ArchLab: a MATLAB tool for the Thrust Line Analysis of masonry arches

Abstract According to Heyman’s safe theorem of the limit analysis of masonry structures, the safety of masonry arches can be verified by finding at least one line of thrust entirely laying within the masonry and in equilibrium with external loads. If such a solution does exist, two extreme configurations of the thrust line can be determined, respectively referred to as solutions of minimum and maximum thrust. In this paper it is presented a numerical procedure for determining both these solutions with reference to masonry arches of general shape, subjected to both vertical and horizontal loads. The algorithm takes advantage of a simplification of the equations underlying the Thrust Network Analysis. Actually, for the case of planar lines of thrust, the horizontal components of the reference thrusts can be computed in closed form at each iteration and for any arbitrary loading condition. The heights of the points of the thrust line are then computed by solving a constrained linear optimization problem by means of the Dual-Simplex algorithm. The MATLAB implementation of presented algorithm is described in detail and made freely available to interested users (https://bit.ly/3krlVxH). Two numerical examples regarding a pointed and a lowered circular arch are presented in order to show the performance of the method.

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A sequential dual simplex algorithm for the linear assignment problem

Operations Research Letters ◽

10.1016/0167-6377(89)90012-6 ◽

1989 ◽

Vol 8 (2) ◽

pp. 117 ◽

Cited By ~ 1

Author(s):

Mustafa Akgül

Keyword(s):

Assignment Problem ◽

Simplex Algorithm ◽

Linear Assignment Problem ◽

Dual Simplex ◽

Linear Assignment ◽

Dual Simplex Algorithm

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Nonlinear Analysis of Cable Net Structures Suspended from Arches with Block and Tackle Suspension System, Taking into Account the Friction of the Pulleys

International Journal of Space Structures ◽

10.1260/026635109789867643 ◽

2009 ◽

Vol 24 (3) ◽

pp. 143-152 ◽

Cited By ~ 14

Author(s):

Krisztián Hincz

Keyword(s):

Structural Analysis ◽

Static Analysis ◽

Simple Structure ◽

Complex Structure ◽

Numerical Procedure ◽

Suspension System ◽

Dynamic Relaxation ◽

Final State ◽

The Stability ◽

External Loads

A numerical procedure for the static analysis of arch-supported tensile structures with block and tackle suspension system is presented. The procedure, based on dynamic relaxation, is suitable for a structural analysis both in the prestressing process and in a final state under external loads. The friction between the pulley and its shaft is also taken into account in the analysis. After the introduction of the developed procedure, two structures are presented as examples. The analysis of a very simple structure validates the procedure, then the analysis of a more complex structure, an arch-supported cable net roof illustrates the stability and efficiency of the procedure.

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Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

Optimizing, Innovating, and Capitalizing on Information Systems for Operations ◽

10.4018/978-1-4666-2925-7.ch004 ◽

2013 ◽

pp. 64-82

Author(s):

Seyed Hadi Nasseri ◽

Ali Ebrahimnejad

Keyword(s):

Linear Programming ◽

Simplex Algorithm ◽

Programming Models ◽

Fuzzy Data ◽

Fuzzy Variables ◽

Fuzzy Environment ◽

Dual Simplex ◽

Linear Programming Problems ◽

Simplex Tableau ◽

Dual Simplex Algorithm

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

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