Parametric Optimization of Metal Rod Structures Using the Modified Gradient Projection Method

Peleshko, Ivan; Yurchenko, V. A.

doi:10.1007/s10778-021-01096-0

Cited by 5 publications

(7 citation statements)

References 14 publications

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“…Step 6. Verification of constraints and construction of a set of numbers (indices) of active constraints [18].…”

Section: Cs X mentioning

confidence: 99%

Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

Peleshko,

Yurchenko,

Rusyn

2023

EEJET

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The object of the study was truss-type rod structures, which were investigated for the purpose of finding the optimal design solution in a mixed (continuous and discrete) space of variables. The parameters of the geometric scheme of the truss, as well as the dimensions of the cross-sections of its elements, were considered as design variables. The stated optimization problem is represented as a nonlinear programming task, in which the objective function and nonlinear constraints of the mathematical model are continuously differentiable functions of the design variables. The system of constraints includes strength and stability inequalities, formulated for the design cross-sections of the rod elements of the structure, which is subject to the effect of the design load combinations of the ultimate limit states. As a part of the system of constraints, the displacement constraints formulated for the specified structural nodes, which is subject to the action of design load combinations of the serviceability limit states, are considered. To solve the stated optimization problem, a method of the objective function gradient on the surface of active constraints was used, with the simultaneous elimination of residuals in the violated restrictions. For design variables, the variation of which must be performed according to a given set of possible discrete values, a discretization procedure for the optimal solution obtained in the continuous space of design variables is proposed. A comparison of the proposed optimization methodology with alternative metaheuristic methods and algorithms reported in the literature was performed. On the considered problem of parametric optimization of a 47-span tower structure, a design solution with a weight of 835,403 kg was obtained, which is 1.53...4.6 % better than the optimal solutions obtained by other authors

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“…Step 6. Verification of constraints and construction of a set of numbers (indices) of active constraints [18].…”

Section: Cs X mentioning

confidence: 99%

Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

Peleshko,

Yurchenko,

Rusyn

2023

EEJET

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“…Thus, the optimization problem of cross-sectional sizes for CFS lipped channel structural member subjected to axial compression is formulated as follow: to find optimum cross-sectional sizes of CFS lipped channel (web height h , flange width b and single edge fold length c ) providing the maximum value of the determined objective function (21) in the feasible region defined by the system of constraints ( 25) -(31), when the profile perimeter (strip width), profile thickness, design lengths of the structural member as well as material properties are constant and specified in advance.…”

Section:  mentioning

confidence: 99%

“…In the paper [1] a parametric optimization problem for single edge fold size in CFS structural members subjected to axial compression has been considered. The purpose function and constraints of the mathematical model has been formulated as continuously differentiable functions, then the parametric optimization problems has been successfully solved using the gradient projection non-linear methods [21,22].…”

Section: Introductionmentioning

confidence: 99%

Searching for a compromise solution in cross-section size optimization problems of cold-formed steel structural members

Yurchenko

Peleshko

2022

OMTC

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A parametric optimization problem of cross-sectional sizes for cold-formed steel lipped channel structural members subjected to axial compression has been considered by the paper. An optimization problem is formulated as to define optimum cross-sectional sizes of cold-formed structural member taking into account post-buckling behavior (web and flange local and distortional buckling) of the member as well as structural requirements when the profile perimeter (strip width), profile thickness, design lengths of the structural member as well as material properties are constant and specified in advance. Maximization of the load-carrying capacity of the cold-formed structural member has been assumed as purpose function. The formulated parametric optimization problem has been solved by exhaustive search method using the software written in Python. As optimization results the cold-formed steel lipped channels with optimum cross-sectional dimensions have been obtained depending on the profile thickness and design lengths of the structural member. In order to obtain optimum solutions for cross-sectional dimensions of the CFS lipped channel structural members which are independent from the design flexural lengths and profile thickness, searching for a compromise solution has been performed by exhaustive search method. The obtained cold-formed steel lipped channel structural members with optimum cross-sectional sizes have higher design buckling resistance under the axial compression at the same material consumption (stripe width) comparing with the cold-formed steel lipped channels proposed by the manufacturer. Web local buckling phenomenon has been occurred in all obtained CFS lipped channel cross-sections with optimum sizes.

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“…(2.1) -(2.3) can be successfully solved using gradient projection nonlinear methods [17,26] in cases when the purpose function and constraints of the mathematical model are continuously differentiable functions, as well as the search space is smooth [10,19]. The method of objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations [8] ensures an effective search for the optimum solution [15]. Additionally, a sensitivity analysis is a useful optional feature [24] that could be used in the scope of numerical algorithms which are developed based on the gradient methods.…”

Section: Problemsmentioning

confidence: 99%

Archives of Civil Engineering

Yurchenko,

Peleshko

2020

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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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Parametric Optimization of Metal Rod Structures Using the Modified Gradient Projection Method

Cited by 5 publications

References 14 publications

Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

Searching for a compromise solution in cross-section size optimization problems of cold-formed steel structural members

Archives of Civil Engineering

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