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The purpose of this paper is the improvement of topology optimization. The scope of the paper is focused on the speedup of optimization.

To achieve the speedup, the method of moving asymptotes (MMA) with constrained condition of level set function is applied instead of solving the Hamilton–Jacobi equation.

The acceleration of convergence of objective function is drastically improved by the implementation of MMA.

Normally, the level set method is solved through the Hamilton–Jacobi equation. However, the possibility of introducing mathematical programming is clear by the constrained condition. Furthermore, the proposed method is suitable for efficiently solving the topology optimization problem in the magnetic field system.

The purpose of this paper is to propose a novel non-probabilistic reliability-based topology optimization (NRBTO) method for continuum structural design under interval uncertainties of load and material parameters based on the technology of 3D printing or additive manufacturing.

First, the uncertainty quantification analysis is accomplished by interval Taylor extension to determine boundary rules of concerned displacement responses. Based on the interval interference theory, a novel reliability index, named as the optimization feature distance, is then introduced to construct non-probabilistic reliability constraints. To circumvent convergence difficulties in solving large-scale variable optimization problems, the gradient-based method of moving asymptotes is also used, in which the sensitivity expressions of the present reliability measurements with respect to design variables are deduced by combination of the adjoint vector scheme and interval mathematics.

The main findings of this paper should lie in that new non-probabilistic reliability index, i.e. the optimization feature distance which is defined and further incorporated in continuum topology optimization issues. Besides, a novel concurrent design strategy under consideration of macro-micro integration is presented by using the developed RBTO methodology.

Uncertainty propagation analysis based on the interval Taylor extension method is conducted. Novel reliability index of the optimization feature distance is defined. Expressions of the adjoint vectors between interval bounds of displacement responses and the relative density are deduced. New NRBTO method subjected to continuum structures is developed and further solved by MMA algorithms.

Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity of interest (QoI) subject to constraints. The purpose of this study is to develop a problem-agnostic automatic differentiation (AD) framework to compute sensitivities of the QoI required for density distribution-based topology optimization in an unstructured co-located cell-centered finite volume framework. Using this AD framework, the authors develop and demonstrate the topology optimization procedure for multi-dimensional steady-state heat conduction problems.

Topology optimization is performed using the well-established solid isotropic material with penalization approach. The method of moving asymptotes, a gradient-based optimization algorithm, is used to perform the optimization. The sensitivities of the QoI with respect to design variables, required for optimization algorithm, are computed using a discrete adjoint method with a novel AD library named residual automatic partial differentiator (Rapid).

Topologies that maximize or minimize relevant quantities of interest in heat conduction applications are presented. The efficacy of the technique is demonstrated using a variety of realistic heat transfer applications in both two and three dimensions, in conjugate heat transfer problems with finite conductivity ratios and in non-rectangular/non-cuboidal domains.

In contrast to most published work which has either used finite element methods or Cartesian finite volume methods for transport applications, the topology optimization procedure is developed in a general unstructured finite volume framework. This permits topology optimization for flow and heat transfer applications in complex design domains such as those encountered in industry. In addition, the Rapid library is designed to provide a problem-agnostic pathway to automatically compute all required derivatives to machine accuracy. This obviates the necessity to write new code for finding sensitivities when new physics are added or new cost functions are considered and permits general-purpose implementations of topology optimization for complex industrial applications.

The purpose of this paper is to develop a topology optimization algorithm considering natural frequencies.

To incorporate natural frequency as design criteria of shell-infill structures, two types of design models are formulated: (1) type I model: frequency objective with mass constraint; (2) type II model: mass objective with frequency constraint. The interpolation functions are constructed by the two-step density filtering approach to describe the fundamental topology of shell-infill structure. Sensitivities of natural frequencies and mass with respect to the original element densities are derived, which will be used for both type I model and type II model. The method of moving asymptotes is used to solve both models in combination with derived sensitivities.

Mode switching is one of the challenges faced in eigenfrequency optimization problems, which can be overcome by the modal-assurance-criterion-based mode-tracking strategy. Furthermore, a shifting-frequency-constraint strategy is recommended for type II model to deal with the unsatisfactory topology obtained under direct frequency constraint. Numerical examples are systematically investigated to demonstrate the effectiveness of the proposed method.

