Analytical study for the development of a new warping function for high order beam theory

This paper presents an analytically and numerical study of the warping phenomenon in short beams, thick plates and anisotropic materials. A transverse shear higher order theory is considered. The equilibrium equations are inspired by the principle of virtual work that has permitted to establish the boundary conditions. The analytical development of a new warping function is inspired by others works found in the literature for three-point bending. The stabilization of this new iterative function under a uniformly distributed pure bending load is used for any type of structure. Analytical results are compared with other existing models in the literature and a simulation using the finite element method.