Abstract
Presented herein is a hierarchy of beam elements which include the effects of transverse shear deformation and rotary inertia. Interdependent interpolations are employed for the deflection and bending rotation fields to obtain a family of virgin elements. By imposing a continuous shear constraint condition on each member of the virgin element family, a series of constrained elements can be generated. Stiffness and consistent mass matrices and consistent load vectors are formulated by Gaussian quadrature using formulas for exact integration. These elements exhibit excellent modeling capabilities and suffer no deficiencies in the range of small thickness/length ratios. One important feature of certain constrained elements is that it is possible to use them to explain the essence of the “reduced integration” stiffness matrices that have appeared in the literature.
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