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Functions | |
| double | arclengthrv (long lcid, nonlinman *nlman, double *ra, double *fa, double *fc, double *fp) |
| void | assamble_attained_load_vector (double *fa, double *fc, double *fp, long n, double lambda, nonlinman *nlman) |
| long | assemble_stiffness_matrix (long lcid, long i, long j, long li) |
| The function assembles the stiffness matrix in dependence on the setup of the arclength method. | |
| long | check_divergence (nonlinman *nlman, matrix &lsm_a, vector &lsm_r, vector &lsm_l, long j, double norf) |
| double | displincr (double *dr1, double *dr2, long n) |
| void | quadeqcoeff (double *ddr, double *v, long n, double ddlambda, double psi, double norfp, double dl, double &a0, double &a1, double &a2) |
| void | seldofinit () |
| The function initializes selected dofs used for the arclength method controling. | |
| void | update_attained_load_vector (double *fa, double *fp, long n, double lambda, double dlambda, nonlinman *nlman) |
| double arclengthrv | ( | long | lcid, | |
| nonlinman * | nlman, | |||
| double * | ra, | |||
| double * | fa, | |||
| double * | fc, | |||
| double * | fp | |||
| ) |
The function solves system of nonlinear algebraic equations by the arc-length method. This method was modified to reach the given value rlambda of the lambda parameter. Rlambda value is reached with required error errl. Only one right hand side vector is supported with respect to nonlinearity and absence of superposition. Up to rlambda value the constant load vector is treated as proportional and then as constant. Proportional vector grows until the nial number of steps is reached.
Notation of internal variables:
| lcid | - load case id | |
| nlman | - pointer to structure conatining setup of the solver | |
| ra | - vector of attained displacements | |
| fa | - attained load vector | |
| fc | - vector of constant load | |
| fp | - vector of proportional load |
Created by JK, 16.8.2001 Rewritten by TKo, JK 08.2011
Definition at line 29 of file arclengthjk.cpp.
References adapt_psi_coeff(), addmultv(), addv(), assemble_attained_load_vector(), assemble_stiffness_matrix(), check_divergence(), compute_req_val(), copymultv(), copyv(), determine_dlambda(), displincr(), nonlinman::dlal, nonlinman::dlam, nonlinman::dlmaxal, nonlinman::dlminal, nonlinman::erral, nonlinman::errl, f, fillm(), fillv(), fullmethod, Gtm, probdesc::hdbcont, mechmat::initmaterialmodels(), internal_forces(), probdesc::jstep, nonlinman::max_tot_al, Mespr, Mm, mode, Mp, Ndofm, nonlinman::nial, nonlinman::niilal, probdesc::nlman, normv(), off, on, Out, print_close(), print_flush(), print_init(), print_step(), nonlinman::psial, hdbcontr::restore_stat(), hdbcontr::save_stat(), Smat, slesolv::solve_system(), solver_restore(), probdesc::ssle, subv(), update_attained_load_vector(), mechmat::updateipval(), and probdesc::zero.
Referenced by general_epressure(), and general_epressure_varsup().
| void assamble_attained_load_vector | ( | double * | fa, | |
| double * | fc, | |||
| double * | fp, | |||
| long | n, | |||
| double | lambda, | |||
| nonlinman * | nlman | |||
| ) |
The function assembles the attained load vector fa. It depends on the two load vectors fc, fp, attained load coefficient lambda and the setup specified in the nlman.
| fa | - array of components of attained load vector | |
| fc | - array of the constant load vector which is added without lambda multiplier. | |
| fp | - array of proportional load vector which is added multiplied by lambda multiplier usually. In certain cases, the vector fp has to be applied until the required value lambdar_p is attained and than the increasing of load level stops. | |
| n | - number of components of fa, fc and fp | |
| lambda | - attained value of the load coefficient | |
| nlman | - structure with setup of handling of lambda and lambda tresholds |
Created by TKo, 08.2011
Definition at line 633 of file arclengthjk.cpp.
