Search

Abstract: The enthalpy method is exploited in tackling a heat transfer problem involving a change of state. The resulting governing equation is then solved with a hybrid finite element – boundary element technique known as the Green element method (GEM). Two methods of approximation are employed to handle the time derivative contained in the discrete element equation. The first involves a finite difference method, while the second utilizes a Galerkin finite element approach. The performance of both methods are assessed with a known closed form solution. The finite element based time discretization, despite its greater challenge, yields less reliable numerical results. In addition a numerical stability test of both methods based on a Fourier series analysis explain the dispersive characters of both techniques, and confirms that replication of correct results is largely attributed to their ability to handle the harmonics of small wavelengths which are usually dominant in the vicinity of a front. [Copyright &y& Elsevier]

Abstract: In the conventional semi-analytical finite strip analysis of folded plates, the boundary conditions and the intermediate support conditions must be satisfied a priori. The admissible functions used as the longitudinal part of the displacement functions are sometimes difficult to find, and they are valid for specific conditions only. In this paper, a general finite strip is developed for the static and vibration analyses of folded plate structures. The geometric constraints of the folded plates, such as the conditions at the end and intermediate supports, are modelled by very stiff translational and rotational springs as appropriate. The complete Fourier series including the constant term are chosen as the longitudinal approximating functions for each of the displacements. As these displacement functions are more general in nature and independent of one another, they are capable of giving more accurate solutions. The potential problem of ill-conditioned matrices is investigated and the appropriate choice of the very stiff springs is also suggested. The formulation is done in such a way to obtain a unified approach, taking full advantage of the power of modern computers. A few numerical examples are presented for comparison with numerical results from published solutions or solutions obtained from the finite element method. The results show that this kind of strips is versatile, efficient and accurate for the static and vibration analyses of folded plates. [Copyright &y& Elsevier]

Abstract: We study the Poisson problem with zero boundary datum in a (finite) polyhedral cylinder with a non-convex edge. Applying the Fourier sine series to the equation along the edge and by a corner singularity expansion for the Poisson problem with parameter, we define the edge flux coefficient and the regular part of the solution on the polyhedral cylinder. We present a numerical method for approximating the edge flux coefficient and the regular part and show the stability. We derive an error estimate and give some numerical experiments. [Copyright &y& Elsevier]