The Numerical Assembly Technique for arbitrary planar beam structures based on an improved homogeneous solution

Abstract

The Numerical Assembly Technique (NAT) is extended to investigate arbitrary planar frame structures with a focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial discretization. To this end, we systematically introduce a frame structure as a set of nodes, beams, bearings, springs, and external loads and formulate the corresponding boundary and coupling conditions. As the underlying homogeneous solution of the governing equations, we use a novel approach recently presented in the literature. This greatly improves the numerical stability and allows the stable computation of very high natural frequencies accurately. We show this improvement by investigating the condition number of the system matrix and also by the use of variable precision arithmetic.

Teaching mechanics with individual exercise assignments and automated correction

“…The technical implementation for statically determined systems can be found in refs. [3, 4], whereas ref. [5] details the treatment of statically undetermined systems and axial/flexural rigid beams.…”