IMPROVEMENT OF CROSS SECTION OF COMPRESSED ELEMENTS BY TOPOLOGICAL RATIONALIZATION

Abstract

The article describes the procedure of direct (rational) design of vertical compressed elements (columns, pylons, stiffening diaphragms, retaining walls). This technology is an exclusive modification of topological (bionic) rationalization. It is based on new energy principles and algorithms for sequential construction of geometric and / or physical-mechanical "image" of the structure. The example of the formation of energy-equivalent columns shows the sequence of computational operations of the method. The solution is built analytically in order to show the nuances of the necessary operations. At the same time, these examples show that the introduced optimization criteria in the form of en → const and U → inf U (here en is the value of the normalized density of potential deformation energy, and U is the potential energy of deformation) determine, including the minimum volume of constructs, as well as their minimum deflections. A fundamental element of the approach is the use of a new criterion of the limit state, which provides an estimate of the intensity of the element. In this case, the properties of the material and the type of stress-strain state are taken into account. The obtained analytical solution was used as a control test for the general computational procedure of the method. In this regard, the article presents the results of the analytical and numerical solution. The efficiency of the computational procedure is confirmed by the speed of its convergence and the minimum difference of geometric parameters (topology) of the structure with test examples. The technological sequence of computational operations of the method is completed by the construction of elements (pylons) with a simple external and complex internal geometry. Keywords: deformation, energy, iteration, voids, cavity, rationalization.