Keywords: structural optimization, dynamics, genetic algorithm, earthquake, active control.

The aim of this paper is the minimization of structural response during an earthquake. The proposed solution way uses actuators. The discrete model of the structure is built on the basis of the finite element method. The nodal dynamic excitation is applied. The time history analysis results the response of all nodes. The control problem is defined as an optimization problem. The objective of the optimization is the time integral of the square of the weighted displacement-velocity function and the square of the weighted control force function. The problem is constrained with the D'Alembert equilibrium equation, the stress inequality constraint and the control force inequality constraint. The genetic algorithm is applied. Linear and nonlinear cases are considered. Examples illustrate the theoretical solution

The foundation of control concepts for mechanical systems is connected with radar work during the Second World War. Applications in civil engineering are related to advances in computational technology, mechanical and electrical engineering during last three decades. The modern trend in active control of civil structures is to use response dependent systems (closed-loop systems). The measured response (output) of the system is used for the input-control force to the system. The paper is focused on mathematical and numerical issues of controllability in engineering practice. In our research we calculate control forces, without discussion about the technical details of actuators. We take into consideration that control forces are technologically constrained. The optimization of the controlled system means that the minimization of the structural response in connection with the minimization of the control energy satisfies all structural, material and technological constraints. The genetic algorithm (GA) is applied. In the former paper, Rosko [11], the Lagrange multiplier method was used for the same examples. The GA provides a wider possibility of technical applications.

The approach of a closed-loop control calculation with help Genetic algorithm gives the same results as the Lagrange multiplier solution with the help of the Riccati matrix. An advantage of this solution is the possibility of problem extensions. Linear and nonlinear cases are analysed.

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