Practical Design Optimization of Real Life Truss Structures Constructed From Basic Modules Using the Genetic Algorithms

This paper presents the change in the optimal cross-sectional areas of 25-bar truss structure due to thermal expansion. The 25-bar spatial truss is commonly used in structural engineering as a benchmark for structural optimization. Previous studies used different optimization methods to compute the optimal cross-sectional areas of the truss structures related to the minimal weight of each bar element. However, most of the previous studies conducted the optimization under mechanical load only and reported almost the same optimal areas and minimum weight with slight variations depending on the method used. However, very little has been done on the structural optimization with the consideration of thermal expansion. This study aimed to investigate the effect of thermal expansion in structural optimization and conducted optimization of this structure under the thermal load and the same mechanical load case with the previous studies. The difference in the optimal areas between with and without thermal expansion is analysed through optimization of both cases using MATLAB Optimization Toolbox. The optimization method used is fmincon with Sequential Quadratic Programming (SQP) . The result shows both an increase and decrease in optimal cross-sectional areas. The optimal weight of the structure increases by 12.26% at the surrounding temperature of 30°C. Therefore, this study highlights the needs of consideration of thermal load in optimizing the cross-sectional areas of the structure for minimum weight and this is particularly of important consideration in designing the truss structures in tropical climate. One of the limitations of this study that the SQP may not be appropriate for large structure and hence the robustness of the method should be tested with more variable.

Mine blast algorithm for optimization of truss structures with discrete variables

A new method for structural optimization is presented for successive approximation of the objective function and constraints in conjunction with Lagrange Multipliers Approach. The focus is on presenting the methodology with simple examples. The basis of the iterative algorithm is that after each iteration it brings the approximate location of the estimated minimum closer to the exact location gradually. In other words, instead of the linear or parabolic term used in Taylor expansion which works based on a short step length, an arc is used that has a constant curvature but a longer step length. Using this approximation, the equations of optimization involve the Lagrange multipliers as the only unknown variables. The equations which depend on the design variables are decoupled linearly as these variables are directly obtained. One mathematical example is solved to explain in details how the method works. Next the method is applied to the optimization of a simple truss structure to explain how the method can be used in structural optimization. The same problems have been solved by penalty method and compared. The results from both methods have been the same. However because of the long step length and reduction in the number of variables, the speed of convergence has been higher in the presented method.

Aiming at the optimization of truss structure, a wolf pack algorithm based on chaos and improved search strategy was proposed. The mathematical model of truss optimization was constructed, and the classical truss structure was optimized. The results were compared with those of other optimization algorithms. When selecting and updating the initial position of wolves, chaos idea was used to distribute the initial value evenly in the solution space; phase factor was introduced to optimize the formula of wolf detection; information interaction between wolves is increased and the number of runs is reduced. The numerical results show that the improved wolf pack algorithm has the characteristics of fewer parameters, simple programming, easy implementation, fast convergence speed, and can quickly find the optimal solution. It is suitable for the optimization design of the section size of space truss structures.

In this study, an attempt is made to minimize the weight of Howe roof and ten member-6 Node trusses, separately. Two constraints, maximum allowable deflection and maximum allowable member stresses have been considered. For the first truss, permissible deflection is not known from the literature; therefore, it is determined using the exhaustive search method. Once magnitudes of the constraints are identified, member cross-sectional areas are varied to get the optimal weight. Both the exhaustive search method and the genetic algorithm have been implemented for this purpose. During the optimization, members tending to form a string may be eliminated from the structure. Doing this, we could further reduce the weights of the trusses and even less than the minimum available in the literature. The second truss is an indeterminate structure, and Maxwell Betti reciprocal theorem is applied to calculate the member forces. Also, further reduction of members is made for this truss, keeping in mind that the truss becomes determinate with the decrease in the member(s).

