Finite element analysis of shells considering transverse shear

Аuthors

Nesterov V. A.

e-mail: misternester@gmail.com

Abstract

Composite materials are intensively used in different structures, for instance for aerospace technic due to its high strength-to-weight and stiffness-to-weight ratios. At the same time composites have some specificity which should be considered, the main one is the low transverse shear stiffness. Taking into account transverse shear strains increases the order of governing equations.
In this paper a new shell finite element considering the transverse shear is proposed. A nodal kinematic parameters vector includes two angles of transverse shear. The constitutive equations of finite element method are obtained by variation approach on the basis of the total potential energy functional for shell.
Seven main kinematic variables define the shell deformation, the deflection w, the longitudinal translations u and v, the angles of rotation of the normal unit vector to the shell midsurface , and the average transverse shear strains
Thus the vector of main nodal variables looks like
.
The order of element stiffness matrix is equal to 28.
The deformed state of composite and sandwich shells of various thicknesses is investigated. The solutions obtained on the basis of two shell models, the new finite element model and the classical shell Kirchhoff one are compared. It is shown that the new finite element eliminates «the shear locking effect».

Keywords:

shell, transverse shear, finite elements method, shear locking effect

References

1. Reissner E. The Effect ofTransverse Shear Deformation onthe Bending ofElastic Plates, Trans. ASME, Journal ofApplied Mechanics, 1945, vol.12, no.2, pp. 69-77.
   
2. Mindlin R.D. Influence ofRotary Inertia and Shear onFlexural Motions ofElastic Plates, Trans. ASME, Journal ofApplied Mechanics, 1951, vol.18, pp. 31-38.
   
3. Vasilev V.V. Mekhanika konstruktsii izkompozitsionnykh materialov (Mechanics ofcomposite structures), Moscow, Mashinostroenie, 1988, 272p.
4. Novozhilov V.V. Teoriya uprugosti (Elasticity theory), Leningrad, Sudpromgiz, 1958, 370p.
5. Nesterov V.A. Mekhanika kompozitnykh materialov, Riga, 2011, vol.47, no.3, pp. 399-418.