engleski

A simple and efficient three-node planar curved beam element based on linked interpolation

We present a new three-node Timoshenko curved- beam finite element for in-plane actions constructed on expanded linked interpolation for a straight beam. Only the displacements and the rotation of the cross-section are interpolated and the element is formulated in a pure displacement-based fashion. At first the displacement fields are enriched in polynomial order to the quartic form associated to two pairs of internal bubble parameters. Then the shear strain constraints are enforced on the displacement interpolations and this parameters are expressed in terms of the rotation degrees of freedom resulting in a new linked interpolation for a curved beam element. At the same time the geometry is approximated using Lagrangean interpolation, so that the element- stiffness assembly is very simple and can easily be implemented in a computer code. The beam kinematics is defined using the global displacement variables in contrast to the commonly used displacement unknowns in the local coordinates, thus avoiding the coordinate transformation for the nodal degrees of freedom. Polynomial geometry of the element can easily be adapted to a straight beam configuration as well as to any other curved beam form and naturally shows no numerical sensitivities for the extremely shallow arches. The element is tested on a set of benchmark problems and shows no shear or membrane locking.

Timoshenko curved-beam finite element, linked interpolation, 3-node element

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