Asymptotic splitting in the three-dimensional problem of linear elasticity for elongated bodies with a structure

✍ Scribed by V.V. Yeliseyev; I.S. Orlov

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 448 KB
• Volume: 63
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(99)00013-1

✦ Synopsis

The equilibrium of linearly-elastic elongated bodies (rods) with an extremely arbitrary geometry and structure subjected to the effects of force and heat is considered. Owing to the presence of a small parameter--the relative thickness--this is a singularly perturbed problem. The asymptotic analysis involves splitting the three-dimensional problem into one-and two-dimensional problems. The one-dimensional problem gives the same result as the classical theory, even when the material is structurally heterogeneous and anisotropic, which invalidates the conventional hypotheses of applied theories. The two-dimensional problems yield not only the parameters of the one-dimensional model, but also a complete solution of the three-dimensional problem. The algorithm used to split the three-dimensional problem is implemented on a computer. It is sometimes more effective than the conventional finite-element, boundary-element and difference methods in the case of elongated bodies.