References addmultv(), and on.
| long assemble_stiffness_matrix | ( | long | lcid, | |
| long | i, | |||
| long | j, | |||
| long | li | |||
| ) |
The function assembles the stiffness matrix in dependence on the setup of the arclength method.
function assembles stiffness matrix if needed
The function assembles the stiffness matrix it depends on the variable Mp->nlman->stmat for possible values (see alias.h).
| lcid | - load case id | |
| i | - index in outer loop | |
| j | - index in inner loop | |
| li | - lower index of the outer loop = number of the first outer increment li=0 if the computation starts from the initial state li>0 if the computation starts from backup |
JK, TKo, 30.8.2010
Definition at line 480 of file arclengthjk.cpp.
| long check_divergence | ( | nonlinman * | nlman, | |
| matrix & | lsm_a, | |||
| vector & | lsm_r, | |||
| vector & | lsm_l, | |||
| long | j, | |||
| double | norf | |||
| ) |
The function performs the divergence check of the inner loop if it is required in the nlman setup. The divergence is detected with help of the least square method where the quadratic approximaton of the error/step_id curve is performed. If the minimum of the approximing quadratic function is exceeded the divergence of the iteration process is assumed and signalized by the nonzero return value. The minimum number of steps of the inner loop is performed depending on the nlman->div_min_steps setup but at least three steps has to be performed for the correct approximation.
| nlman | - pointer to the structure with the setup of the nonlinear solver | |
| lsm_a | - matrix used for the least square method. It will be used for the storage of contributions from the particular inner loop steps. | |
| lsm_r | - right hand side for the least square method. It will be used for the storage of contributions from the particular inner loop steps. | |
| lsm_l | - left hand side vector (unknown parameters of quadratic function) | |
| j | - inner loop step id | |
| norf | - error norm (norm of unbalanced forces) |
| 0 | - no divergence detected | |
| 1 | - divergence was detected |
Created by TKo, 08.2011
Definition at line 707 of file arclengthjk.cpp.
References nonlinman::check_div, nonlinman::div_min_steps, lsm_quad(), Mp, on, and probdesc::zero.
Referenced by arclengthrv().
| double displincr | ( | double * | dr1, | |
| double * | dr2, | |||
| long | n | |||
| ) |
The function computes square of generalized norm of vector of displacemnt increments. The function returns either square of vector norm computed from the selected componets or it returns increment of distance between selected nodes. It is used in the arclength method.
| dr1 | - array with components of the first vector of displacement increments | |
| dr2 | - array with components of the second vector of displacement increments | |
| n | - number of components of displincr array |
Created by JK,
Definition at line 741 of file arclengthjk.cpp.
References alldofs, nonlinman::displnorm, Mp, probdesc::nlman, nodesdistincr, nonlinman::nsdofal, nonlinman::nxal, nonlinman::nyal, nonlinman::nzal, print_err(), nonlinman::probdimal, nonlinman::seldofal, seldofs, seldofscoord, selecnodes, and ss().
| void quadeqcoeff | ( | double * | ddr, | |
| double * | v, | |||
| long | n, | |||
| double | ddlambda, | |||
| double | psi, | |||
| double | norfp, | |||
| double | dl, | |||
| double & | a0, | |||
| double & | a1, | |||
| double & | a2 | |||
| ) |
Function computes coefficients of the quadratic equation used in the arclength method. The coefficients are computed with respect to type of load/displacement control.
| ddr | - increment of load coefficient lambda for the given step | |
| v | - vector of displacement increments | |
| n | - total number of DOFs (i.e. size of ddr and v arrays) | |
| ddlambda | - correction of increment of load coefficient lambda | |
| psi | - proportional weight coeffient (swithces between load/displacement control) | |
| norfp | - norm of proportional load vector | |
| dl | - length of arc | |
| a0 | - zero order coefficient (output) | |
| a1 | - first order coefficient (output) | |
| a2 | - second order coefficient (output) |
Created by JK,
The function determines increment of lambda (delta lambda).
