Free vibration and buckling of laminated beams via hybrid Ritz solution for various penalized boundary conditions (PDF Download Available)

Buckling and free vibration of laminated beams with arbitrary boundary conditions using a refined HSDT (PDF Download Available)

This paper presents a static analysis of laminated cross-ply beams by using an unavailable uni ed higher order shear deformation theory (HSDT) for composite beams which includes the thickness stretching effect. The generalized governing equations are derived by employing the principle of virtual work. Navier-type closed-form solution is obtained for several beams subjected to several kinds of loads (sinusoidal, uniform, linear and point load). In nite HSDTs for beams can be further developed just by modifying the shear strain shape functions. Several hybrid type shear strain shape functions were introduced to evaluate the generality of the proposed theory. The stretching effects for the accurate prediction of the transverse stresses are analyzed. Numerical results of some HSDTs for beams are compared with the elasticity solutions and other HSDTs. Convergence studies were carried out to determine the necessary half-wave number for the different models.

This paper presents a static analysis of laminated beams by using a 6 degree-of-freedom hybrid type quasi-3D higher order shear deformation theory (HSDT). The governing equations are derived by employing the principle of virtual work and solved by means of Hermite-Lagrangian finite element method for laminated beams with several boundary conditions. A mixed interpolation, 1 C cubic Hermite and a 0 C linear Lagrange interpolation are used for the kinematic variables. Different types of shear strain shape functions were introduced a priori and in general manner to model the displacement field of the laminated beams. Convergence studies were performed in order to validate the HSDTs solved through finite element method and the results are compared with a Navier solution. Numerical results of the present generalized quasi-3D theory are also compared with FEM solutions predicted by other HSDT and with experimental results.

No abstract