The paper considers parametric optimization problems for the steel bar structures formulated as nonlinear programming ones with variable unknown cross-sectional sizes of the structural members, as well as initial prestressing forces introduced into the specified redundant members of the structure. The system of constraints covers load-bearing capacity constraints for all the design sections of the structural members subjected to all the design load combinations at ultimate limit state, as well as displacement constraints for the specified nodes of the bar system, subjected to all design load combinations at serviceability limit state. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimization problem. A numerical technique to determine the optimal number of the redundant members to introduce the initial prestressing forces has been offered for high-order statically indeterminate bar structures. It reduces the dimension for the design variable vector of unknown initial prestressing forces for considered optimization problems.
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A new computer-aided methodology for design and optimization of steel structures based on hybrid genetic algorithm with gradient learning of the best individual has been reported. The optimum design problem is formulated as the structural-parametric mathematical programming task with Boolean, integer and real design variables. In this way, cross sectional sizes of structural members, node coordinates as well as topology parameters can be considered as design variables. The system of constraints includes load-carrying capacity and stiffness conditions for structural members and entire steel construction according to building standards and regulations. Architectural, technological and other requirements can be integrated to constraint system as well. Determination of purpose function takes into account design specifications and ability to formulate the analytical expression as function of design variables. Hybrid genetic algorithm based on the parallel operations of genetic operators and update gradient method was used for solving the structural-parametric optimization task. Proposed technique was realized with elaborated software. Numerical example with new optimal design decision of plane two-hinged transverse frame with lattice structural members demonstrates the effectiveness of the proposed optimization methodology.
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