An efficient 3D curved beam finite element

Jerzy Rakowski; Przemysław Litewka

Jerzy Rakowski Poznań University of Technology
Przemysław Litewka Poznań University of Technology

Abstract

The purpose of this paper is to create an efficient finite element for the static analysis of 3D arch structures. It is the circural in-plane element with possibility of out-of-plane action. In the element the influences of shear and axial forces on arch displacements are taken into account. The base is the set of exact shape functions, which fulfil the differential equilibrium equation of 3D arch. These shape functions allow us to obtain the exact element stiffness matrix. The element was tested in several numerical examples, results were compared with available analytical solutions and other numerical results. A very good agreement of the results was obtained.

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References

[1] J .-K. Choi, J .-K. Lim. General curved beam elements based on the assumed strain fields. Computers and Structures, 55(3): 379-386, 1995.
[2] P. Litewka, J. Rakowski. An efficient curved beam finite element. International Journal for Numerical Methods in Engineering, 40: 2629-2652, 1997.
[3] P. Litewka, J. Rakowski. The exact thick arch finite element. Computers and Structures, 68: 369- 379, 1998.
[4] S. J. Pantazopoulou. Low-order interpolation functions for curved beams. Journal of Engineering Mechanics, 118(2): 329- 350, 1992.
[5] G. Rakowski, R. Solecki. Curved Bars. Static Calculations (in Polish). Arkady, Warszawa, 1966.