Linear elastic analysis of thin laminated beams with uniform and symmetric cross-section

Abstract

This paper deals with analyses of linear elastic thin beams which are consisted of the homogeneous orthotropic layers. The cross-sections of these beams are assumed uniform and symmetric. Governing equations of one-dimensional model are derived on the base of the Timoshenko's beam theory. An evaluation of shear correction factor consists in conservation of the shear strain energy. This factor is calculated in this paper but only in the cases of the static problem. The general static solution for the flexural and axial displacement and for the slope of the cross-section is found. Further, the possibility of calculation of the free vibrations of beams are also presented. The obtained results for the static solution are compared with the results of numerical solution based on the finite element method. The numerical model is prepared in software package MARC. As a tested example is used the uniformly loaded simply supported beam with various cross-sections.

Keywords

• Linear elastic beam
• Orthotropic layers
• Timoshenko's beam theory
• Static solution
• Free vibrations