In recent decades, due to the limitations of resources and equipment in the construction of engineering projects, the optimal use of existing facilities for reducing the overall costs of the projects has been of great importance. Due to the significant advances in optimization techniques, the application of these methods in engineering sciences, especially civil and structural engineering, has received more attention than before. In the last years, various optimization methods and algorithms have been used for optimization purposes, including metaheuristic algorithms. In this paper, the optimum design of truss structures is considered utilizing Atomic Orbital Search (AOS) as one of the recently developed metaheuristic algorithms. The applicability of this technique in the weight optimization of complex truss structures is in perspective. Four of the benchmark problems in the truss optimization field, such as 10-bar, 25-bar, 52-bar, and 160-bar truss structures, are used as design examples. A simple penalty approach is implemented in AOS as a constraint handling scheme, while a comprehensive statistical analysis is also conducted through multiple optimization runs. The results of the AOS are compared to the results of other methods from the literature, while the AOS demonstrates a good level of weight reduction capability in dealing with these complex design problems.KeywordsTruss structureAtomic orbital searchMetaheuristic algorithmOptimization first section

Primary load-bearing members used in glass structures, such as columns consisting of glass panels, are frequently subjected to in-plane loading. Its allowable stress for safety design appears to be a significant subject. By analyzing the results of static (without repeated loading) and cycling compression loading tests, the authors explore the mechanical features and failure mechanism of the tempered glass panels subjective to in-plane compression loading, including its ultimate stress and buckling load. In addition, a statistical method based on the experimental results is adopted to evaluate the allowable compressive stress. The experimental results show that the ultimate loads of specimens with high slenderness ratios satisfy Euler's critical load formula. In contrast, the ultimate loads of specimens with low thickness ratios distribute in a certain variance range. For the cycling loading test, after 30 times of repeated loading with maximum stress equivalent to 2/3 of the ultimate static stress, the average strength is almost the same or bigger than that of static loading tests. No fatigue fracture due to repeated loading was found for the tempered glass panels. Consequently, the allowable stress for in-plane compressive loading can be formulated based on Euler's critical load formula for a glass panel with a bigger slenderness ratio. The formulation for the allowable compressive stress of a glass panel with a smaller slenderness ratio is promoted using statistical analysis with a 95 percent confidence level for the safety design.

A Harmony Search (HS) and Genetic Algorithms (GA), two powerful metaheuristic search techniques, are used for minimum weight designs of different truss structures by selecting suitable profile sections from a specified list taken from American Institute of Steel Construction (AISC). A computer program is coded in MATLAB interacting with SAP2000-OAPI to obtain solution of design problems. The stress constraints according to AISC-ASD (Allowable Stress Design) and displacement constraints are considered for optimum designs. Three different truss structures such as bridge, dome and tower structures taken from literature are designed and the results are compared with the ones available in literature. The results obtained from the solutions for truss structures show that optimum designs by these techniques are very similar to the literature results and HS method usually provides more economical solutions in multi-element truss problems.

The optimization of the structures is difficult because the variables have different physical property or different quantitative attribute. The shape and cross-section optimization of spatial grid structures is performed by an improved genetic algorithm. The constraint conditions are composed of the structural deformation, the stability of the compressive members, the slender ratios, and etc. The treatment of the constraint conditions and the optimization function gives an unconstrained analytic function by adopting Lagrange multipliers. The method enhances the running efficiency of the genetic algorithm. The programme for structural optimization containing the mixed codes of continuous real variables, discontinuous real variables, and integer variables is coded by using MATLAB Toolbox functions for genetic algorithm. The analysis of examples shows that the programme is reliable, and the convergence of the algorithm is fast as well.

This paper presents a new efficient genetic algorithm for truss structure optimization. In many optimum design problems, values of design valiables are real numbers. We have proposed the Center Neighborhood Crossover (CNX) for real coded genetic algorithms. CNX is a powerful tool for function optimizations. Since it is uncertain that these operators are able to work for practical design problems efficiently, it is necessary to examine some crossover operators for practical use. In the present study, we verified and compared the performance of several crossover operators using benchmark functions. Furthermore, we tried to optimize a truss structure problem using these operators. By considering the results mentioned above, we developed the two-stage for truss structure optimization. This method bring us the efficient search and the high-accurate optimum solution.

