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Heat transfer and stress analysis in metallic and coated exhaust valves are performed by an adaptive space‐time finite element method. Results indicated that coatings of ordinary thickness cannot protect a coated valve operating in an uncooled engine. A new approach for designing the inner geometry of the metallic part in a coated hollow valve is presented. The purpose of the cavity is changed from cooling to insulating. Controlling the valve temperature and the heat flows out is done by changing the geometry of the cavity. The optimum is sought between the hollow geometry of the valve and its coating thickness while the outer geometry is that of an ordinary valve. Exhaust valves with optimal geometry are presented. A reduction of 40% of the heat flows out is obtained, compared to the heat flows out from a metallic valve operating in a cooled engine. By comparison, reduction of the heat flows out from a coated, ordinary geometry valve amounts to only 20%.

Deals with the formulation and application of temporal and spatial spectral element approximations for the solution of convection‐diffusion problems. Proposes a new high‐order splitting space‐time spectral element method which exploits space‐time discontinuous Galerkin for the first hyperbolic substep and space continuous‐time discontinuous Galerkin for the second parabolic substep. Analyses this method and presents its characteristics in terms of accuracy and stability. Also investigates a subcycling technique, in which several hyperbolic substeps are taken for each parabolic substep; a technique which enables fast, cost‐effective time integration with little loss of accuracy. Demonstrates, by a numerical comparison with other coupled and splitting space‐time spectral element methods, that the proposed method exhibits significant improvements in accuracy, stability and computational efficiency, which suggests that this method is a potential alternative to existing schemes. Describes several areas for future research.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming and powder metallurgy are briefly discussed. The range of applications of finite elements on the subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for the last five years, and more than 1100 references are listed.

This paper aims to propose a parallel-in-space-time finite-element method (FEM) for transient motor starting analyses. Although the domain decomposition method (DDM) is suitable for solving large-scale problems and the parallel-in-time (PinT) integration method such as Parareal and time domain parallel FEM (TDPFEM) is effective for problems with a large number of time steps, their parallel performances get saturated as the number of processes increases. To overcome the difficulty, the hybrid approach in which both the DDM and PinT integration methods are used is investigated in a highly parallel computing environment.

First, the parallel performances of the DDM, Parareal and TDPFEM were compared because the scalability of these methods in highly parallel computation has not been deeply discussed. Then, the combination of the DDM and Parareal was investigated as a parallel-in-space-time FEM. The effectiveness of the developed method was demonstrated in transient starting analyses of induction motors.

The combination of Parareal with the DDM can improve the parallel performance in the case where the parallel performance of the DDM, TDPFEM or Parareal is saturated in highly parallel computation. In the case where the number of unknowns is large and the number of available processes is limited, the use of DDM is the most effective from the standpoint of computational cost.

This paper newly develops the parallel-in-space-time FEM and demonstrates its effectiveness in nonlinear magnetoquasistatic field analyses of electric machines. This finding is significantly important because a new direction of parallel computing techniques and great potential for its further development are clarified.

A generalized time finite element method is considered for time integration of non‐linear equations of motion arising from dynamic problems. A simple three‐time level family of schemes is obtained. Evaluation of the schemes shows that the proposed approach may lead to unconditionally stable algorithms for non‐linear problems. Numerical examples show the accuracy and efficiency of the proposed algorithm in comparison to Newmark's average acceleration method and four order accurate explicit algorithm.

The purpose of this paper is to investigate the influence of forced, in-line oscillation of a circular cylinder on an incoming incompressible flow field at different Reynolds numbers.

A space-time finite element approach is employed to model the flow around an oscillating cylinder.

The results show that two (2S), four (2P, two pair) and three vortices (P+S, one pair and one single) are shed in each cycle. In addition, a 2P _o mode is also observed, which is similar to the 2P mode but the vortices of the 2P _o mode differ in strength. The 2P mode of vortex shedding is observed along the entire wake of the flow field and 2P _o mode in the far wake. In some cases, the vortex street is transformed as it travels towards the exit to produce new patterns. One such pattern is observed for the first time in the present work, which is referred to as 2P _o * mode. The drag and lift coefficients observed are perfectly periodic at a Reynolds number of 200 and they reach a chaotic pattern as the Reynolds number is increased to a value of 350.

Originality of the paper lies in the observation of 2P vortex shedding mode or its variants in the downstream of the cylinder.

A rigorous Finite Element (FE) formulation based on an enthalpy technique is developed for solving coupled nonlinear heat conduction/mass diffusion problems with phase change. The FE formulation consists of a fully coupled heat conduction and solute diffusion formulation, with solid‐liquid phase change, where the effects of pressure and convection are neglected. A full enthalpy method is employed eliminating singularities which result from abrupt changes in heat capacity at the phase interfaces. The FE formulation is based on the fixed grid technique where the elements are two dimensional, four noded quadrilaterals with the primary variables being enthalpy and average solute concentration. Temperature and solid mass fraction are calculated on a local level at each integration point of an element. A fully consistent Newton‐Raphson method is used to solve the global coupled equations and an Euler backward difference scheme is used for the temporal discretization. The solution of the enthalpy‐temperature relationship is carried out at the integration points using a Newton‐Raphson method. A secant method employing the regula falsi technique takes into account sudden jumps or sharp changes in the enthalpy‐temperature behaviour which occur at the phase zone interfaces. The Euler backward difference integration rule is used to calculate the solid mass fraction and its derivatives. A practical example is analysed and results are presented.