Publicación: A LOCKING-FREE FINITE ELEMENT METHOD FOR THE BUCKLING PROBLEM OF A NON-HOMOGENEOUS TIMOSHENKO BEAM
Fecha
2011
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ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
Resumen
THE AIM OF THIS PAPER IS TO DEVELOP A FINITE ELEMENT METHOD WHICH ALLOWS COMPUTING THE BUCKLING COEFFICIENTS AND MODES OF A NON-HOMOGENEOUS TIMOSHENKO BEAM. STUDYING THE SPECTRAL PROPERTIES OF A NON-COMPACT OPERATOR, WE SHOW THAT THE RELEVANT BUCKLING COEFFICIENTS CORRESPOND TO ISOLATED EIGENVALUES OF FINITE MULTIPLICITY. OPTIMAL ORDER ERROR ESTIMATES ARE PROVED FOR THE EIGENFUNCTIONS AS WELL AS A DOUBLE ORDER OF CONVERGENCE FOR THE EIGENVALUES USING CLASSICAL ABSTRACT SPECTRAL APPROXIMATION THEORY FOR NON-COMPACT OPERATORS. THESE ESTIMATES ARE VALID INDEPENDENTLY OF THE THICKNESS OF THE BEAM, WHICH LEADS TO THE CONCLUSION THAT THE METHOD IS LOCKING-FREE. NUMERICAL TESTS ARE REPORTED IN ORDER TO ASSESS THE PERFORMANCE OF THE METHOD.
