Topological Synthesis of Compliant Mechanisms Using Spanning Tree Theory

2004 ◽  
Vol 127 (4) ◽  
pp. 753-759 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Spanning Tree ◽  
Maximum Stress ◽  
Spanning Trees ◽  
Compliant Mechanisms ◽  
Deformation Analysis ◽  
Discrete Optimization Problem ◽  
Minimum Number ◽  
Synthesis Procedure ◽  
And Performance ◽  
Topological Synthesis

This paper introduces the spanning tree theory to the topological synthesis of compliant mechanisms, in which spanning trees connect all the vertices together using a minimum number of edges. A valid topology is regarded as a network connecting input, output, support, and intermediate nodes, which contains at least one spanning tree among the introduced nodes. Invalid disconnected topologies can be weeded out if no spanning tree is included. No further deformation analysis and performance evaluation is needed to invalidate disconnected topologies. Problem-dependent objectives are optimized for topological synthesis of compliant mechanisms. Constraints about maximum input displacement and force, maximum stress and overlapping connections are directly imposed during optimization process. The discrete optimization problem is solved by genetic algorithm with penalty function handling constraints. Two examples are given to verify the effectiveness of the proposed synthesis procedure.

Spanning Tree Based Topological Optimization of Compliant Mechanisms

2005 ◽  
Author(s):  
Hong Zhou ◽  
Kwun-Lon Ting
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Compliant Mechanisms ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Topological Optimization ◽  
Deformation Analysis ◽  
Discrete Optimization Problem ◽  
Minimum Number ◽  
And Performance

In graph theory, spanning trees connect all the vertices together using minimum number of edges. A topological optimization method of compliant mechanisms is presented based on spanning tree theory. A valid topology is regarded as a network connecting input, output, support and intermediate nodes, which contains at least one spanning tree among the introduced nodes. Invalid disconnected topologies can be weeded out if no spanning tree is included. No further deformation analysis and performance evaluation is needed for invalid disconnected topologies. Problem-dependent objectives are optimized for topological optimization of compliant mechanisms. Constraints about maximum input displacement and input force, maximum stress and overlapping connections are directly imposed during the optimization process. The discrete optimization problem is solved by genetic algorithm with penalty function handling constraints. An example is presented to verify the effectiveness of the proposed optimization procedure.

scholarly journals Sectorization for Water Distribution Systems with Multiple Sources: A Performance Indices Comparison

Water ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 131
Author(s):  
Jezabel D. Bianchotti ◽  
Melina Denardi ◽  
Mario Castro-Gama ◽  
Gabriel D. Puccini
Keyword(s):  
Distribution Systems ◽  
Water Distribution ◽  
Distribution Networks ◽  
Performance Criteria ◽  
Performance Indices ◽  
Multiple Sources ◽  
Multiobjective Problems ◽  
Open Questions ◽  
Minimum Number ◽  
And Performance

Sectorization is an effective technique for reducing the complexities of analyzing and managing of water systems. The resulting sectors, called district metering areas (DMAs), are expected to meet some requirements and performance criteria such as minimum number of intervention, pressure uniformity, similarity of demands, water quality and number of districts. An efficient methodology to achieve all these requirements together and the proper choice of a criteria governing the sectorization is one of the open questions about optimal DMAs design. This question is addressed in this research by highlighting the advantages of three different criteria when applied to real-word water distribution networks (WDNs). To this, here it is presented a two-stage approach for optimal design of DMAs. The first stage, the clustering of the system, is based on a Louvain-type greedy algorithm for the generalized modularity maximization. The second stage, the physical dividing of the system, is stated as a two-objective optimization problem that utilises the SMOSA version of simulated annealing for multiobjective problems. One objective is the number of isolation valves whereas for the second objective three different performance indices (PIs) are analyzed and compared: (a) standard deviation, (b) Gini coefficient and (c) loss of resilience. The methodology is applied to two real case studies where the first two PIs are optimized to address similar demands among DMAs. The results demonstrate that the proposed method is effective for sectorization into independent DMAs with similar demands. Surprisingly, it found that for the real studied systems, loss of resilience achieves better performance for each district in terms of pressure uniformity and demand similarity than the other two specific performance criteria.

