Determination of support reactions of rod constructions obtained by morphogenesis.

 Volodymyr Skochko ^1*
1Architectural Structures Department of Kyiv National University of Construction and Architecture. 
Received: 06/01/2018, Accepted: 10/03/2018, Correction dated: 10/07/2018. 
DOI: https://doi.org/10.32557/useful-2-3-2018-0005
HDL: http://hdl.handle.net/20.500.12334/13
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*Corresponding author: e-mail: vladimir.and.friends@gmail.com, address: Povitroflotsky Avenue, 31, Kyiv, 03680 Ukraine
Under a creative commons license. Volume 2, Issue 3, 2018, pages: 29-42.

     

Author Keywords: rod structures, geometrical morphogenesis, discrete geometry

Abstract

This article shows a method for determining the support reactions of rod architectural structures, the position of free nodes of which was previously obtained by discrete geometrical morphogenesis (shaping). At the same time, the order and principle of defining and forming all the necessary discrete data on the topological features of the model, its boundary conditions, external loads and the distribution of internal forces are considered. The algorithm is based on logical operations and matrix transformations.

1. Introduction

Most of the rod structures of coatings have a difficult configuration and are statically indeterminate due to the large number of supports and the specifics of their fixing. Therefore, the calculation of support reactions in order to determine the potential loads from these structures can become a challenge and require the use of modern numerical methods of complex modelling. If all internal forces in the rods (connections) that are attached to the supporting nods are known, then the determination of the values of the support reactions themselves is reduced to the operation of adding the vector components of the internal forces in these rods. Thus, the search of support reactions again indicates the need to calculate the components of the stress-strain state of the entire structure. For the use of numerical methods and the corresponding software, it is necessary to specify all the geometric, physical and mechanical structure parameters, which, as a rule, requires considerable effort and time. However, if it is a question of pre-design works or sketch designing, the time spent by designers on the evaluation of non-final solutions may not be appropriate. In this case, methods of geometrical morphogenesis can be useful. One of these methods is the static geometric method of discrete geometry [1], which allows realizing morphogenesis of the rod structure with pre-defined topological features and expected pattern of distribution of the density of internal forces in all rods. This method is applicable for momentless constructions, the rods of which work only on compression or tension. However, there is no unified methodology for the shaping of all necessary discrete data, relating to topological features, boundary conditions, external loads and the distribution of internal forces of the computational model. At the same time, the development of a systematic approach to the preparation of all these data is a very urgent task, since on the basis of the results of solving it, the tasks of shaping and determining support reactions can also be solved.

References

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Please cite as: V. Skochko, “Determination of support reactions of rod constructions obtained by morphogenesis.” USEFUL online journal, vol. 2, no. 3, pp. 29–42, Oct. 2018. DOI: https://doi.org/10.32557/useful-2-3-2018-0005