Boundary integral equation methods for the elastic and thermoelastic waves in three dimensions

In this paper, we consider the boundary integral equation (BIE) method for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the Fredholm integral equations of the first kind. The innovative contribution of this work lies in the proposal of the new regularized formulations for the hyper-singular boundary integral operators (BIO) associated with the time-harmonic elastic and thermoelastic wave equations. With the help of the new regularized formulations, we only need to compute the integrals with weak singularities at most in the corresponding variational forms of the boundary integral equations. The accuracy of the regularized formulations is demonstrated through numerical examples using the Galerkin boundary element method (BEM).Comment: 24 pages, 6 figure

An unconditionally stable algorithm for generalized thermoelasticity based on operator-splitting and time-discontinuous Galerkin finite element methods

An efficient time-stepping algorithm is proposed based on operator-splitting and the space–time discontinuous Galerkin finite element method for problems in the non-classical theory of thermoelasticity. The non-classical theory incorporates three models: the classical theory based on Fourier’s law of heat conduction resulting in a hyperbolic–parabolic coupled system, a non-classical theory of a fully-hyperbolic extension, and a combination of the two. The general problem is split into two contractive sub-problems, namely the mechanical phase and the thermal phase. Each sub-problem is discretized using the space–time discontinuous Galerkin finite element method. The sub-problems are stable which then leads to unconditional stability of the global product algorithm. A number of numerical examples are presented to demonstrate the performance and capability of the method

Development of an integrated BEM approach for hot fluid structure interaction

The 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 convective viscous integral formulation was derived and implemented in the general purpose computer program GP-BEST. The new convective kernel functions, in turn, necessitated the development of refined integration techniques. As a result, however, since the physics of the problem is embedded in these kernels, boundary element solutions can now be obtained at very high Reynolds number. Flow around obstacles can be solved approximately with an efficient linearized boundary-only analysis or, more exactly, by including all of the nonlinearities present in the neighborhood of the obstacle. The other major accomplishment was the development of a comprehensive fluid-structure interaction capability within GP-BEST. This new facility is implemented in a completely general manner, so that quite arbitrary geometry, material properties and boundary conditions may be specified. Thus, a single analysis code (GP-BEST) can be used to run structures-only problems, fluids-only problems, or the combined fluid-structure problem. In all three cases, steady or transient conditions can be selected, with or without thermal effects. Nonlinear analyses can be solved via direct iteration or by employing a modified Newton-Raphson approach

Development of an integrated BEM for hot fluid-structure interaction

One of the most difficult problems in engine structural component durability analysis is the determination of the temperatures and fluxes in the structural components directly in contact with the hot gas flow path. Currently there exists no rational analytical or numerical technique which can effectively deal with this problem. Since the temperature distribution in the structural components are strongly influenced by both the fluid flow and the deformation as well as the cooling system in the structure, the only effective way to deal with this problem is to develop an integrated solid mechanics, fluid mechanics and heat transfer analysis for this problem. Herein, the Boundary Element Method (BEM) is chosen as the basic analysis tool principally because the definition of quantities like fluxes, temperatures, displacements, and velocities are very precise on a boundary based discretization scheme. One fundamental difficulty is that a BEM analysis requires a considerable amount of analytical work which is not present in other numerical methods. During the past year, all of this analytical work was completed and a two dimensional, general purpose code was written. A portion of the work is summarized

Dynamics of thermoelastic thin plates: A comparison of four theories

Four distinct theories describing the flexural motion of thermoelastic thin plates are compared. The theories are due to Chadwick, Lagnese and Lions, Simmonds, and Norris. Chadwick's theory requires a 3D spatial equation for the temperature but is considered the most accurate as the others are derivable from it by different approximations. Attention is given to the damping of flexural waves. Analytical and quantitative comparisons indicate that the Lagnese and Lions model with a 2D temperature equation captures the essential features of the thermoelastic damping, but contains systematic inaccuracies. These are attributable to the approximation for the first moment of the temperature used in deriving the Lagnese and Lions equation. Simmonds' model with an explicit formula for temperature in terms of plate deflection is the simplest of all but is accurate only at low frequency, where the damping is linearly proportional to the frequency. It is shown that the Norris model, which is almost as simple as Simmond's, is as accurate as the more precise but involved theory of Chadwick.Comment: 2 figures, 1 tabl