In this paper, a topology optimization method considering natural frequencies is proposed by the author, which is useful for the design of shell-infill structures to avoid the occurrence of resonance in dynamic conditions.

The purpose of this paper is to examine and illustrate the development of a methodology for generating swarms using lossless flocking.

A general methodology for swarm design is described. Examples of this approach in the literature are examined. A general requirement for lossless flocking is developed. The requirement is used in developing two swarm behaviors.

It is possible to apply the approach to the lossless flocking and to use the swarm condition to develop two swarm behaviors which satisfy this condition in many situations.

This paper illustrates the general swarm engineering method and demonstrates how it can be properly applied.

The swarm engineering method is used to develop the “quark” model, a new physicomimetic model.

The numerical treatment of non‐linear engineering phenomena often involves some sort of mathematical simplification. In many cases, the system under investigation is linearized about an operating point using the linear part of the Taylor’s series expansion. This allows local representation for use in incremental or iterative methods using well‐established computational tools for linear algebra. Demonstrates a different linearization technique that generally provides a higher quality fit to a certain class of functions than the standard Taylor linearization. This class of functions is general enough to represent all systems of algebraic equations. Presents a graphical demonstration of the quality of fit along with a discussion of why this alternative linearization provides a high quality fit. Also presents an engineering application of the linearization.

Based on a report to the non‐profit organization, The Foundation for the Future, this article aims to review methodological approaches to forecasting the long‐term future.

This is not an analysis of the particular content of the next 500 or 1,000 years but a comparative analysis of methodologies and epistemological approaches best utilized in long‐range foresight work. It involves an analysis of multiple methods to understand long‐range foresight; literature review; and critical theory.

Methodologies that forecast the long‐term future are likely to be more rewarding – in terms of quality, insight, and validity – if they are eclectic and layered, go back in time as far as they go in the future, that contextualize critical factors and long‐term projections through a nuanced reading of macrohistory, and focus on epistemic change, the ruptures that reorder how we know the world.

The article provides frameworks to study the long‐range future. It gives advice on how best to design research projects that are focused on the long‐term. Limitations include: no quantitative studies were used and the approach while epistemologically sensitive remains bounded by Western frameworks of knowledge.

The article provides methodological and epistemological guidance as to the best methods for long range foresight. It overviews strengths and weaknesses of various approaches.

This is the only research project to analyze methodological aspects of 500‐1,000 year forecasting. It includes conventional technocratic views of the future as well as Indic and feminist perspectives. It is among the few studies to link macrohistory and epistemic analysis to study the long‐term.

VARIATION IN “TYPICAL VALUE” PARAMETERS IT has previously been shown that the effect of freeing the controls on the lateral stability of an aircraft may be taken account of by changes both in the values of the derivatives lp, lr, np and nr (wing), which hitherto have had typcial values, and also of the variables x, y and t themselves. It is therefore desirable to have information on the effect on the stability boundaries of changes in these derivatives. It may also happen that the values of yv and tan Θo in the case of a particular aircraft may be known to differ from those here adopted in the drawing of stability charts. The versatility of these charts (later to be given) will therefore be considerably increased if rules are expounded for assessing the effects of changes in any of those derivatives which were formerly fixed. This we proceed to do.

The potential advantage of extreme value theory in modeling management phenomena is the central theme of this paper. The statistics of extremes have played only a very limited role in management studies despite the disproportionate emphasis on unusual events in the world of managers. An overview of this theory and related statistical models is presented, and illustrative empirical examples provided.

The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele‐Shaw model.

The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi‐static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non‐Newtonian.

Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power‐law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries.

With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so‐called “meshless” scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill‐time errors that might be addressed by introducing suitable projections. The general question of “rate of convergence” of these schemes requires analysis. Numerical results here suggest first‐order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods.

This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed “on‐the‐fly” for each “active point” to form a dynamic virtual mesh of active elements that evolves with the moving interface.