Topology design involves working with multiple fields. The primary information are the quantities defining the design, and one can argue that for practical purposes this is the only information of real interest. In topology optimization the design variables define the density distribution of material and the optimization problem makes a certain objective function minimal while other objectives are satisfied as constraints in a mathematical programming statement. The evaluation of the objective and constraint functions will involve state variables that relate the design variables to physical behavior, and various physical responses may be involved; these fields will typically be coupled in multi-physics applications. Computational procedures for topology design (and for design optimization as a whole) thus encompass discretization schemes for design and state fields together with algorithms for optimization and for analysis. The prevailing computational approach to structural design and topology design in particular is to view the optimization procedure as a problem in the design variables only. This means that analysis is treated as a function call that provides information on function values and derivatives as a function of design. In optimization terms this is a nested format. Computational challenges are thus by the nature of the problem two-fold and successful implementations rely on both efficient analysis (and the associated sensitivity analysis) and on the efficiency of optimization algorithms. The basic concept of topology optimization and how to apply the methodology to multi-physics devices will be illustrated by considering some recent work on design of structural parts of aircraft and cars, of channel fluid-flow problems, and of waveguides. One of the issues that will be discussed is how simpler models may be used if they still give good designs that can be validated.

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A class of finite element schemes for nonstationary thermal convection problems with temperature-dependent coefficients are considered. Such variable coefficients make the diffusion and the buoyancy terms nonlinear, whose estimates are key points in our analysis. Because of an argument based on the energy method, optimal error estimates for the velocity and the temperature without any stability conditions have been established. A model of the practical melting glass convection is then computed by a finite element method based on such a scheme mathematically justified. Some numerical results are demonstrated to investigate differences of the energy efficiency among some data configurations.

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Numerical simulations of hydrogen dispersion in a partially open space are performed in this paper. The transient behavior of hydrogen and the process of hydrogen accumulation in the space are discussed. Also, the effects of changing vent pressure on the distribution of hydrogen concentration are shown. Based on the results, the way of choosing proper vent position is considered.

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On designing and developing products, the finite element analysis of three dimensional (3-D) eddy current-thermal coupling problems is very useful. This paper shows a large-scale 3-D eddy current-thermal coupling computation for a transformer tank using the domain decomposition method.

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An optimization problem of both-ends-clamped beam which is subjected to a concentrated load is considered. In this paper, an iterative method that uses numerical integration is adopted. Through the comparison with the analytical solution, the characteristic of the optimum solution is discussed.

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FEM is a very important tool for various applications in a wide range of engineering fields. Recently, thanks to the improvement in computer hardware and parallel algorithms, FEM models have become quite large and complex. In such situations, due to lack of infomation, one needs to handle uncertainty in the objects subjected to analysis, in the conditions the analysis is performed, or in the applied mathematical models. SFEM is one way to handle uncertainty in FE analysis. It resembles the purterbation method. Because of the high computational cost, it has previously been considered that it is difficult to apply SFEM to large scale problems. In this study, an improved SFEM is proposed. We propose two apploaches to improve SFEM. The first one, from computational point of view, is to use grid environment. The second one, from mathematical point of view, is to apply seed method and optimize it to the grid environment.

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Connectivity of bolted joints is strongly dependent on the equilibrium relations among the pretension, the compliance of adjacent region, and the external force. The compliance of adjacent region, in particular, is evaluated by the stiffness of a hypothetical conical elastic body just beneath the head of bolts. Whereas, the connectivity would be affected by the change of the contacted area around the bolt head, when an eccentric force is applied, which results in the size change of bolt in some case. In this paper, the contact condition of bolted joint is evaluated by the use of the contact element of nonlinear FEM, the results of which are reported here in after.

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