TAILIEUCHUNG - Ebook Stress analysis of fiber - Reinforced composite materials: Part 2

(BQ) The book shows how thermally induced stresses and strains due to curing, add to or subtract from those due to applied loads. Another important element, and one unique to this book, is an emphasis on the difference between specifying the applied loads, ., force and moment results, often the case in practice, versus specifying strains and curvatures and determining the subsequent stresses and force and moment results. This represents a fundamental distinction in solid mechanics. | CHAPTER Classical Lamination Theory Laminate Stiffness Matrix To this point in the development of classical lamination theory it is clear that if we are given the strains and curvatures at a point x y on the reference surface fe Sy Y K Ky and K then we can compute the strain distributions through the thickness of the laminate. By using the stress-strain relations we can compute the stress distributions. By using the transformation relations we can determine the stresses and strains in the principal material system and by using the definitions of the stress resultants we can compute the force and moment resultants acting at that point. If we specify that the given strains and curvatures are the same at every point on the reference surface of a laminate of a given length and width then we can determine the total forces and moments acting on the edges of the laminate. These steps are all a result of the plane stress assumption and the Kirchhoff hypothesis. Figure illustrates the connection between these steps. What remains in the development of classical lamination theory is to be able to specify the force and moment resultants acting at a point x y on the reference surface and then to be able to compute the strains and curvatures of that point on the reference surface that these resultants cause. We want to fill in the missing link in the upper left portion of Figure namely compute the reference surface strains and curvatures knowing the stress resultants. With these computed reference surface strains and curvatures we can then as in the previous examples compute the strain and stress distributions through the thickness of the laminate. Relating the stress resultants to the reference surface strains and curvatures is an important step. In the application of composite materials to structures we are often given the forces and moments that act on a laminate and we want to know the stresses and strains that are caused by these loads. Having a relation between the

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