The modification of a node-to-node algorithm for the modelling of beam connections in RFEM and SCIA using the explicit method

Abstract

The “node-to-node” (NTN) algorithm is one of the simplest and oldest contact discretization methods [1]. It is, therefore, used in cases where a more sophisticated method is not needed. Beam connections between 1D elements are a great example of an area of application of NTN discretization. Each connection is modelled by a hinge at the end of every connected 1D element. The explicit method is important with regard to many linear and non-linear dynamics problems. The central difference method is usually used in the Finite Element Method to solve explicit schemes. This and similar methods suffer significant errors if the time step exceeds the critical time step, which is directly derived from the element stiffness and tends towards zero as connected nodes get closer to each other. This is very inconvenient for NTN contacts, as with them there is usually only a small distance (or even zero distance) between the nodes and a rigid connection in a particular direction. This paper presents a modification that enables hinges that are rigid in a particular direction to be calculated using the explicit method.