engleski

Configuration-dependent interpolation in higher-order 2D beam finite elements

In this paper we discuss interpolation functions for the field variables and their variations in relation to geometrically non-linear planar beam finite elements of Reissner's type within the context of a non-standard, configuration-dependent interpolational setting. The commonly used Lagrangian interpolation is known to be capable to return exact solution for the boundary values of the field variables in linear analysis and, when used in conjunction with reduced integration or the related mixed-type approach, is free of shear-locking. On its own, however it may not provide the exact field distribution over the element.\\ To obtain the exact field distribution in linear analysis simply using the correct interpolation function and without applying reduced integration, a different kind of interpolation, called the linked interpolation is needed, in which the unknown displacement function do not depend only on the nodal displacements, but also on the nodal rotations.\\ A formulation which effectively generalises the idea of linked interpolation to non-linear two-noded beam elements exists (the helicoidal interpolation) and is based on the fact that the tangent to the beam centroidal axis and the normal of the cross section follow the same transformation rule. This kind of interpolation, which is necessarily non-linear in the field variables, i.e. configuration-dependent can also be obtained starting from the condition of constant Reissner's strain measures. In this paper we propose an extension of such configuration-dependent interpolation to higher order elements.\\ The numerical analysis performed on representative examples shows very good results of the configuration-dependent interpolation for both full and reduced integration. Certain amount of improvement in accuracy of the results with respect to the standard Lagrangian interpolation with reduced integration is also noticed.

Non-linear analysis; Reissner-Simo beam theory; configuration dependent interpolation

nije evidentirano