Finite element formulation of laminated beams with capability to model the thickness expansion

Abstract

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.

Trigonometric-series solution for analysis of laminated composite beams

“…For numerical methods, finite element method has been widely used to analyze composite beams [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. For analytical approach, Navier solution is the simplest one, which is only applicable for simply supported boundary conditions ( [18][19][20]).…”

Effects of transverse normal strain on bending of laminated composite beams

“…Due to the advantages of stiffness-to-weight's ratio and anisotropy material properties, laminated composite (LC) beams have recently attracted a number of researches with different models and approaches. Many beam models with various kinematics have been investigated to predict accurately their static, buckling and vibration behaviours such as layer-wise theories (LWT) [1,2], equivalent single-layer theories (ESLTs) [3][4][5][6][7], zigzag theories (ZZT) [8][9][10] and Carrera's unified formulation (CUF) [11,12] . .…”

“…For numerical approaches, the finite element method is widely used for analysis of static and vibration of LC beams [6,[29][30][31][32][33][34][35][36][37][38]. For analytical methods, Navier procedure [3] is the simplest one for analysis of LC beams, however this approach is only suitable for simply-supported boundary conditions (BCs).…”

Free vibration of axially loaded composite beams using a four-unknown shear and normal deformation theory

“…The buckling occurs around P = 2.92×10 9 N, 6.48×10 9 N and 8.45×10 9 N for C-F, S-S and C-C beams, which correspond to zero natural frequency. DBT) ( [15,17]) and quasi-3D theories [24,36] in Table 7. A good agreement between the present results and those of previous studies can be seen.…”