Simplex Search Behavior in Nonlinear Optimization

It is often a desire in many fields such as mathematics, physics, and engineering to solve bound constrained minimization problems. Non-derivative based direct search methods each use a specific method of function sampling in an attempt to home in on the minimizers of a given function. Here we focus on threes simplex based direct search methods: the original simplex search provided by the description of Spendley,Hext and Himsworth; a variation on its theme provided by Nelder and Mead; and a sequential version of Torczon\u27s multidirectional search. It is a common assumption that these searches are easily implemented and used. This research addresses this claim and suggests that these searches are more intricate and should be implemented and used in a careful fashion.We first provide a formal description of each algorithm using a common notation, providing a means of direct comparison between algorithms. We then discuss the importance of resolving seemingly small ambiguities in these algorithms before using them for optimization. For this, we provide an anomaly specific to the Nelder-Mead algorithm in which the search fails to converge to a constrained stationary point. We conclude with some preliminary results of execution of these algorithms on a specific set of objective functions

The role of the servant leadership on the relation between ethical climate perception and innovative work

Globalization and changes in technology forced enterprises to adopt contemporary management approaches in order to gain a sustainable competitive edge. To this end, human resources gained a great interest as a managerial tool to sustain that advantage. While managers are expected to display appropriate leadership style and to create a suitable climate, employees are anticipated to display adaptive performance and innovative work behaviors. This study, therefore, aims at investigating the relationship among key variables for human capital management in terms of innovative practices. A survey is carried out with 254 employees in hospitality business in Turkish Republic of Northern Cyprus and it is concluded that ethical climate perception has a positive effect on innovative work behavior. Furthermore, a mediation role of servant leadership on the relationship between ethical climate perception and innovative work behavior is observed.peer-reviewe

A plasticity model for powder compaction processes incorporating particle deformation and rearrangement

This article is available open access through the publisher’s website at the link below. Copyright @ 2008 Elsevier Ltd.This paper develops a mechanistic model of granular materials that can be used with a commercial finite element package (ABAQUS). The model draws on the ideas of critical state soil mechanics and combines them with the theory of envelopes to develop an elasto-plastic model with a non-associated flow rule. The model incorporates both local deformation at the granule contacts, and rearrangement of the granules so that jointly they account for any bulk deformation. The mechanics of the model closely reflect the physicality of the material behaviour and the model parameters are closely linked (although not simplistically identical) to the characteristics of the granules. This not only gives an insight into the material behaviour, but also enables the model to be used to facilitate design of the material, its processing properties and, hence, component development. The model is used to simulate drained triaxial tests, settlement of a powder in a bin, and some examples of die pressing. Simulations are compared with experimental data and with predictions obtained using other models

Failure analysis based on microvoid growth for sheet metal during uniaxial and biaxial tensile tests

The aim of the presented investigations is to perform an analysis of fracture and instability during simple and complex load testing by addressing the influence of ductile damage evolution in necking processes. In this context, an improved experimental methodology was developed and successfully used to evaluate localization of deformation during uniaxial and biaxial tensile tests. The biaxial tensile tests are carried out using cruciform specimen loaded using a biaxial testing machine. In this experimental investigation, Stereo-Image Correlation technique has is used to produce the heterogeneous deformations map within the specimen surface. Scanning electron microscope is used to evaluate the fracture mechanism and the micro-voids growth. A finite element model of uniaxial and biaxial tensile tests are developed, where a ductile damage model Gurson-Tvergaard-Needleman (GTN) is used to describe material deformation involving d`amage evolution. Comparison between the experimental and the simulation results show the accuracy of the finite element model to predict the instability phenomenon. The advanced measurement techniques contribute to understand better the ductile fracture mechanism

Three-dimensional molecular dynamics simulations of void coalescence during dynamic fracture of ductile metals

Void coalescence and interaction in dynamic fracture of ductile metals have been investigated using three-dimensional strain-controlled multi-million atom molecular dynamics simulations of copper. The correlated growth of two voids during the coalescence process leading to fracture is investigated, both in terms of its onset and the ensuing dynamical interactions. Void interactions are quantified through the rate of reduction of the distance between the voids, through the correlated directional growth of the voids, and through correlated shape evolution of the voids. The critical inter-void ligament distance marking the onset of coalescence is shown to be approximately one void radius based on the quantification measurements used, independent of the initial separation distance between the voids and the strain-rate of the expansion of the system. The interaction of the voids is not reflected in the volumetric asymptotic growth rate of the voids, as demonstrated here. Finally, the practice of using a single void and periodic boundary conditions to study coalescence is examined critically and shown to produce results markedly different than the coalescence of a pair of isolated voids.Comment: Accepted for publication in Physical Review

Effect of stress-triaxiality on void growth in dynamic fracture of metals: a molecular dynamics study

The effect of stress-triaxiality on growth of a void in a three dimensional single-crystal face-centered-cubic (FCC) lattice has been studied. Molecular dynamics (MD) simulations using an embedded-atom (EAM) potential for copper have been performed at room temperature and using strain controlling with high strain rates ranging from 10^7/sec to 10^10/sec. Strain-rates of these magnitudes can be studied experimentally, e.g. using shock waves induced by laser ablation. Void growth has been simulated in three different conditions, namely uniaxial, biaxial, and triaxial expansion. The response of the system in the three cases have been compared in terms of the void growth rate, the detailed void shape evolution, and the stress-strain behavior including the development of plastic strain. Also macroscopic observables as plastic work and porosity have been computed from the atomistic level. The stress thresholds for void growth are found to be comparable with spall strength values determined by dynamic fracture experiments. The conventional macroscopic assumption that the mean plastic strain results from the growth of the void is validated. The evolution of the system in the uniaxial case is found to exhibit four different regimes: elastic expansion; plastic yielding, when the mean stress is nearly constant, but the stress-triaxiality increases rapidly together with exponential growth of the void; saturation of the stress-triaxiality; and finally the failure.Comment: 35 figures, which are small (and blurry) due to the space limitations; submitted (with original figures) to Physical Review B. Final versio

A General Solution to the Aircraft Trim Problem

Trim defines conditions for both design and analysis based on aircraft models. In fact, we often define these analysis points more broadly than the conditions normally associated with trim conditions to facilitate that analysis or design. In simulations, these analysis points establish initial conditions comparable to flight conditions. Based on aerodynamic and propulsion systems models of an aircraft, trim analysis can be used to provide the data needed to define the operating envelope or the performance characteristics. Linear models are typically derived at trim points. Control systems are designed and evaluated at points defined by trim conditions. And these trim conditions provide us a starting point for comparing one model against another, one implementation of a model against another implementation of the same model, and the model to flight-derived data. In this paper we define what we mean by trim, examine a variety of trim conditions that have proved useful and derive the equations defining those trim conditions. Finally we present a general approach to trim through constrained minimization of a cost function based on the nonlinear, six-degree-of freedom state equations coupled with the aerodynamic and propulsion system models. We provide an example of how a trim algorithm is used with a simulation by showing an example from JSBSim