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

Ismail Mechab (1, 2) , Noureddine El Meiche (1, 2) , Fabrice Bernard (3)

1 UMSM - Université Mustapha Stambouli de Mascara [Algérie] = University Mustapha Stambouli [Mascara, Algeria]
2 UDL - جامعة جيلالي اليابس [سيدي بلعباس، الجزائر] = Université Djillali Liabès [Sidi Bel Abbès, Algérie] = Djillali Liabes University [Sidi Bel Abbès, Algeria]
3 LGCGM - Laboratoire de Génie Civil et Génie Mécanique

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.

Mots clés: Warping function; Higher order theory; Principle of virtual work; Three-point bending; Finite element method

Domaines: Mécanique des matériaux [physics.class-ph]; Génie mécanique [physics.class-ph]

Ismail Mechab, Noureddine El Meiche, Fabrice Bernard. Analytical study for the development of a new warping function for high order beam theory. Composites Part B: Engineering, 2017, 119, pp.18-31. ⟨10.1016/j.compositesb.2017.03.006⟩. ⟨hal-01508439⟩