NUMERICAL VERIFICATION OF ONE APPROACH OF BIONIC RATIONALIZATION OF STRUCTURES

Abstract

. The paper provides the procedure of forward-engineering (intelligent) beam design. This technology is an exclusive modification of topological (bionic) optimization. It is based on the new energy principles and the algorithms for successive construction of geometric and/or physical-mechanical “pattern” of a structure. The sequence of computational operations of the method in question is illustrated on example of forming beams of energetically uniform strength. The solution is built analytically to show the nuances of the operations required. Simultaneously, the proceeding examples show that the introduced optimization criteria in the form of e n → const and U → inf U (here, e n is the value of the normalized potential deformation energy density, and U is the potential deformation energy) cause, including, the minimum volume of constructs, and their minimum deflections. A fundamental element of the given approach is the use of a new criterion for the limit state, which provides an estimate of the element’s stress. In this case, the properties of the material and the type of the stress and strain state are taken into account. The analytical solution obtained was used as a checkup test for the general computational procedure of the method in question. In this connection, the paper features the results of analytical and numerical solutions. The efficiency of the computational procedure is confirmed by the rate of its convergence and the minimal variation of geometrical construction parameters (topology) with test cases. It is shown that the resultant stepwise complex beam structure can be simplified through unification, which is carried out by the method of dynamic programming. The technological flow of computational operations of the method in question is completed by the construction of elements (beams) with basic external and complex internal geometry. The feasibility of the theoretical results obtained is confirmed by their implementation in the construction of various projects.