Multi-layer higher-order finite elements for the analysis of free-edge stresses in composite laminates

Abstract

The analysis of the free-edge stress distributions in composite laminates under uniaxial tension is approached by a finite element technique based on a multi-layer higher-order laminate theory.Several finite elements corresponding to different through-thickness assumed distributions of the displacement unknowns are developed.Numerous stacking sequences are examined in the applications. The results are compared with the ones obtained by various investigators with other modelling approaches.The use of the proposed technique is demonstrated to be simple and effective both for the analysis of in-plane and out-of-plane distributions of intralaminar and, noticeably, interlaminar stress components.

A higher-order displacement model for stress concentration problems in general lamination configurations

“…4. It can be seen that the peak stress near free edge obtained from the present model agrees well those of multilayered higher-order theory [19]. Although the stress peak value close to the free edge could be accurately predicted, the shear stresses computed from the present model are unable to come down to zero at free edge.…”

“…The layerwise models are able to generally predict the free-edge stresses of laminated structures whereas the layerwise approach requires huge computing efforts as the number of unknown functions depends on the number of layers of laminates. In addition to analytical methods, Gaudenzi et al [19] presented a multilayer higher-order finite element for interlaminar stress analysis near free edge in composite laminates. Moorthy layerwise displacement finite element to predict free-edge stresses in the angle-ply laminated plates in bending.…”

A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates

“…Free edge stress fields are very localised and exhibit steep gradients before reaching the inner laminate regions where the assumptions of the classical laminate plate theory can be used. The accurate determination of the corresponding three-dimensional stress state (often involving singularities) is a difficult problem and various methods either purely numerical (Gaudenzi et al, 1998;Krueger and O'Brien, 2001;Goyal et al, 2004) or using approximate closed form analytical approach (Mittelstedt and Becker, 2007;Nosier and Maleki, 2008;Wimmer and Pettermann, 2008) were developed. Ply separation results from the increase of the out of plane normal stress and interlaminar shear stresses.…”

Efficient computation of order and mode of three-dimensional stress singularities in linear elasticity by the boundary finite element method

“…the works of Wang and Crossman, 1977;Whitcomb et al, 1982;Rohwer, 1982;Whitcomb and Raju, 1983;Wu, 1987;Ye, 1990;Lessard et al, 1996;Lindemann and Becker, 2002a or Artel and Becker, in press) and such approaches where especially adapted FEM formulations are used (see e.g. Spilker, 1980;Spilker and Chou, 1980;Wang and Yuan, 1983a,b;Gruttmann and Wagner, 1994;Robbins and Reddy, 1996;Gaudenzi et al, 1998 or Mannini andGaudenzi, 2003). However, beside the well known standard methodologies FDM and FEM, the employment of other numerical approaches has been reported as well: Ö ry et al (1984) have used the method of transfer matrices whereas Davi (1996) has employed a Boundary Element Method (BEM) formulation.…”