Numerical simulation of free edge effects in laminated composites using 3D equations of elasticity and p-version LSFEF
- Univ. of Kansas, Lawrence, KS (United States). Dept. of Mechanical Engineering
This paper presents a numerical investigation of the free edge effects in laminated composites using p-version least squares finite element formulation (LSFEF) of the three dimensional equations of elasticity. In laminated composites with non-isotropic lamina material properties, the existence of high free edge shear stresses has been observed experimentally and has also been documented through analytical studies. However, the question of their magnitude may still be unresolved. Many numerical studies, including using finite element method, have been reported to address this issue. However, in almost all of such studies, the basic question of how well the governing equations are satisfied by the computed solution still remains unresolved. Unless one can quantitatively establish that 3D equations of elasticity are satisfied by the computed solution, the free edge phenomenon simulated by the computed solution remains questionable. In the FEM, based on Galerkin approach, there is no direct measure of error since these formulations are based on weak form, thus it is difficult to ascertain whether the computed solutions satisfies the differential equations or not. In the paper, the authors propose a p-version LSFEF of the 3 D equations of elasticity and utilize it to simulate the free edge effect problem. In this approach, the authors use the original differential equation in the FE process (i.e., no weak form), hence it is possible to judge whether the 3 D equations of elasticity are satisfied by the computed solution. With this formulation, a converged error functional for finite values of free edge shears will undoubtedly establish their smoothness, while an unconverged error functional with progressively increasing p-levels and refined meshes yielding progressively increasing free edge shear values, would indicate singularity of the shears at the free edge. The paper presents details of p-version LSFEF, numerical studies and comparison with the results reported in the literature.
- OSTI ID:
- 357764
- Report Number(s):
- CONF-980213--
- Country of Publication:
- United States
- Language:
- English
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