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A UNIFIED TIMOSHENKO BEAM B‐SPLINE RAYLEIGH–RITZ METHOD FOR VIBRATION AND BUCKLING ANALYSIS OF THICK AND THIN BEAMS AND PLATES
Author(s) -
WANG S.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970215)40:3<473::aid-nme75>3.0.co;2-u
Subject(s) - timoshenko beam theory , rotary inertia , rayleigh–ritz method , vibration , buckling , structural engineering , beam (structure) , ritz method , plate theory , isotropy , shear (geology) , materials science , physics , engineering , finite element method , composite material , optics , acoustics
First, the shear‐locking phenomenon in the w ψB k SRRM 1–3 is investigated and the shear‐locking terms are identified in both one‐dimensional beam and two‐dimensional plate analyses. Subsequently the shear‐locking free conditions are proposed and under the guidance of these conditions the Timoshenko beam B‐spline Rayleigh–Ritz method, designated as TB k SRRM, is formulated for vibration analysis of beams based on Timoshenko beam theory and vibration and buckling analysis of isotropic plates or fibre‐reinforced composite laminates based on the first‐order shear deformation plate theory (SDPT). In TB k SRRM the number of degrees of freedom is exactly the same as that when the Bernoulli–Euler beam theory or classical plate theory (CPT) is used. However, the TB k SRRM includes the through‐thickness shearing and rotary inertia effects in full. Several numerical applications are presented and they show that this unified approach is extremely efficient for both thick and thin beams and plates. © 1997 by John Wiley & Sons, Ltd.