Return type:

fclib_global

Returns:

problem on success; NULL on failure

siconos.fclib.fclib_read_local(path)

read local problem

Return type:

fclib_local

Returns:

problem on success; NULL on failure

siconos.fclib.fclib_read_global_rolling(path)

read global rolling problem

Return type:

fclib_global_rolling

Returns:

problem on success; NULL on failure

siconos.fclib.fclib_read_solution(path)

read solution

Return type:

fclib_solution

Returns:

solution on success; NULL on failure

siconos.fclib.fclib_read_guesses(path, number_of_guesses)

read initial guesses

Return type:

fclib_solution

Returns:

vector of guesses on success; NULL on failure output number of guesses in the variable pointed by ‘number_of_guesses’

siconos.fclib.fclib_delete_global(problem)

delete global problem

siconos.fclib.fclib_delete_local(problem)

delete local problem

siconos.fclib.fclib_delete_global_rolling(problem)

delete global rolling problem

siconos.fclib.fclib_delete_solutions(data, count)

delete solutions or guesses

siconos.fclib.fclib_create_int_attributes_in_info(path, attr_name, attr_value)

create and set attributes of tyoe int in info