Extracting the left and right critical eigenvectors from the LDU-decomposed non-symmetric Jacobian matrix in stability problems

摘要: In the previous publications of authors, an eigenanalysis-free computational procedure has been proposed to extract bifurcation buckling mode(s) from LDL T -decomposed symmetric stiffness matrix in vicinity a stability point. Any eigensolver, for instance, inverse iteration or subspace method, is not necessary. The verified numerical examples and well works multiple clustered problems too. This present paper will extend LDU-decomposed non-symmetric Jacobian matrix, which both left right critical eigenvectors relevant point may be extracted similar way. idea mathematical totally independent physical problem solved, so that it applicable any square including plasticity with non-associated flow rules, contact fluid-structure interaction. linear-algebraic background eigenvalue firstly described. then mention role play analysis LDU-procedure proposed. Numerical elastoplastic are illustrated verification discussion. APPENDICES, bench model visualizes mechanical meaning singular vectors rectangular matrix.