Development of an integrated BEM approach for hot fluid structure interaction

In the present work, the boundary element method (BEM) is chosen as the basic analysis tool, principally because the definition of temperature, flux, displacement and traction are very precise on a boundary-based discretization scheme. One fundamental difficulty is, of course, that a BEM formulation requires a considerable amount of analytical work, which is not needed in the other numerical methods. Progress made toward the development of a boundary element formulation for the study of hot fluid-structure interaction in Earth-to-Orbit engine hot section components is reported. The primary thrust of the program to date has been directed quite naturally toward the examination of fluid flow, since boundary element methods for fluids are at a much less developed state

Mixed variational principles for dynamic response of thermoelastic and poroelastic continua

AbstractThe primary objective of the present work is to make further connections between variational methods on the one hand and reversible and irreversible thermodynamics on the other. This begins with the development of a new stationary principle, involving mixed field variables, for continuum problems in infinitesimal dynamic thermoelasticity. By defining Lagrangian and dissipation functions in terms of physically-relevant contributions and invoking the Rayleigh formalism for damped systems, we are able to recover the governing equations of thermoelasticity as the Euler–Lagrange equations. This includes the balance laws of linear momentum and entropy-energy, the constitutive models for elastic response and heat conduction, and the natural boundary conditions. By including energy contributions associated with second sound phenomena, one eliminates the paradox of infinite thermal propagation speeds and the resulting set of governing equations has an elegant symmetry, which is most easily seen in the Fourier wave number domain. A related formulation for dynamic poroelasticity yields two new stationary mixed variational principles. Depending upon the selection of primary field variables, these governing equations can also exhibit an elegant structure, which can deepen our understanding of the underlying phenomena and the thermoelastic–poroelastic analogy. In addition to the theoretical significance, the variational formulations developed here can provide the basis for a class of optimization-based methods for computational mechanics