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 w BkSRRM1{3 is investigated and the shear-locking terms are identi ed 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 bre-reinforced composite laminates based on the rst-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 e ects in full. Several numerical applications are presented and they show that this uni ed approach is extremely e cient for both thick and thin beams and plates.