Semi-analytical modeling of composite beams using the scaled boundary finite element method

The 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. The current work is devoted to the development of some SBFEM elements for thin-walled beams 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-like elements of Timoshenko type. Using the virtual work principle gives a system of differential equations of a gyroscopic type. The solution is given using the matrix exponential function. Knowing the deformation of the beam, the stresses, strains and curvatures can be calculated and a failure criterion can be used to assess the laminate. The SBFEM has been tested and compared with a finite element model and it gives good results. (C) 2015 Elsevier Ltd. All rights reserved.