A numerically stable exact method for analysis of partial-interaction composite beams based on Timoshenko beam theory. (15th December 2022) - Sun, Qikai; Zhang, Nan; Liu, Xiao
Highlights: An exact method is proposed for the analysis of two-layer composite beams. The inversion operation on the matrices is avoided to ensure the numerical stability. The numerical stability of this method is verified by using multi-span beams. The effect of shear deformations on the interfacial shear slips is clarified. Abstract: The traditional direct stiffness matrix method may occur numerical instability for analysis of partial-interaction composite beams with long spans. To solve this problem, this paper proposes a numerically stable exact method called the coefficient matrix method for analysis of two-layered partial-interaction composite beams using the Timoshenko beam theory. By replacing the nodal displacements with the undetermined parameters of shape function obtained by the governing equation as primary unknown coefficients, the coefficient matrix method can avoid the inversion operation on the matrices in obtaining the direct stiffness matrix. Thus, numerical stability can be ensured. Finally, the coefficient matrix method is validated against experimental, ANSYS and other theoretical results in the literature with good agreement. And the effect of shear deformation on shear slips at the interface of the sub-beams by varying shear connector stiffness, shear-to-Young's modulus ratios, and span-to-depth ratios are discussed.