The present treatise is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity. He has unfortunately found himself unable to proceed with it, and I have therefore been obliged to take upon myself the whole of the work and the whole of the responsibility. I wish to a...

The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. However, this cannot happen without addressing proper attention to the soundness of these algorithms. This PhD thesis discusses the formal verification of co...

The paper discusses the oscillations of systems with arbitrary elastic characteristics under arbitrary excitation. It presents a simple method for deriving forced motions from free undamped motions. A detailed treatment of free motions is given first. Special methods are offered for the evaluation of the time integral $t=\int (dt/dx) dx$ over the i...

This paper treats the large-amplitude radial oscillations of a perfectly elastic, incompressible cylindrical tube of infinite length due to suddenly applied pressures on its lateral surfaces. The motion is studied for materials with essentially arbitrary strain-energy density. Sufficient conditions for periodic motions and a formula for the period ...

A system of n masses, equal or not, interconnected by nonlinear “symmetric” springs, and having n degrees of freedom is examined. The concept of normal modes is rigorously defined and the problem of finding them is reduced to a geometrical maximum-minimum problem in an n-space of known metric. The solution of the geometrical problem reduces the cou...