Analysis of Inelasticity Effect Due to Damage on Stress Distributions in Composite Laminates

A damage mechanics model characterizing damage behavior of composite materials proposed earlier by the authors is employed to analyze the damage effects on stress field near the free edge in symmetrically laminated graphite/epoxy composites of finite dimensions under umaxial tension. A quasi-three-dimensional finite element analy sis is developed for the present investigation. The results from the damaged and undam aged stress distributions of [0/90°]s, [90/0°]s, and [±45°] s laminates are compared and examined. The processes of initiation and development of damage zone in these composite laminates are also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68869/2/10.1177_073168449301200805.pd

A New Triangular Hybrid Displacement Function Element for Static and Free Vibration Analyses of Mindlin-Reissner Plate

A new 3-node triangular hybrid displacement function Mindlin- Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking-free formulae of Timoshenko’s beam theory are chosen as the deflection, rotation, and shear strain along each element boundary. Thirdly, seven fundamental analytical solutions of the displacement function F are selected as the trial functions for the assumed resultant fields, so that the assumed resultant fields satisfy all governing equations in advance. Finally, the element stiffness matrix of the new element, denoted by HDF-P3-7β, is derived from the modified principle of complementary energy. Together with the diagonal inertia matrix of the 3-node triangular isoparametric element, the proposed element is also successfully generalized to the free vibration problems. Numerical results show that the proposed element exhibits overall remarkable performance in all benchmark problems, especially in the free vibration analyses

A comparison of Finite Elements for Nonlinear Beams: The absolute nodal coordinate and geometrically exact formulations

Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other