ADAPTATION OF THE LANCZOS ALGORITHM FOR THE SOLUTION OF BUCKLING EIGENVALUE PROBLEMS

  • ALFREDO R. DE FARIA Instituto Tecnológico de Aeronáutica, Department of Mechanical Engineering, São José dos Campos, SP, Brasil

Abstract

AN ADAPTATION OF THE CONVENTIONAL LANCZOS ALGORITHM IS PROPOSED TO SOLVE THE GENERAL SYMMETRIC EIGENVALUE PROBLEM [K]{X} = Λ[KG]{X} IN THE CASE WHEN THE GEOMETRIC STIFFNESS MATRIX [KG] IS NOT NECESSARILY POSITIVE-DEFINITE. THE ONLY REQUIREMENT FOR THE NEW ALGORITHM TO WORK IS THAT MATRIX [K] MUST BE POSITIVE-DEFINITE. FIRSTLY, THE ALGORITHM IS PRESENTED FOR THE STANDARD SITUATION WHERE NO SHIFTING IS ASSUMED. SECONDLY, THE ALGORITHM IS EXTENDED TO INCLUDE SHIFTING SINCE THIS PROCEDURE MAY BE IMPORTANT FOR ENHANCED PRECISION OR ACCELERATION OF CONVERGENCE RATES. NEITHER VERSION OF THE ALGORITHM REQUIRES MATRIX INVERSION, BUT MORE RESOURCES IN TERMS OF MEMORY ALLOCATION ARE NEEDED BY THE VERSION WITH SHIFTING.

Author Biography

ALFREDO R. DE FARIA, Instituto Tecnológico de Aeronáutica, Department of Mechanical Engineering, São José dos Campos, SP, Brasil

Associate Professor in the department of mechanical engineering. CNPq fellowship holder (PQ 1D). Publications: 32 papers in refereed international journals and 48 papers in refereed international conferences.

Published
2017-09-30
Section
Articles