INFLUENCE OF USING DISCRETE CROSS-SECTION VARIABLES FOR ALL TYPES OF TRUSS STRUCTURAL OPTIMIZATION WITH DYNAMIC CONSTRAINTS FOR BUCKLING (original) (raw)
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DISCRETE VARIABLE TRUSS STRUCTURAL OPTIMIZATION USING BUCKLING DYNAMIC CONSTRAINTS
Using continuous variables in truss structural optimization results in solutions which have a large number of different cross section sizes whose specific dimensions would in practice be difficult or expensive to create. This approach also creates optimal models which if varied, even slightly, result in structures which do not meet constraint criteria. This research proposes the discretization of cross section sizes to standard sizes of stock produced for the particular cross section and material, and a 1mm precision for node location when using shape optimization. Additionally, Euler buckling constraints are added to all models in order to achieve optimal solutions which can find use in practical application. Several standard test models of trusses from literature, which use continuous variables, are compared to the discrete variable models under the same conditions. Models are optimized for minimal weight using sizing, shape, topology, and combinations of these approaches.
Effects of Introducing Dynamic Constraints for Buckling to Truss Sizing Optimization Problems
In this paper the effects of adding buckling constraints to truss sizing optimization for minimizing mass are investigated. Introduction of buckling testing increases the complexity of the optimization process as Euler buckling criteria changes with each iteration of the optimization process due to the changes in element cross section dimensions. The resulting models which consider this criteria are practically applicable. For the purposes of showing the effects of dynamic constraints for buckling, optimal parametric standard test models of 10 bar, 17 bar, and 25 bar trusses from the literature are tested for buckling and compared to the models with the added constraint. Models which do not consider buckling criteria have a considerable number of elements which do not meet buckling criteria. The masses of these models are substantially smaller than their counterparts which consider buckling.
COMPARISON OF APPROACHES TO 10 BAR TRUSS STRUCTURAL OPTIMIZATION WITH INCLUDED BUCKLING CONSTRAINTS
Applied Engineering Letters, 2017
The complex problem of truss structural optimization, based on the discrete design variables assumption, can be approached through optimizing aspects of sizing, shape, and topology or their combinations. This paper aims to show the differences in results depending on which aspect, or combination of aspects of a standard 10 bar truss problem is optimized. In addition to standard constraints for stress, cross section area, and displacement, this paper includes the dynamic constraint for buckling of compressed truss elements. The addition of buckling testing ensures that the optimal solutions are practically applicable. An original optimization approach using genetic algorithm is verified through comparison with literature, and used for all the optimization combinations in this research. The resulting optimized model masses for sizing, shape, and topology or their combinations are compared. A discussion is given to explain the results and to suggest which combination would be best in a generalized example.
MEANS AND EFFECTS OF CONSTRAINING THE NUMBER OF USED CROSS-SECTIONS IN TRUSS SIZING OPTIMIZATION
Transactions of FAMENA, 2020
This paper looks at sizing optimization results, and attempts to show the practical implications of using a novel constraint. Most truss structural optimization problems, which consider sizing in order to minimize weight, do not consider the number of different cross-sections that the optimal solution can have. It was observed that all, or almost all, cross-sections were different when conducting the sizing optimization. In practice, truss structures have a small, manageable number of different cross-sections. The constraint of the number of different cross-sections, proposed here, drastically increases the complexity of solving the problem. In this paper, the number of different cross-sections is limited, and optimization is done for four different sizing optimization problems. This is done for every number of different cross-section profiles which is smaller than the number of cross-sections in the optimal solution, and for a few numbers greater than that number. All examples are optimized using dynamic constraints for Euler buckling and discrete sets of cross-section variables. Results are compared to the optimal solution without a constrained number of different cross-sections and to an optimal model with just a single cross-section for all elements. The results show a small difference between optimal solutions and the optimal solutions with a limited number of different profiles which are more readily applicable in practice.
Optimal design considering buckling of compressive members is an important subject in structural engineering. The strength of compressive members can be compensated by initial geometrical imperfection due to the manufacturing process; therefore, geometrical imperfection can affect the optimal design of structures. In this study, the metaheuristic teaching-learning-based-optimization (TLBO) algorithm is applied to study the geometrical imperfection-sensitivity of members' buckling in the optimal design of space trusses. Three benchmark trusses and a real-life bridge with continuous and discrete design variables are considered, and the results of optimization are compared for different degrees of imperfection, namely 0.001, 0.002, and 0.003. The design variables are the cross-sectional areas, and the objective is to minimize the total weight of the structures under the following constraints: tensile and compressive yielding stress, Euler buckling stress considering imperfection, nodal displacement, and available cross-sectional areas. The results reveal that higher geometrical imperfection degrees significantly change the critical buckling load of compressive members, and consequently, increase the weight of the optimal design. This increase varies from 0.4 to 119% for different degrees of imperfection in the studied trusses.
IOP Conference Series: Materials Science and Engineering, 2019
This paper proposed a way to solve the problem of the optimum size of the truss, taking into account the local buckling constraint of compression elements of the truss. The consideration of dynamic constraint for buckling increases the complexity of the iterative algorithm to solve the truss optimization problem, because the dynamic constraint expresses condition involving the cross-sectional variable. The author has established an iterative algorithm to optimize trusses with stresses constraints (under strength conditions for tensile elements, buckling conditions for compression elements) and displacements. The iterative algorithm is established based on the correlation coefficients of internal forces between elements. The constraints of the problem are established on the basis of the results of internal forces, displacement and governing equation by finite element method. Based on the established algorithm, the authors had written the program to solve the optimization problem of p...
Comparing Truss Sizing and Shape Optimization Effects for 17 Bar Truss Problem
Advanced Engineering Letters
This article aims to demonstrate the difference in results for minimal weight optimization for a 17 bar truss sizing and shape optimization problem. In order to attain results which can be produced in practice Euler bucking, minimal element length, maximal stress and maximal displacement constraints were used. Using the same initial setup, optimization was conducted using particle swarm optimization algorithm and compared to genetic algorithm. Optimal results for both algorithms are compared to initial values which are analytically calculated. The individual element lengths are observed, along with the overall weight, surface area and included number of different cross-sections.