ISOGEOMETRIC METHODS IN DYNAMIC ANALYSIS OF CURVED BEAMS INCLUDING WARPING AND DISTORTIONAL EFFECTS

Abstract eng:
In this research effort, Isogeometric tools are employed either in the Analog Equation Method (AEM), a boundary element based method, or in the Finite Element Method for the analysis of curved homogenous beams of arbitrary cross section (thin- or thick- walled) taking into account nonuniform warping, shear deformation effects (shear lag due to both flexure and torsion) and distortion. A set of distortional (in-plane warping) parameters have been considered and multiplied by the corresponding distortional functions, which constitute together with the warping ones the Navier equations for 2-D elasticity problem. Onedimensional boundary value problems described by second-order differential equations are formulated with respect to the displacement and rotation components as well as to the independent in- and out-of-plane warping parameters and solved. The in- and out-of-plane warping functions as well as the geometric constants including the additional ones due to warping and distortion (stiffness matrices) are evaluated employing a pure BEM approach. In order to derive the differential equations of motion with respect to the kinematical components, the terms of inertia contributions have to be added in the previous ones and, thus, the spatial mass matrix can be derived. Numerical results are worked out to illustrate the method, designate its efficiency, accuracy and computational cost, as well as verify its integrity comparing with the results of 3-D FEM (Finite Element Method) models.

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