6 Structural Analysis 6.1 Overview In this chapter,the basic theory needed for the determination of the stresses, strains,and deformations in fiber composite structures is outlined.Attention is concentrated on structures made in the form of laminates because that is the way composite materials are generally used. From the viewpoint of structural mechanics,the novel features of composites (compared with conventional structural materials such as metals)are their marked anisotropy and,when used as laminates,their macroscopically hetero- geneous nature. There is a close analogy between the steps in developing laminate theory and the steps in fabricating a laminate.The building block both for theory and fabrication is the single ply,also referred to as the lamina.This is a thin layer of the material (typical thickness around 0.125 mm for unidirectional carbon/epoxy "tape"and 0.25 mm for a cross-ply fabric or"cloth")in which all of the fibers are aligned parallel to one another or in an orthogonal mesh.The starting point for the theory is the stress-strain law for the single ply referred to its axes of material symmetry,defined here as the 0-1,2,3 material axes.In constructing a laminate, each ply is laid-up so that its fibers make some prescribed angle with a reference axis fixed in the laminate.Here the laminate axes will be defined as the x-,y-,and z-axes. All later calculations are made using axes fixed in the structure (the structural axes).In a finite element model,the material properties are usually entered in the material axes.The lay-up of the laminate is defined in the laminate axes.The laminate theory described in this chapter will indicate how the properties of the laminate are derived.The transformation from the laminate axes to the global structural axes is then completed during the solution process.Because the designer can select his own lay-up pattern (because the laminate stress-strain law will depend on that pattern),it follows that the designer can design the material (as well as the structure). For more detailed discussions of the topics covered in this chapter,see Refs.1-7.For background material on the theory of anisotropic elasticity, see Refs.8-10. 1716 Structural Analysis 6.1 Overview In this chapter, the basic theory needed for the determination of the stresses, strains, and deformations in fiber composite structures is outlined. Attention is concentrated on structures made in the form of laminates because that is the way composite materials are generally used. From the viewpoint of structural mechanics, the novel features of composites (compared with conventional structural materials such as metals) are their marked anisotropy and, when used as laminates, their macroscopically hetero￾geneous nature. There is a close analogy between the steps in developing laminate theory and the steps in fabricating a laminate. The building block both for theory and fabrication is the single ply, also referred to as the lamina. This is a thin layer of the material (typical thickness around 0.125 mm for unidirectional carbon/epoxy "tape" and 0.25 mm for a cross-ply fabric or "cloth") in which all of the fibers are aligned parallel to one another or in an orthogonal mesh. The starting point for the theory is the stress-strain law for the single ply referred to its axes of material symmetry, defined here as the 0-1, 2, 3 material axes. In constructing a laminate, each ply is laid-up so that its fibers make some prescribed angle with a reference axis fixed in the laminate. Here the laminate axes will be defined as the x-, y-, and z-axes. All later calculations are made using axes fixed in the structure (the structural axes). In a finite element model, the material properties are usually entered in the material axes. The lay-up of the laminate is defined in the laminate axes. The laminate theory described in this chapter will indicate how the properties of the laminate are derived. The transformation from the laminate axes to the global structural axes is then completed during the solution process. Because the designer can select his own lay-up pattern (because the laminate stress-strain law will depend on that pattern), it follows that the designer can design the material (as well as the structure). For more detailed discussions of the topics covered in this chapter, see Refs. 1-7. For background material on the theory of anisotropic elasticity, see Refs. 8-10. 171