A research on the new mathematical models in structural design

Thanks to the close relationship that the mathematics have established with various disciplines including architecture and the computer-aided design technology which has an expanding area of use with ever-growing development of the technology, it has become likely to use different mathematical models in the design process. Structure design through mathematical models has brought the geometry and material parameters forward. The theory of complexity plays an important role in the structure design with respect to the modeling of the dynamics in the system. It makes the load-bearing system a designable system that there are many parameters which are different from each other and the process of exploring the relationships between them. Geometry constitutes the form of this system and the first parameter that catches the attention. Each created form consists of geometry, and the structure design is required for the form to be able to remain standing. In architecture, the material along with geometry constitutes the main components in formation of the design texture, form and the appearance of the building. In the light of the finite element analysis as the major method in structure design, Arup optimizer, dynamic relaxation, evolutionary shape optimizer and evolutionary structural optimizer have been examined. Catenary, curvature, minimal surface and nurbs models resulting from these analyses have been studied. Arup optimizer chooses the most suitable repetition elements that will help it self-organize itself in the whole system and individually analyzes these elements. Dynamic relaxation enables the optimization of the topological form arch structure that helps self-formation of the material by gravity. Evolutionary shape optimizer analyzes the structural element layout that causes minimum displacement to choose the most suitable area for the freeform. Evolutionary structure optimizer carries out the analyses to decrease the vector tension in the system. The chain in the catenary model among the structure models takes the form of the curve emerging against the gravity. Curvature is the form that occurs through the older breaking point?s bending as a result of that the threshold value of the breaking point of the material has increased with the developing technology and new materials. Minimal surfaces are the forms that have a minimum surface-tension potential energy and the minimum area. Nurbs is a curve of non-uniform lines, and these curves are used in calculation of the possible line and surface connections that may be taken as reference for the structure of freeform structures by mapping the geometry. In those structure systems where mathematics create a model for, the simulation created electronically has constituted an interface which the architects and engineers can be used jointly by leaving the bothering and complicated calculation of the past.