A modified elliptic integral method and its application in three-dimensional honeycombs

In this paper, a modified elliptic integral method for the geometrically nonlinear analysis of Timoshenko beam is developed. Based on the elliptic integral method constructed by Sinclair, the proposed method also considers the axial, shearing and bending deformations of the beam, which makes up the deficiency of Sinclair's method without considering the shearing deformation at the fixed-end. In the geometrically nonlinear analysis of the three-dimensional honeycombs, the proposed method can be used to describe the unit cell as the elliptic integral equations, and the closed nonlinear equations can be obtained and solved by Newton iteration method. The numerical examples and three-point bending experiment indicate that, compared with Sinclair's method, the results obtained by the proposed method are in good agreement with those of the numerical simulation and experiment, especially for the beam with larger ratio of height to length. Therefore, the modified elliptic integral method developed in this paper has higher accuracy and wider range of application in the analysis of honeycombs.