EVOLUTION OF SHANGHAI STOCK MARKET BASED ON MAXIMAL SPANNING TREES

2012 ◽  
Vol 27 (03) ◽  
pp. 1350022 ◽  
Author(s):  
CHUNXIA YANG ◽  
YING SHEN ◽  
BINGYING XIA
Keyword(s):  
Stock Market ◽  
Stock Prices ◽  
Spanning Tree ◽  
Stock Price ◽  
Spanning Trees ◽  
Turning Points ◽  
Single Step ◽  
P Value ◽  
Power Law Distribution ◽  
Structure Variation

In this paper, using a moving window to scan through every stock price time series over a period from 2 January 2001 to 11 March 2011 and mutual information to measure the statistical interdependence between stock prices, we construct a corresponding weighted network for 501 Shanghai stocks in every given window. Next, we extract its maximal spanning tree and understand the structure variation of Shanghai stock market by analyzing the average path length, the influence of the center node and the p-value for every maximal spanning tree. A further analysis of the structure properties of maximal spanning trees over different periods of Shanghai stock market is carried out. All the obtained results indicate that the periods around 8 August 2005, 17 October 2007 and 25 December 2008 are turning points of Shanghai stock market, at turning points, the topology structure of the maximal spanning tree changes obviously: the degree of separation between nodes increases; the structure becomes looser; the influence of the center node gets smaller, and the degree distribution of the maximal spanning tree is no longer a power-law distribution. Lastly, we give an analysis of the variations of the single-step and multi-step survival ratios for all maximal spanning trees and find that two stocks are closely bonded and hard to be broken in a short term, on the contrary, no pair of stocks remains closely bonded for a long time.

The closed-subpopulation method and estimation of population size from mark-recapture and ancillary data

2000 ◽  
Vol 78 (2) ◽  
pp. 320-326 ◽  
Author(s):  
Frank AM Tuyttens
Keyword(s):  
Population Size ◽  
Ancillary Data ◽  
Mark Recapture ◽  
Animal Populations ◽  
Accuracy And Precision ◽  
Population Size Estimates ◽  
Minimum Number ◽  
Flexible Framework ◽  
And Performance ◽  
Better Than

The algebraic relationships, underlying assumptions, and performance of the recently proposed closed-subpopulation method are compared with those of other commonly used methods for estimating the size of animal populations from mark-recapture records. In its basic format the closed-subpopulation method is similar to the Manly-Parr method and less restrictive than the Jolly-Seber method. Computer simulations indicate that the accuracy and precision of the population estimators generated by the basic closed-subpopulation method are almost comparable to those generated by the Jolly-Seber method, and generally better than those of the minimum-number-alive method. The performance of all these methods depends on the capture probability, the number of previous and subsequent trapping occasions, and whether the population is demographically closed or open. Violation of the assumption of equal catchability causes a negative bias that is more pronounced for the closed-subpopulation and Jolly-Seber estimators than for the minimum-number-alive. The closed-subpopulation method provides a simple and flexible framework for illustrating that the precision and accuracy of population-size estimates can be improved by incorporating evidence, other than mark-recapture data, of the presence of recognisable individuals in the population (from radiotelemetry, mortality records, or sightings, for example) and by exploiting specific characteristics of the population concerned.

Investigation of Strength and Dynamic Characteristics for the Rolling Mill

2013 ◽  
Vol 706-708 ◽  
pp. 1405-1408
Author(s):  
Xi Ping Guo ◽  
Shuang Zhou
Keyword(s):  
Natural Frequency ◽  
Dynamic Characteristics ◽  
Rolling Mill ◽  
Maximum Stress ◽  
Weak Link ◽  
Deformation Analysis ◽  
Vibration Model ◽  
Strength And Stiffness ◽  
Stress And Deformation ◽  
Diagram Analysis

Stress and deformation analysis of 950 mill housing was done by means of ANSYS to calculate the maximum stress and deformation. Strength and stiffness of the mill roll were checked to meet requirements. Carries on the modal analysis to the rolling-mill housing, obtains its first 10 steps the natural frequency and the mode of vibration, through the vibration model diagram analysis frame of the weak link,and it is significant for similar mill housing designs.