| ddr | - Delta r + u | |
| u | - u = K^{-1}*(fa-fi) | |
| v | - v = K^{-1}*fp | |
| ddrprev | - Delta r (not updated by the vector u) | |
| n | - number of unknowns | |
| ddlambda | - Delta lambda | |
| psi | - proportional coefficient between load and displacement vectors | |
| norfp | - the norm of proportional vector | |
| dl | - length of the arc | |
| dlambda | - delta lambda (output of this function) | |
| stop | - indicator of end of iteration (output of this function) | |
| nlman | - pointer to structure with arclength setup (it is used for full arclength method) | |
| gm | - pointer to structure with the factorised stiffness matrix (it is used for full arclength method) |
Created by JK, 30.8.2010
The function modifies the psi coefficient according to the ddlambda increment adaptively. If the increment decreases comparing to the initial/reference ddlambda increment (ddlamda0) than the value should be also decreased and thus the arclength is controlled rather by the displacements than by the load. The initial/reference value of the load increment ddlambda0 and proportional coefficient psi0 are updated at the beginning of the main iteration loop and if the ddlambda changes the sign comparing to the ddlambda 0 (peak point of loading curve).
| i | - step id | |
| ddlambda | - actual increment of the load coefficeint lambda | |
| ddlambda0 | - initial/reference value of the load coefficeint lambda increment (input/output parameter) | |
| psi0 | - initial/reference value of the proportional coefficeint (input/output parameter) | |
| psi | - actual value of the proportional coefficeint (input/output parameter) |
Created by Tomas Koudelka 07.2011
Definition at line 810 of file arclengthjk.cpp.
References adapt_psi_coeff(), alldofs, determine_dlambda(), displincr(), nonlinman::displnorm, nonlinman::dlam, fullmethod, linearizedmeth, maxvalue, minangle, minvalue, Mp, probdesc::nlman, nodesdistincr, nodetermination, print_err(), quadeqcoeff(), seldofs, seldofscoord, selecnodes, sgn(), and solv_polynom_2().
| void seldofinit | ( | ) |
The function initializes selected dofs used for the arclength method controling.
The function initializes dof numbers for the particular types of displacement control. It is used in the arclength method.
Created by JK,
Definition at line 549 of file arclengthjk.cpp.
References alldofs, nonlinman::displnorm, mechtop::give_dof(), mechtop::give_ndofn(), gtopology::gnodes, Gtm, length(), Mp, Mt, probdesc::nlman, nodesdistincr, nonlinman::nsdofal, nonlinman::nsnal, nonlinman::nxal, nonlinman::nyal, nonlinman::nzal, nonlinman::seldofal, seldofs, seldofscoord, selecnodes, nonlinman::selnodal, gnode::x, gnode::y, and gnode::z.
| void update_attained_load_vector | ( | double * | fa, | |
| double * | fp, | |||
| long | n, | |||
| double | lambda, | |||
| double | dlambda, | |||
| nonlinman * | nlman | |||
| ) |
The function updates the attained load vector fa. It depends on the two load vectors fc, fp, attained load coefficient lambda, load coefficient increment and the setup specified in the nlman.
| fa | - array of components of attained load vector | |
| fp | - array of proportional load vector which is added multiplied by lambda multiplier usually. In certain cases, the vector fp has to be applied until the required value lambdar_p is attained and than the increasing of load level stops. | |
| n | - number of components of fa, fc and fp | |
| lambda | - attained value of the load coefficient | |
| dlambda | - added lambda increment | |
| nlman | - structure with setup of handling of lambda and lambda tresholds |
Created by TKo, 08.2011
Definition at line 662 of file arclengthjk.cpp.
References addmultv(), and on.
Referenced by arclengthrv().
1.6.2