Conceptual configuration design of line-foldable deployable space truss structures employing graph theory

2022 ◽  
pp. 095440622110621
Author(s):  
Shoufei Wang ◽  
Yong Zhao
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Geometric Dimension ◽  
Maximum Clique ◽  
Truss Structures ◽  
Configuration Design ◽  
Topological Graph ◽  
Space Truss ◽  
Configuration Synthesis ◽  
Chordless Cycle

From the perspective of the truss as a whole, this research investigates the conceptual configuration design for deployable space truss structures that are line-foldable with the help of graph theory. First, the bijection between a truss and its graph model is established. Therefore, operations can be performed based on graph models. Second, by introducing Maxwell’s rule, maximum clique, and chordless cycle, the principle of conceptual configuration synthesis is analyzed. A corresponding procedure is formed and it is verified by a truss with seven nodes. Third, assisted by some theorems of graph theory, the simplified double-color topological graph of deployable space truss structures is acquired and it also displays the procedure with a case. Finally, based on the above analysis, it obtains the optimal conceptual configurations. This novel research lays the foundation for kinematic synthesis and geometric dimension designs.

Conceptual Configuration Synthesis of Line-Foldable Deployable Space Truss Structures Utilizing Graph Theory and Entropy

2021 ◽  
Author(s):  
Shoufei Wang ◽  
Yong Zhao
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Geometric Dimension ◽  
Maximum Clique ◽  
Entropy Change ◽  
Truss Structures ◽  
Space Truss ◽  
Linear Configuration ◽  
Configuration Synthesis ◽  
Necessary And Sufficient

Abstract From the perspective of the truss as a whole, this research presents an approach to synthesizing conceptual configurations for deployable space truss structures that are line-foldable with the help of graph theory and entropy. First, according to graph theory, the bijection between a truss and its graph model is established by defining a bijective mapping between set elements. Therefore, operations can be performed based on graph models. Second, the principle of configuration evolution is interpreted by employing Maxwell’s rule, it also discusses the necessary and sufficient condition of configuration evolution. Configurations of evolution belong to three phases: space configuration, transformation configuration, and linear configuration. And it finds that the reasonable transformation configuration plays a key role. Further, maximum clique detection depending on backtracking is used to screen out unreasonable transformation configurations. Third, it introduces entropy, and the phenomenon of entropy change in configuration evolution is revealed and induction weights of rigid links are defined. It calculates the weight value of a transformation configuration by adding up induction weights of rigid links removed, also, weight values are used to classify transformation configurations. Finally, based on the previous analysis, a procedure to synthesize transformation configurations is formed and it is verified by a truss model with 7 nodes. This research lays the foundation for geometric dimension design and engineering applications.

scholarly journals Finding Maximum Clique in Stochastic Graphs Using Distributed Learning Automata

2015 ◽  
Vol 23 (01) ◽  
pp. 1-31 ◽  
Author(s):  
Alireza Rezvanian ◽  
Mohammad Reza Meybodi
Keyword(s):  
Community Structure ◽  
Dominating Set ◽  
Learning Automata ◽  
Random Variables ◽  
Graph Model ◽  
Maximum Clique ◽  
Distribution Functions ◽  
Maximum Clique Problem ◽  
Stochastic Graphs ◽  
Stochastic Graph

Because of unpredictable, uncertain and time-varying nature of real networks it seems that stochastic graphs, in which weights associated to the edges are random variables, may be a better candidate as a graph model for real world networks. Once the graph model is chosen to be a stochastic graph, every feature of the graph such as path, clique, spanning tree and dominating set, to mention a few, should be treated as a stochastic feature. For example, choosing stochastic graph as the graph model of an online social network and defining community structure in terms of clique, and the associations among the individuals within the community as random variables, the concept of stochastic clique may be used to study community structure properties. In this paper maximum clique in stochastic graph is first defined and then several learning automata-based algorithms are proposed for solving maximum clique problem in stochastic graph where the probability distribution functions of the weights associated with the edges of the graph are unknown. It is shown that by a proper choice of the parameters of the proposed algorithms, one can make the probability of finding maximum clique in stochastic graph as close to unity as possible. Experimental results show that the proposed algorithms significantly reduce the number of samples needed to be taken from the edges of the stochastic graph as compared to the number of samples needed by standard sampling method at a given confidence level.

Conceptual configuration synthesis of line-foldable type quadrangular prismatic deployable unit based on graph theory

2018 ◽  
Vol 121 ◽  
pp. 563-582 ◽  
Author(s):  
Chuang Shi ◽  
Hongwei Guo ◽  
Meng Li ◽  
Rongqiang Liu ◽  
Zongquan Deng
Keyword(s):  
Graph Theory ◽  
Configuration Synthesis

Mechanical Structural Interference Detection for Dedicated Hybrid Transmissions

2021 ◽  
Vol 143 (9) ◽  
Author(s):  
Hanqiao Sun ◽  
Xiangyang Xu ◽  
Yanfang Liu ◽  
Peng Dong ◽  
Shuhan Wang ◽  
...  
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Planetary Gear ◽  
Modeling Method ◽  
Structural Synthesis ◽  
Original Graph ◽  
Power Sources ◽  
Detection Approach ◽  
Hybrid Transmission ◽  
Planetary Gear System

Abstract Planetary gear set (PGS) has been one of the best components to constitute a transmission configuration, including the dedicated hybrid transmission (DHT). Using different synthesis approaches, the DHT configurations can be obtained through algorithms. However, different synthesis results correspond to different connection states of the planetary gear system. There are a certain number of results that violate the motion requirements of the mechanical principal need to be detected and removed. Therefore, this paper presents a novel modeling method to systematically remove the interference structures, with graph theory in structural synthesis. Based on the original graph theory, this paper proposes an equivalent replacement modeling method to convert the motor graph model into a brake-like graph model. Based on the conversion, avoid the appearance of the hanging points in the graph model. By applying the proposed approach, a DHT structure proves the feasibility of the method. The proposed detection approach can systematically detect all the PGS-based transmission with multi-PGSs, multi-shifting elements, and multi-power sources.

scholarly journals p-box: a new graph model

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Mauricio Soto ◽  
Christopher Thraves-Caro
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Directed Path ◽  
Outerplanar Graphs ◽  
New Model ◽  
Model Based ◽  
Representative Element ◽  
International Audience ◽  
Graph Families

Graph Theory International audience In this document, we study the scope of the following graph model: each vertex is assigned to a box in ℝd and to a representative element that belongs to that box. Two vertices are connected by an edge if and only if its respective boxes contain the opposite representative element. We focus our study on the case where boxes (and therefore representative elements) associated to vertices are spread in ℝ. We give both, a combinatorial and an intersection characterization of the model. Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path). We also study the particular case where each representative element is the center of its respective box. In this particular case, we provide constructive representations for interval, block and outerplanar graphs. Finally, we show that the general and the particular model are not equivalent by constructing a graph family that separates the two cases.

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