/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials. This allows us to derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design. Thus it is shown that the so-called artificial interpolation model in many circumstances actually falls within the framework of microstructurally based models. Single material and multi-material structural design in elasticity as well as in multi-physics problems is discussed.

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Material interpolation schemes in topology optimization

The paper presents a compact Matlab implementation of a topology optimization code for compliance minimization of statically loaded structures. The total number of Matlab input lines is 99 including optimizer and Finite Element subroutine. The 99 lines are divided into 36 lines for the main program, 12 lines for the Optimality Criteria based optimizer, 16 lines for a mesh-independency filter and 35 lines for the finite element code. In fact, excluding comment lines and lines associated with output and finite element analysis, it is shown that only 49 Matlab input lines are required for solving a well-posed topology optimization problem. By adding three additional lines, the program can solve problems with multiple load cases. The code is intended for educational purposes. The complete Matlab code is given in the Appendix and can be down-loaded from the web-site http://www.topopt.dtu.dk.

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A 99 line topology optimization code written in Matlab

Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.

Topology optimization approaches: A comparative review

In this paper we seek to summarize the current knowledge about numerical instabilities such as checkerboards, mesh-dependence and local minima occurring in applications of the topology optimization method. The checkerboard problem refers to the formation of regions of alternating solid and void elements ordered in a checkerboard-like fashion. The mesh-dependence problem refers to obtaining qualitatively different solutions for different mesh-sizes or discretizations. Local minima refers to the problem of obtaining different solutions to the same discretized problem when choosing different algorithmic parameters. We review the current knowledge on why and when these problems appear, and we list the methods with which they can be avoided and discuss their advantages and disadvantages.

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Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima

Abstract Purpose The aim of this study was to examine how victims of intimate partner violence (IPV) differ in terms of vulnerability factors and risk of being re-victimized, by comparing victims of the two most consistently identified IPV male perpetrator subtypes: the Partner Only (PO) violent and the Generally Violent (GV). Methods The current study analyzed IPV reported to the Swedish police and consisted of a sample of 1479 cases of male-to-female perpetrated IPV. The material mainly consisted of IPV risk assessments conducted by the police. Results The results showed that vulnerability factors were significantly more common among victims of GV perpetrators, including inconsistent attitudes or behaviors, extreme fear of the perpetrator, inadequate support or resources, an unsafe living situation, and health problems. Moreover, victims of GV perpetrators were generally assessed by the police with a significantly higher risk of being re-victimized by IPV. Finally, in relation to the victim vulnerability factors most strongly associated with an elevated assessed risk for IPV re-victimization, the presence of extreme fear of the perpetrator and having an unsafe living situation were significantly related to such outcomes for both groups of victims. Conclusion In sum, the results of this study contribute to the scant body of knowledge on IPV victim subtypes and their vulnerability profiles. In addition to facilitating the risk assessment of repeated IPV, such knowledge could also indicate what type of support different victim subtypes require in order to prevent IPV. 

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Vulnerability Factors of Intimate Partner Violence Among Victims of Partner Only and Generally Violent Perpetrators

We consider shape and topology optimization of elastic continua where equilibrium is governed by the elliptic Cauchy-Navier’s system of PDEs. The domain of integration, Ω, is fixed, and the design parametrization is done by letting the elasticity tensor depend linearly on a design function ρ. To get binary values of ρ representing material or not at each point of Ω, we use a regularized penalty function which also guarantees existence of solutions.

Three Dimensional Shape and Topology Optimization in Cauchy-Navier’s PDE

Rural Differences in Victim Vulnerability and Revictimization of Intimate Partner Violence.

ABSTRACT This study aimed to examine the importance of differentiating between partner violent men in terms of immigrant or native Swedish background, when assessing risk for intimate partner violence (IPV) recidivism. A quantitative design was used with a sample of 1263 alleged male perpetrators reported for IPV-related crimes to the Swedish police. Data consisted of police officers’ risk assessments using the Swedish version of the Brief Spousal Assault Form for the Evaluation of Risk (B-SAFER). Results showed that risk factors such as 'Violent threats or thoughts', and 'Violent attitudes', were more common for perpetrators with an immigrant background. In contrast, risk factors such as 'General criminality' and 'Substance use problems' were more common among native perpetrators. Furthermore, in relation to the importance of specific risk factors for an elevated risk of IPV recidivism, such risk was elevated for perpetrators with a native background when ‘Violent threats or thoughts’, ‘General criminality’ and ‘Relationship problems’ were present. Corresponding factors for immigrant perpetrators consisted of ‘Escalation’ and ‘General criminality’. These results are essential for the police to recognize and understand since only victims in IPV cases with an elevated assessed risk will be eligible for risk management and protective actions.

Joakim Petersson

Papers

Vulnerability Factors of Intimate Partner Violence Among Victims of Partner Only and Generally Violent Perpetrators

Three Dimensional Shape and Topology Optimization in Cauchy-Navier’s PDE

Rural Differences in Victim Vulnerability and Revictimization of Intimate Partner Violence.

Risk factors for intimate partner violence among native and immigrant male partners in Sweden