U. Introduction In Doyle and Bricksen [1956. p. 77] it is observed that the Cauchy stress tensor 0 can be derived by varying the internal energy e with respect to the Riemannian metric on space: oab =Zpae/agab. Their formula has gone virtually unnoticed in the elasticity literature. In this lecture we shall explain some of the reasons why this formula is, in fact, of fundamental significance. S...

Abstract Hydroelastic responses of floating elastic surfaces to incident nonlinear waves solitary and cnoidal type are studied. There N number the deformable surfaces, these represented by thin plates variable properties different sizes rigidity. The coupled motion fluid solved simultaneously within framework linear beam theory for structures Level I Green–Naghdi fluid. water surface elevation,...

The propagation of magneto-thermoelastic disturbances in an elastic half-space caused by the application of a thermal shock on the stress-free bounding surface in contact with vacuum is investigated. The theory of thermoelasticity III proposed by Green and Naghdi is used to study the interaction between elastic, thermal, and magnetic fields. Small-time approximations of solutions for displaceme...

The equations of motion of lossless compressible nonclassical fluids under the so-called Green–Naghdi theory are considered for two classes of barotropic fluids: (i) perfect gases and (ii) liquids obeying a quadratic equation of state. An exact reduction in terms of a scalar acoustic potential and the (scalar) thermal displacement is achieved. Properties and simplifications of these model nonli...

The Serre–Green–Naghdi (SGN) equations, also known as the fully-nonlinear Boussinesq wave equations, accurately describe the behaviour of dispersive shoaling water waves. This article presents and validates a novel combination of methods for the numerical approximation of solutions to the SGN equations. The approach preserves the robustness of the original finite-volume Saint-Venant solver, in ...