The Causal Tracing Method of Fast Moving Consumer Goods Logistics Quality Based on Extended Spanning Tree

2013 ◽  
Vol 694-697 ◽  
pp. 3480-3483
Author(s):  
Shou Wen Ji ◽  
Zeng Rong Su ◽  
Zhi Hua Zhang
Keyword(s):  
Consumer Goods ◽  
Fast Moving ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Logic Model ◽  
Fast Moving Consumer Goods ◽  
Tracing Algorithm ◽  
Tracing Method ◽  
Logistics Quality

The paper analyzes the extended spanning trees elements corresponding to fast-moving consumer goods (FMCG) logistics quality. According to extended spanning tree, we establish a logic model of FMCGs logistics quality causal tracing. At last, the paper gives out tracing algorithm and specific tracing process of FMCG logistics quality based on extended spanning tree.

Synthesis of Distributed Compliant Mechanisms for Adaptive Structures Application: An Elasto-Kinematic Approach

1997 ◽  
Author(s):  
Laxminarayana Saggere ◽  
Sridhar Kota
Keyword(s):  
Smart Materials ◽  
High Performance ◽  
Compliant Mechanisms ◽  
Shape Change ◽  
Current Trend ◽  
Adaptive Structures ◽  
Topology Generation ◽  
Synthesis Procedure ◽  
Actuation Scheme ◽  
Kinematic Approach

Abstract Compliant mechanisms are a class of mechanisms that achieve desired force and motion transmission tasks by undergoing elastic deformations as opposed to rigid-body displacements in the conventional rigid-link mechanisms. Most of the previously reported synthesis studies in compliant mechanisms related to either partially-compliant mechanisms or fully-compliant mechanisms with joint compliance. Methods developed for fully-compliant mechanisms with link compliance addressed the issue of topology generation for desired deflections at discrete points on the mechanism. This paper presents a new, first-principles based synthesis procedure for fully-compliant mechanisms with link compliance — that is, distributed-compliant mechanisms — for continuous shape change requirements in a particular segment of a mechanism. The general approach presented in this paper for the synthesis of distributed compliant mechanisms is shown to be well suited for application in the design of adaptive structures, an emerging class of high-performance structural systems. The current trend in the design of adaptive structures is to embed structures with force or strain inducing “smart” materials to serve as distributed actuators. Potential advantages of using the distributed compliance scheme over the distributed actuation scheme in the design of adaptive structures include a significant reduction in the number of required actuators and controls.

On the number of leaves of a euclidean minimal spanning tree

1987 ◽  
Vol 24 (4) ◽  
pp. 809-826 ◽  
Author(s):  
J. Michael Steele ◽  
Lawrence A. Shepp ◽  
William F. Eddy
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Random Variables ◽  
Minimal Spanning Tree ◽  
Absolutely Continuous ◽  
Mean And Variance ◽  
Number Of Leaves ◽  
The Mean ◽  
Vertex Degrees ◽  
Minimal Spanning Trees

Let Vk,n be the number of vertices of degree k in the Euclidean minimal spanning tree of Xi, , where the Xi are independent, absolutely continuous random variables with values in Rd. It is proved that n–1Vk,n converges with probability 1 to a constant α k,d. Intermediate results provide information about how the vertex degrees of a minimal spanning tree change as points are added or deleted, about the decomposition of minimal spanning trees into probabilistically similar trees, and about the mean and variance of Vk,n.

scholarly journals Matchings, Cycle Bases, and the Maximum Genus of a Graph

10.37236/2479 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Michal Kotrbčík ◽  
Martin Škoviera
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Perfect Matching ◽  
Intersection Graph ◽  
Matching Number ◽  
Maximum Genus ◽  
Cycle Space ◽  
Intersection Graphs ◽  
Connected Graphs ◽  
Cycle Bases

We study the interplay between the maximum genus of a graph and bases of its cycle space via the corresponding intersection graph. Our main results show that the matching number of the intersection graph is independent of the basis precisely when the graph is upper-embeddable, and completely describe the range of matching numbers when the graph is not upper-embeddable. Particular attention is paid to cycle bases consisting of fundamental cycles with respect to a given spanning tree. For $4$-edge-connected graphs, the intersection graph with respect to any spanning tree (and, in fact, with respect to any basis) has either a perfect matching or a matching missing exactly one vertex. We show that if a graph is not $4$-edge-connected, different spanning trees may lead to intersection graphs with different matching numbers. We also show that there exist $2$-edge connected graphs for which the set of values of matching numbers of their intersection graphs contains arbitrarily large gaps.

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