# Equilibrium, Universal Solutions, and Inflation

• Jay D. Humphrey
• Sherry L. Delange
Chapter

## Abstract

Let us begin by recalling three important observations from Chapters 1 and 2. First, equilibrium requires that ΣF = 0 and ΣM = 0. Second, if a body is in equilibrium, then each of its parts are likewise in equilibrium. Third, there may exist at each point p in a body (cf. Fig. 2.4) nine components of stress, six of which are independent, which we denote as σ(face)(direction) relative to the coordinate system of choice. Because stress may vary from point to point within a body, the components at a nearby point q may have different values. (Note: It is usually convenient to refer components at different points to the same coordinate system.) Now, if we consider a small cube of material, centered about point p which is located at (x, y, z) and has stresses σ xx , σ xy , ..., σ zz , then the stresses on the faces of the cube may differ from those at the center; that is, if the xx component at the center of the cube is σ xx , then on the positive and negative faces of the cube, at distances ±Δx/2 from the center, we may have σ xx + Δσ xx and σ xx − Δσ xx , respectively (i.e., values slightly greater than or less than that at point p).

## Keywords

Abdominal Aortic Aneurysm Radial Stress Maximum Shear Stress Circumferential Stress Universal Solution
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