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A numerical method is presented and applied to the solution of two-dimensional steady-state, anisotropic heat conduction problems. The solution method employs the boundary-fitted coordinate system technique which transforms the region under study onto a fixed rectangular domain where computations are done easily. Consequently, the procedure eliminates the shape of the boundary as a complicating factor. The method is quite general and can handle any multiply-connected, arbitrary-shaped region. Two examples, a solid disk and an eccentric annulus, are worked out to demonstrate the utility of the method. Isotherm results check with previously published solutions.

A finite element stress analysis is presented of a trunnion pipe anchor. The structure is analyzed for the case of internal pressure and various end moment loadings. Stress results were post-processed and decomposed into average and linear varying (through the wall thickness). These decomposed values were then interpreted within the ASME Boiler and Pressure Vessel Code to estimate primary and secondary stress indices. Several computer runs were made for a variety of structural sizes and empirical formulas were developed expressing the stress indices as a function of certain dimensionless ratios.

The propagation and scattering of SH-waves of general form is investigated using the boundary element method. Attention is focused on semi-infinite regions containing subsurface cavities. The analysis is carried out within the context of linear elastodynamic theory formulated as an integral equation. Using a time-dependent Green’s function for the half space, the boundary integral equation is developed and is discretized into a finite set of algebraic relations. A time-stepping algorithm is constructed for the solution of general boundary value—initial value problems. Results of this solution technique are presented for the two-dimensional case of transient waves scattering off of buried stress-free cavities.

The melting of a semi-infinite solid subjected to a step change in temperature is solved according to a non-Fourier heat conduction law postulated by Cattaneo and Vernotte. Unlike the classical Fourier theory which predicts an infinite speed of heat propagation, the non-Fourier theory implies that the speed of a thermal disturbance is finite. The effect of this finite thermal wave speed on the melting phenomenon is determined. The problem is solved by following a similar method as used by Carslaw and Jaeger for the corresponding Fourier problem. Non-Fourier results differ from Fourier theory only for small values of time. Comparing the temperature profiles and the solid-liquid interface location for aluminum, differences between the two theories were significant only for times on the order of 10−9–10−11 s and in a region within approximately 10−4–10−5 cm from the boundary surface. However, these results are based on an approximate value of the thermal relaxation time.