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  • Publicado : 9 de enero de 2012
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mathematical models, namely the shear-deformable (Timoshenko) model and the shearindeformable (Euler-Bernoulli) model, are presented. Since the Timoshenko beam theory is higher order than theEuler-Bernoulli theory, it is known to be superior in predicting the transient response of the beam. The superiority of the Timoshenko model is more pronounced for beams with a low aspect ratio. It isshown that use of an Euler-Bernoulli based controller to suppress beam vibration can lead to instability caused by the inadvertent excitation of unmodelled modes. BEAM189 is an element suitable foranalyzing slender to moderately stubby/thick beam structures. This element is based on Timoshenko beam theory. Shear deformation effects are included. This element is well-suited for linear, largerotation, and/or large strain nonlinear applications. BEAM189 includes stress stiffness terms, by default, in any analysis with NLGEOM ,ON. The provided stress stiffness terms enable the elements toanalyze flexural, lateral, and torsional stability problems (using eigenvalue buckling or collapse studies with arc length methods). The beam elements are based on Timoshenko beam theory, which is a firstorder shear deformation theory: transverse shear strain is constant through the cross section; that is, cross sections remain plane and undistorted after deformation. BEAM188/BEAM189 elements can beused for slender or stout beams. Due to the limitations of first order shear deformation theory, only moderately "thick" beams may be analyzed. The accuracy in modeling composite shells is goverenedby the first order shear deformation theory (usually referred to as Mindlin/Reissner shell theory). In Euler – Bernoulli beam theory, shear deformations are neglected, and plane sections remainplane and normal to the longitudinal axis. In the Timoshenko beam theory, plane sections still remain plane but are no longer normal to the longitudinal axis. The difference between the normal to the...
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