Topology optimization in the case of different boundary conditions by an iterative method

Abstract

Optimal design with thousands of variables is a great challenge in engineering calculations. In this paper an iteration based topology design technique is introduced for the optimization of linearly elastic continuum type structures under single parametric static loading and different displacement boundary conditions. The support optimization is discussed briefly, as well. The investigated problem is utilized by minimization of the weight of the structure subjected to displacement constraints. The numerical procedure is based on an iterative formula which is formed by the use of the Kuhn-Tucker condition of the Lagrangian function of the constraint mathematical programming problem. The application is illustrated by numerical examples. Mathematical Subject Classification: 74P15Recently the topology optimization is one of the most "popular" topic in the expanding field of optimal design. A great number of papers indicates the importance of the topic [1,[3][4][5]7,9,11,23,25,27,28]. The popularity comes one part from the needs of the industry (car, airplane, etc.) and other part from the complexity of the problem which is a great challenging for the researchers. In present stage the field of topology optimization can be divided into two subfields: optimal design of skeletal structures (trusses, grids, etc.,) deals with the simultaneous optimization of the member sizes