I understand how it works in single DOF system. But, how to build the incremental stiffness\damping matix for nonlinear analysis of nDOFs structures? There is no practice in the book except the fomulation in the attached file.
https://programmersought.com/article/86259165983/
http://www.scientificlib.com/en/Mathematics/LX/NewmarkBetaMethod.html
https://in.mathworks.com/matlabcentral/fileexchange/71007-newmark-beta-method-for-nonlinear-single-dof-systems
https://docs.plm.automation.siemens.com/data_services/resources/nxnastran/12/help/tdoc/en_US/pdf/bas_nonlinear.pdf
https://www.semanticscholar.org/paper/Incremental-Stiffness-Method-for-Finite-Element-of-McNamara-Marcal/fa82b6d2e7b993a61e132ba571567f6080f4ff57
Stiffness and matrix for each state will be computed from the current displacement and element forces conditions.
For linear model, damping matrix can be computed from Raleygh formula.
But for nonlinear model, the damping matrix is not a constant because it depends on the stiffness matrix, so it must be changed accordingly. Or it can be estimated as a constant matrix.
Alternatively we can use element with damping feature. In this case, there is no need to recalculate the damping matrix, because it will be done automatically.
Dear Every Body
May be this link also can help as the reference in using damping for inelastic analysis.
https://opensees.berkeley.edu/wiki/index.php/Rayleigh_Damping_Command
Article Problems encountered from the use (or misuse) of Rayleigh damping
Best Regards
- Badges
- Science topic
- Similar topics
- Biological Science
- Physiology
- Physiological Processes
- Stress