Balanced, symmetric laminates

Ply orientations in a laminate are taken with reference to a particular loading direction, usually taken to be the direction of the maximum applied load, which, more often than not, coincides with the fibre direction to sustain the maximum load, and this is defined as the 0° direction. It is usual to choose balanced, symmetric laminates in design. A balanced laminate is one in which there are equal numbers of-1-0 and - 0 plies a symmetric laminate is one in which the plies are symmetric in terms of geometry and properties with respect to the laminate mid-plane. Hence, a laminate with a stacking sequence 0/90/-I-45/-45/-45/-I-45/90/0, which is written (0/90/ 45), is both balanced and symmetric. Balanced, symmetric laminates have a simplicity of response. In contrast, an unbalanced, asymmetric laminate will, in general, shear, bend, and twist under a simple axial loading. 

Some special classes of laminates are worth mentioning at this point. Symmetric laminates were already defined earlier. For symmetric laminates, the B matrix is zero (Bij = Q). Balanced laminates are laminates in which for every +6 ply (6 0 or 90) there is another —6 ply somewhere in the stacking sequence. For... 

Balanced and symmetric laminates AsBoDp Unbalanced laminates ApBoDg Fully orthotropic angle-ply laminates AgBoDg Extensionally isotropic laminates AjBoDs Fully isotropic laminates AiBoDp... 

Although the word balanced is ambiguous and not definitive, the common meaning for a balanced laminate is a laminate in which all equal-thickness laminae at angles 0 other than 0° and 90° to the reference axis occur only in 0 pairs. The individual -n O and - 0 layers are not necessarily adjacent to each other. Note also that balanced laminates are required to be symmetric about the laminate middle surface, so there must be two + Q laminae and two - 0 laminae for each 0 pair. The behavioral characteristics of a balanced laminate are that shear-... 

In order to minimize coupling, the aerospace industry usually selects laminates that are both balanced (i.e. they have as many +45° layers as they have —45° layers) and symmetric about their mid-plane. Balancing eliminates extension-shear coupling whereas symmetry eliminates all B-matrix terms, preventing coupling between in-plane and out-of-plane deformation/load. Grouping of more than four layers of the same orientation is not normally permitted to avoid large inter-lamina stresses,... 

For a balanced (same number of 0) and symmetrical system (+0 or -0 at same distance above and below the midplane) the laminate solution is... 

P(3) Laminates that are subject to bending-stretching-torsion coupling are defined as generally orthotropic. Typically, generally orthotropic laminates have a symmetrical and balanced stacking sequence of plies, with an appreciable amount (more than about 20%) of reinforcement orientated at other than 0° and 90° (e.g. +45° or -45°). 

For many composite applications the laminate is not orthotropic, but anisotropic, though this can exist in many particular forms, one of which occurs when an orthotropic laminate is loaded in a direction which does not coincide with one of the principal axes, or when the lay-up is symmetric but not balanced about a principal reference axis. A [0°/+45°/90°]s laminate is balanced and quasi-isotropic. As a general rule, all laminates should be symmetrically laid up about their mid-plane to avoid stretching bending coupling. 

If the ply illustrated in Fig. 9 is used in the construction of a balanced and symmetrical 0/90 laminate and is mechanically tested, a bilinear stress-strain curve is... 

Balanced construction RP in which properties are symmetrical along the laminate flat plane. 

All laminates should be balanced to achieve in-plane orthotropic behavior. To achieve balance, for every layer centered at some positive angle +0, there must exist an identical layer oriented at -9 with the same thickness and material properties. If the laminate contains only 0° and/or 90° layers, it satisfies the requirements for balance. Laminates may be midplane symmetric but not balanced, and vice versa. Figure 4.1 le is symmetric and balanced, whereas Fig. 4.1 Ig is balanced but unsymmetric. 

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