Optimal Density Distribution Research Articles

A study on the shape extraction process in the structural topology optimization using homogenized material

The shape and topology optimization of structures as an optimal density distribution problem is considered. An artificial material model, whose elastic moduli are contrived to stay close to the lower side of the Hashin-Shtrikman bounds, is introduced to obtain the efficient relationship between the effective elastic moduli and the density of the given material. The introduction of the new model results in optimal density distribution which is readily applicable to real structural patterns with the least possible porous regions. Also, a density redistribution algorithm is suggested in order to suppress checker-board patterns without the use of the higher order elements. This algorithm combined with the new artificial material introduced is shown to effectively work in extracting the optimal structure shape from the computed density distribution.

Numerical Analysis Method for Homologous Deformation Problem Using the Topology Optimization Technique Based on the Homogenization Theory.

The purpose of this study is to develop a topology optimization method to get a given detormation mode, such as a homologous structure. A minimization problem of a square error in relation to a given deformation and an active deformation is formulated for a linear elastic structure. To solve this problem the homogenized elastic constants are employed and a topology optimization is replaced with an optimal density distribution problem. using the similar method proposed by Bendsoe and Kikuchi. The homogenized elastic constants are calculated by the homogenization method for a microstructure having a rectangular hole. Using this method, a structural deformation is controlled to a given deformation. Simple examples are presented to confirm the validity of this optimization method.

Automatic Large-Scale Mesh Generation Based on Fuzzy Knowledge Processing and Computational Geometry. With a Newl Function for Three-Dimensional Adaptive Remeshing.

This paper describes a new adaptive remeshing technique for the three-dimensional finite element analysis based on the fuzzy knowledge processing and the computational geometry. First, a three dimensional geometry model is defined through some solid modelling operations, and analysis conditions are attached on each part of the model. A tetrahedral finite element model is generated following an initial density distribution of nodes specified by a user. After its analysis is finished, a posteriori error estimation is performed. An optimal density distribution of nodes is estimated, and a new finite element model is created. These procedures are iterated fully automatically until solution accuracy satisfies the criterion specified by a user. The error estimation method proposed by Zienkiewicz and Zhu (Z-Z estimator) is applied to the system, and its practical performances are demonstrated through its application to some static heat conduction problems of three-dimensional complex geometry.

Two accurate algorithms for calculating the energy fluence profile in inverse radiation therapy planning

Two accurate algorithms for calculating the required incident energy fluence distributions from the optimal irradiation density distribution in inverse radiation therapy planning have been developed. The algorithms are characterized by a high speed and accuracy and an ability to handle both divergent and parallel beams even for extremely heterogeneous target volumes. The fastest algorithm is based on a longitudinal distance weighting method, whereas the slower but more accurate algorithm uses an area weighting method which has the advantage that it also works very well at low spatial resolutions. Both algorithms have been inverted for forward calculation of the delivered absorbed dose distribution from known fluence profiles. This is essential for the validation of the resultant dose distributions since the projected irradiation density has been determined from dose distributions calculated with convolution methods. A shortcoming of the longitudinal distance weighting algorithm for forward calculation is that it requires a higher spatial resolution in the energy fluence to minimize the discretization noise caused by interpolation. The area weighting algorithm on the other hand requires a longer calculation time. When the forward calculation time is also taken into account, the more accurate area weighting method is the most advantageous algorithm from the point of view of total calculation time.

Problem of optimal density distribution in the bearing components of articles formed from integral foam plastics

The physicomechanical characteristics (PMC) of foam plastics (FP) vary over a broad range not only for the different composite compositions and fabrication processes employed for the production of articles, but also within the limits of chemically homogeneous groups [i-3]. Complete utilization of the potential of FP with minimal outlays is ensured by combined efforts of builders and technologists in designing the component and during its fabrication [i]. During the formulation of foamed plastics, the lower the average apparent density, the lower the initial heating temperature of the mold, and the higher the rate of heat removal from the surface of the article, the greater the macroheterogeneity. The character of the macroheterogeneities has undergone considerable experimental investigation [i-4], but the literature contains no systematized data on functional relationships between PMC and the above-indicated parameters. Laws governing the density distribution over the thickness of the plastic, especially the panels of enclosures, have been thoroughly investigated [4]. Density distributions for two FP formulations are presented in Fig. i: Grade PPU-317 foam polyurethane and Grade FRP-I phenolformaldehyde FP. Note that the lower the mold-heating temperature, the more clearly the integral properties of the FP are expressed, i.e., an increase in homogeneity, as a rule, requires additional energy outlays and complication of mold design. Idealization in the form of multilayer, or, more frequently, a three-layer system is widely used in designing plates and panels of integral foam plastics (IFP). This schematization does not always ensure sufficient accuracy for evaluation of the stress-strain state (SSS).

Urban Spatial Structure with Open Space

Urban open spaces such as parks, open squares, parkways, etc, are considered as amenity resources or local public goods and incorporated into neoclassical urban land-use theory. Models characterizing Pareto efficient allocations and competitive equilibrium allocations with open space are presented. The ‘fiscal profitability principle’ suggested by Margolis is confirmed to be applicable to determine an efficient distribution of open space. Many interesting results are established. For example, if utility function is Cobb-Douglas or log-linear, then rich will locate farther away from poor, irrespective of the distribution of open space; the optimal density distribution of open space is uniform if the spillover effects of open space are neglected, and it is decreasing with the distance from the CBD when the spillover effects of open space are taken into account.

A Dynamic Feedback Approach to Modelling Spatial Population Density

This paper presents an approach to modelling population density as a function of space and time, both of which are treated over a continuous domain. An equilibrium (or alternatively, an optimal) distribution of urban population density is specified exogenously. The rate of change of the actual population density is then considered to be a function of the deviations between the actual and the equilibrium (or optimal) density distributions, over time. This adjustment process is interpreted as being realized by internal migration, immigration/emigration, and/or natural growth. A formal specification of the models results in integral—differential equations. A solution procedure that uses double Laplace transforms and partial Laplace transforms with respect to space and time is outlined. Properties relating to the limiting distributions are discussed. An example that makes use of exponential functions is presented; and procedures for computing explicit, and possibly heuristic, solutions are noted.