Abstract
The efficiency and accuracy of the elements proposed by the Finite Element Method (FEM) considerably depend on the interpolating functions, namely shape functions, used to formulate the displacement field within an element. In this paper, a new insight is proposed for derivation of elements from a mechanical point of view. Special functions namely Basic Displacement Functions (BDFs) are introduced which hold pure structural foundations. Following basic principles of structural mechanics, it is shown that exact shape functions for non-prismatic thin curved beams could be derived in terms of BDFs. Performing a limiting study, it is observed that the new curved beam element successfully becomes the straight Euler-Bernoulli beam element. Carrying out numerical examples, it is shown that the element provides exact static deformations. Finally efficiency of the method in free vibration analysis is verified through several examples. The results are in good agreement with those in the literature.
Highlights
Curved structural members are frequently used by civil and mechanical engineers in industrial applications
Considering the effects of shear deformation and rotary inertia dramatically increases the complexity of analysis; on the other hand, ignoring these effects may lead to significant inaccuracies for thick curved beams and even higher modes of vibration for thin curved beams
Comparing Eq (13) with the vector of equivalent nodal forces proposed by Finite Element Method (FEM) i.e. Eq (4a); the exact shape functions are derived in terms of Basic Displacement Functions (BDFs) as
Summary
Curved structural members are frequently used by civil and mechanical engineers in industrial applications. Later Raveendranath et al [32] developed a three-noded curved beam element assuming a quartic polynomial as a priori for the flexural rotation and the other interpolation functions were obtained via solving force-moment and moment-shear equilibrium equations simultaneously. Dawe [5,6] studied various curved beam elements with different polynomial orders for interpolation of tangential and radial displacements He reported that a quintic-quintic model converged faster and gave more accurate results for various configurations of arches. Yang et al [7] derived the governing differential equations for free in-plane vibrations of general curved beam elements They used Galerkin finite element method with Lagrangian-type shape functions. Combining the concepts of flexibility and stiffness methods, a step-by-step procedure is outlined to derive exact shape functions for interpolation of the tangential and radial displacements of a general curved beam element. Several numerical examples are provided to show the efficiency of the method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
