P. Raveendranath et al., Free vibration of arches using a curved beam element based on a coupled polynomial displacement field, COMPUT STRU, 78(4), 2000, pp. 583-590
The performance of a curved beam finite element with coupled polynomial dis
tributions for normal displacement (w) and tangential displacement (u) is i
nvestigated for in-plane flexural vibration of arches. A quartic polynomial
distribution for u is derived from an assumed cubic polynomial field for M
t using force-moment equilibrium equations. The coupling of these displacem
ent fields makes it possible to express the strain held in terms of only si
x generalized degrees of freedom leading to a simple two-node element with
three degrees of freedom per node. Numerical performance of the element is
compared with that of the other curved beam elements based on independently
assumed field polynomials. The formulation is shown to be free from any sp
urious constraints in the limit of inextensional flexural vibration modes a
nd hence does not exhibit membrane locking. The resulting well-conditioned
stiffness matrix with consistent mass matrix shows excellent convergence of
natural frequencies even for very thin deep arches and higher vibrational
modes. The accuracy of the element for extensional flexural motion is also
demonstrated. (C) 2000 Elsevier Science Ltd. All rights reserved.