Analysis of transverse cracking and stiffness loss in cross-ply laminates with hygrothermal conditions

Nonlinear vibration of matrix cracked laminated beams containing carbon nanotube reinforced composite layers in thermal environments

“…This means the 90-ply contains a periodic array of cracks. There are several modified shear-lag models proposed [12][13][14][15][16][17][18]. A comparison and assessment of 2-D shear-lag models for the analysis of symmetric and balanced laminates may be found in Joffe and Varna [29].…”

“…For movable end conditions, these equations can be expressed as (15) and for immovable end conditions, these equations can be expressed as (16) where t is time, and A 11 , B 11 and D 11 are the plate stiffnesses, and defined by…”

“…Han and Hahn [14] established a relationship between the loading (including residual thermal stress) and the matrix crack density. Adda-Bedia and his co-authors [15][16][17][18] investigated the thermal effects on the stiffness loss of laminates with transverse cracking based on a shear-lag model. In the aforementioned studies [9,[12][13][14][15][16][17][18], however, the fiber reinforcements are usually assumed to be distributed uniformly in each ply and the fiber volume fraction does not vary spatially at the macroscopic level.…”

“…There are several models to describe the matrix crack [9][10][11][12][13][14][15][16][17][18], in which the shear-lag model [9,[12][13][14][15][16][17][18] is one of the effective approaches to solve the stress and strain fields in the interior of composites with matrix crack uniformly distributed throughout the length of beam. Highsmith and Reifsnider [9] proposed a one-dimensional (1-D) shear-lag model based on the assumption that the shear stain acted only in a thin resin-rich region.…”

“…Ω L is the linear frequency of the beam, while ω L is the corresponding dimensionless form of linear frequency. Eq (15). and(16) can be rewritten in the following dimensionless form:…”