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A scheme for imposing constraints and improving conditioning of structural stiffness matrices
Author(s) -
Martín F.,
BenaventCliment A.,
Gallego R.
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1181
Subject(s) - stiffness matrix , direct stiffness method , lagrange multiplier , stiffness , constraint (computer aided design) , matrix (chemical analysis) , finite element method , coefficient matrix , constraint algorithm , kinematics , mathematical optimization , mathematics , scheme (mathematics) , mass matrix , minification , structural engineering , mathematical analysis , engineering , geometry , physics , classical mechanics , materials science , eigenvalues and eigenvectors , quantum mechanics , neutrino , nuclear physics , composite material
This paper presents a scheme for incorporating kinematic constraints (rod constraint, diaphragm constraint) in beam‐type finite element models. The formulation employs minimization using Lagrange multipliers and does not require the arrangement of the coefficient matrix. Unlike the classical formulation—which imposes the constraints after assembling the global stiffness matrix of the structure—in the proposed scheme the constraints are applied twice: first to the stiffness matrix of the individual elements before assembly and then to the global stiffness matrix of the structure after assembly. As a result, the condition number of the coefficient matrix is remarkably reduced. The validity of the proposed scheme is demonstrated through numerical examples. Copyright © 2008 John Wiley & Sons, Ltd.