A mathematical theory of the guillotine

To Bernard Coleman for his 60^th birthday     

The added mass of a deformable cylinder moving in a liquid

Let an infinitely long cylinder move perpendicular to its length in an infinite mass of liquid which is at rest at infinity. If the cylinder is rigid, the whole effect of the presence of the liquid may be represented by adding to the inertia per unit length of the solid cylinder the mass per unit length of the displaced fluid. If, however, the cylinder is elastically deformable, the mass of the moving fluid depends on the change in shape of the, initially circular, cross-sections of the cylinder. Thus the added mass is no longer a constant, but a function of the pressure exerted by the fluid on the solid cylinder.     

A semi-inverse shape optimization problem in linear anti-plane shear

The design of a semi-infinite fillet for efficient stress transmission is considered. The problem is treated within the context of anti-plane shear deformations of a homogeneous, isotropic, linearly elastic solid. Under a remote state of simple shear, it is desired to determine the shape of the traction-free lateral boundaries of a symmetric plane domain so that the shear stress distribution on the finite end is as uniform as possible. A semi-inverse approach for a particular class of semi-infinite profiles is used to examine this issue.     

Detachment instabilities in membranes

Summary Some free boundary value problems involving the equilibrium of elastic membranes are examined. Each membrane is clamped along a part of the boundary and uniformly loaded along another part. The clamped part is weakened by a crack. As the exterior load increases, the crack tends to extend and, for a certain critical value of the load, may run catastrophically.

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Sommario Si esaminano alcuni problemi di frontiera libera relativi all'equilibrio delle membrane elastiche. Ciascuna membrana è incastrata lungo una parte del contorno e caricata uniformemente lungo l'altra. La parte incastrata é indebolita da una fessura. Quando il carico esterno cresce, la fessura tende ad estendersi e, per un certo valore critico del carico, può progredire catastroficamente.

     

Some Ambiguities in the Complex Variable Method in Elasticity

The application ad litteram of the complex variable method for solving plane elastic problems according to the classical procedure of analytic continuation may present some ambiguities. These can be resolved after a careful application of the Schwarz Reflection Principle in constructing the stress functions.