Truss structures are optimized with respect to minimum weight with constraints on the value of some displacement and on the member stresses. The truss is considered made of an uncertain material, i.e. the value of the material constants are not known in a deterministic way, and each member may then exhibit a different value of stiffness, within a limited range of variation. The optimization must be done so that optimal solutions remain feasible for each value that the material constants may take for the considered uncertainty. In the present work a nonprobabilistic approach to uncertainty is used, and a variation of the material moduli with a, probabilistically speaking, uniform distribution over a convex and linearly bounded domain is considered. The two-step method is used to include the uncertainty within the optimization, where a diagonal quadratic approximation is used for the Objective function and the constraints. Solutions for some of the most classical truss examples are found and compared with those obtained using nominal values of material constants.

A new fuzzy strategy for size and topology optimization of truss structures

To solve structural optimization problems, it is necessary to integrate a structural analysis package and an optimization package. Since most structural analysis packages suffer from closeness of system, it is very difficult to integrate it with an optimization package. To overcome the difficulty, we propose a possible alternative, DAMDO, which integrate Design, Analysis, Modeling, Definition, and Optimization phases into an integration environment as follows. (1) Design first generate many possible structural design alternatives. Each design alternative consists of many design variables X. (2) Analysis employ the structural analysis software to analyze all structural design alternatives to obtain their internal forces and displacements. They are the response variables Y. (3) Modeling employ artificial neural networks to build model Y = f(X) to obtain the relationship functions between the design variables X and the response variables Y. (4) Definition employ the design variables X and the response variables Y to define the objective function and constraint functions. (5) Optimization employ the optimization software to solve the optimization problem consisting of the objective function and the constraint functions to produce the optimum design variables X*. Optimization of truss structures was used to validate the DAMDO approach. The empirical results show that the truss optimization problems can be solved by the DAMDO approach, which employ neural networks to integrate the structural analysis package and optimization package without requiring direct integration of the two packages. This approach is promising in many engineering optimization domains which need to couple an analysis package and an optimization one to obtain the optimum solutions.

Large space truss structure is widely used in spacecrafts. The vibration of this kind of structure will cause some serious problems. For instance, it will disturb the work of the payloads which are supported on the truss, even worse, it will deactivate the spacecrafts. Therefore, it is highly in need of executing vibration control for large space truss structure. Large space intelligent truss system (LSITS) is not a normal truss structure but a complex truss system consisting of common rods and active rods, and there are at least one actuator and one sensor in each active rod. One of the key points in the vibration control for LSITS is the location assignment of actuators and sensors. The positions of actuators and sensors will directly determine the properties of the control system, such as stability, controllability, observability, etc. In this paper, placement optimization of actuators and sensors (POAS) and decentralized adaptive fuzzy control methods are presented to solve the vibration control problem. The electro-mechanical coupled equations of the active rod are established, and the optimization criterion which does not depend upon control methods is proposed. The optimal positions of actuators and sensors in LSITS are obtained by using genetic algorithm (GA). Furthermore, the decentralized adaptive fuzzy vibration controller is designed to control LSITS. The LSITS dynamic equations with considering those remaining modes are derived. The adaptive fuzzy control scheme is improved via sliding control method. One T-typed truss structure is taken as an example and a demonstration experiment is carried out. The experimental results show that the GA is reliable and valid for placement optimization of actuators and sensors, and the adaptive fuzzy controller can effectively suppress the vibration of LSITS without control spillovers and observation spillovers.

Several methods have been used to solve structural optimum design problems since the creation of a need for light weight design of structures and there is still no single method for solving the optimum design problems in structural engineering field that is capable of providing efficient solutions to all of the structural optimum design problems. Therefore, there are several proposed and utilized methods to deal with optimum design issues and problems, that sometimes give promising results and sometimes the solutions are quite unacceptable. This issue with metaheuristic algorithms, which are suitable approaches to solve these set of problems, is quite usual and is supported by the “No Free Lunch theorem”. Researchers try harder than the past to propose methods capable of presenting robust and optimal solutions in a wider range of structural optimum design problems, so that to find an algorithm that can cover a wider range of structural optimization problems and obtain a better optimum design. Truss structures are one of these problems which have extremely complex search spaces to conduct search procedures by metaheuristic algorithms. This paper proposes a method for optimum design of truss sizing problems. The presented method is used against 6 well-known benchmark truss structures (10 bar, 17 bar, 18 bar, 25 bar, 72 bar and 120 bar) and its results are compared with some of the available studies in the literature. The performance of the presented algorithm can be considered as very acceptable.