The Modified Optimum Reliable Beam Design Problem Solved by Penalty Approach

journal article - other

English

The purpose of the paper is to present and discuss a special modification of stochastic programming related method based on penalty approach that was originally developed and further improved by Branda and Dupacova for general problems involving probabilistic constraints. The authors of this paper discuss method’s importance and implementation for obtaining of approximating optimal solutions of specific civil engineering design problems. The discussed stochastic programming formulation has a two-stage structure, involves differential equation based constraints, related initial and boundary conditions and joint probabilistic constraints representing reliability requirements. It is important to recognize that such a formulation is widely applicable in the considered engineering area. Hence, a suitable transformation of an aforementioned optimization program based on several discretizations can allow the use of this method for a large set of studied optimal design problems. Therefore, engineering requirements coming from practitioners and asking method’s robust usability under various quantitative or even qualitative model changes can be satisfied. The authors illustrate their general ideas dealing with a so called optimum reliable beam design problem which reduced and modified versions have been recently studied by Mrazkova, Popela, Sabartova, Kokrda, and Kudela. Following the above mentioned framework, the problem is formulated, the underlying stochastic program is built and transformed by using a finite element method. Then, the penalty approach is modified and set up for the developed two-stage scenario-based reformulation, its implementation in Matlab is tested, and obtained results are discussed. Furthermore, model changes inspired by practitioners are introduced and the modified penalty method is applied again. At the end, comparisons and conclusions are made.

Stochastic optimization, Finite element method, Penalty approach

KOKRDA, L.; VENCLOVSKÝ, J.; LANÍKOVÁ, I.; ŠTĚPÁNEK, P.