SBFEM elements for thin‐walled composite beams with arbitrary layup

Abstract

AbstractThe scaled boundary finite element method (SBFEM) is a semi‐analytical method in which only the boundary is discretized. The results on the boundary are scaled into the domain with respect to a scaling center which must be “visible” from the whole boundary. For beam‐like problems the scaling center can be selected at infinity and only the cross‐section is discretized. Two new elements for thin‐walled beams have been developed on the basis of the first order shear deformation theory. The beam sections are considered to be multilayered laminate plates with arbitrary layup. The arbitrary cross‐section is discretized with beam elements of Timoshenko type. Using the virtual work principle gives the SBFEM equation, which is a system of differential equations of a gyroscopic type. The solution is calculated using the matrix exponential function. The elements have been tested and compared with a finite element model and they give good results. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)