A UNIFIED TIMOSHENKO BEAM B‐SPLINE RAYLEIGH–RITZ METHOD FOR VIBRATION AND BUCKLING ANALYSIS OF THICK AND THIN BEAMS AND PLATES

First, the shear-locking phenomenon in the wψBkSRRM1–3 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 TBkSRRM, 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 TBkSRRM 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 TBkSRRM 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.

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