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Showing 4 results for Graph Theory

A. Kaveh, H.a. Rahimi Bondarabady, L. Shahryari,
Volume 4, Issue 3 (9-2006)
Abstract

The main aim of this paper is to extend the recently developed methods for calculating the buckling loads of planar symmetric frames to include the effect of semi-rigidity of the joints. This is achieved by decomposing a symmetric model into two submodels and then healing them in such a manner that the :::union::: of the eigenvalues of the healed submodels result in the eigenvalues of the entire model. Thus the critical load of the frame is obtained using the eigenvalues of its submodels.
Sh. Afandizadeh, M. Yadak, N. Kalantar,
Volume 9, Issue 1 (3-2011)
Abstract

The congestion pricing has been discussed as a practical tool for traffic management on urban transport networks. The traffic congestion is defined as an external diseconomy on the network in transport economics. It has been proposed that the congestion pricing would be used to reduce the traffic on the network. This paper investigates the cordon-based second-best congestion-pricing problems on road networks, including optimal selection of both toll levels and toll locations. A road network is viewed as a directed graph and the cutest concept in graph theory is used to describe the mathematical properties of a toll cordon by examining the incidence matrix of the network. Maximization of social welfare is sought subject to the elastic-demand traffic equilibrium constraint. A mathematical programming model with mixed (integer and continuous) variables is formulated and solved by use of two genetic algorithms for simultaneous determination of the toll levels and cordon location on the networks. The model and algorithm are demonstrated in the road network of Mashhad CBD.
A. Kaveh, S. Beheshti,
Volume 11, Issue 2 (6-2013)
Abstract

For the analysis of structures, the first step consists of configuration processing followed by data generation. This step is the most time consuming part of the analysis for large-scale structures. In this paper new graph products called triangular and circular graph products are developed for the formation of the space structures. The graph products are extensively used in graph theory and combinatorial optimization, however, the triangular and circular products defined in this paper are more suitable for the formation of practical space structural models which can not be generated easily by the previous products. The new products are employed for the configuration processing of space structures that are of triangular or a combination of triangular and rectangular shapes, and also in circular shapes as domes and some other space structural models. Cut out products are other new types of graph products which are defined to eliminate all of the connected elements to the considered node to configure the model or grid with some vacant panels inside of the model. The application of the presented graph products can be extended to the formation of finite element models.
A. Kaveh, M.s. Massoudi ,
Volume 12, Issue 2 (6-2014)
Abstract

Formation of a suitable null basis is the main problem of finite elements analysis via force method. For an optimal analysis, the selected null basis matrices should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrices. In this paper, an efficient method is developed for the formation of the null bases of finite element models (FEMs) consisting of tetrahedron elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs with the FEM and selecting appropriate subgraphs and forming the self-equilibrating systems (SESs) on these subgraphs. Two examples are presented to illustrate the simplicity and effectiveness of the presented graph-algebraic method.

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