Stiffness matrices of thin-walled composite beam with mono-symmetric I- and channel-sections on two-parameter elastic foundation

Abstract

For the coupled analysis of thin-walled composite beam under the initial axial force and on two-parameter elastic foundation with mono-symmetric I-and channel-sections, the stiffness matrices are derived. The stiffness matrices developed by this study are based on the homogeneous forms of simultaneous ordinary differential equations using the eigen-problem. For this, from the elastic strain energy, the potential energy due to the initial axial force and the strain energy considering the foundation effects, the equilibrium equations and force-displacement relationships are derived. The exact displacement functions for displacement parameters are evaluated by determining the eigenmodes corresponding to multiple non-zero and zero eigenvalues. Then the element stiffness matrix is determined using the force-displacement relationships. For the purpose of comparison, the finite element model based on the classical Hermitian interpolation polynomial is presented. In order to verify the accuracy and the superiority of the beam elements developed herein, the numerical solutions are presented and compared with results from the Hermitian beam elements and the ABAQUS's shell elements. Particularly, the influence of the initial compressive and tensile forces, the fiber orientation, and the boundary conditions on the coupled behavior of composite beam with mono-symmetric I-and channel-sections is parametrically investigated.