Abstract
The paper has proposed a mathematical model for parametric optimization problem of the steel lattice portal frame. The design variable vector includes geometrical parameters of the structure (node coordinates), as well as cross-sectional dimensions of the structural members. The system of constraints covers load-carrying capacities constraints formulated for all design sections of structural members of the steel structure subjected to all ultimate load case combinations. The displacements constraints formulated for the specified nodes of the steel structure subjected to all serviceability load case combinations have been also included into the system of constraints. Additional requirements in the form of constraints on lower and upper values of the design variables, constraints on permissible minimal thicknesses, constraints on permissible maximum diameter-to-thickness ratio for the structural members with circle hollow sections, as well as the conditions for designing gusset-less welded joints between structural members with circle hollow sections have been also considered in the scope of the mathematical model. 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 formulated parametric optimization problem. New optimal layouts of the steel lattice portal frame by the criterion of the minimum weight, as well as minimum costs on manufacturing and erection have been presented.
Highlights
Over the past 50 years, numerical optimization and the finite element method have individually made significant advances and have together been developed to make possible the emergence of structural optimization as a potential design tool
The system of constraints covers load-carrying capacities constraints formulated for all design sections of structural members of the steel structure subjected to all ultimate load case combinations
The displacements constraints formulated for the specified nodes of the steel structure subjected to all serviceability load case combinations have been included into the system of constraints
Summary
Over the past 50 years, numerical optimization and the finite element method have individually made significant advances and have together been developed to make possible the emergence of structural optimization as a potential design tool. Great efforts have been devoted to integrate optimization procedures into the CAD facilities With these new developments, lots of computer packages are able to solve relatively complicated industrial design problems using different structural optimization techniques. Applied optimum design problems for bar structures in some cases are formulated as parametric optimization problems, namely as searching problems for unknown structural parameters, which provide an extreme value of the specified purpose function in the feasible region defined by the specified constraints [1]. The searching for the optimum solution has been performed by varying the structural parameters providing the required load-carrying capacity of structural members and the minimum value of manufacturing costs
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