Minimum Weight Design Research Articles

On the equivalence of minimum compliance and stress-constrained minimum weight design of trusses under multiple loading conditions

This article is devoted to topology optimization of trusses under multiple loading conditions. Compliance minimization with material volume constraint and stress-constrained minimum weight problem are considered. In the case of a single loading condition, it has been shown that the two problems have the same optimal topology. The possibility of extending this result for problems involving multiple loading conditions is examined in the present work. First, the compliance minimization problem is formulated as a multicriterion optimization problem, where the conflicting criteria are the compliances of the different loading conditions. Then, the optimal topologies of the stress-constrained minimum weight problem and the multicriterion compliance minimization problem for a simple test example are compared. The results verify that when multiple loading conditions are involved, the stress-constrained minimum weight topology cannot be obtained in general by solving the compliance minimization problem.

Classical and modern optimization methods in minimum weight design of elastic rotating disk with variable thickness and density

Rotating disks work mostly at high angular velocity and this results a large centrifugal force and consequently induce large stresses and deformations. Minimizing weight of such disks yields to benefits such as low dead weights and lower costs. This paper aims at finding an optimal disk profiles for minimum weight design using the Karush-Kuhn-Tucker method (KKT) as a classical optimization method, simulated annealing (SA) and particle swarm optimization (PSO) as two modern optimization techniques. Some semi-analytical solutions for the elastic stress distribution in a rotating annular disk with uniform and variable thickness and density proposed by the authors in the previous works have been used. The von Mises failure criterion of optimum disk is used as an inequality constraint to make sure that the rotating disk does not fail. The results show that the minimum weight obtained for all three methods is almost identical. The KKT method gives a profile with slightly less weight (6% less than SA and 1% less than PSO) while the implementation of PSO and SA methods are easier and provide more flexibility compared with those of the KKT method. The effectiveness of the proposed optimization methods is shown.

A hybrid HS-CSS algorithm for simultaneous analysis, design and optimization of trusses via force method

In this paper, a hybrid heuristic method is developed using the harmony search (HS) and charged system search (CSS), called HS-CSS. In this algorithm the use of HS improves the exploitation property of the standard CSS. An energy formulation of the force method is developed and the analysis, design and optimization are performed simultaneously using the standard CSS and HS-CSS. New goal functions are introduced for minimization, and the CSS and the HS-CSS are employed for continuous optimization. An efficient method is introduced using the CSS and HS-CSS for designing structures having members of prescribed stress ratios. Finally, the minimum weight design of truss structures is formulated using the CSS and HS-CSS algorithms and applied to some benchmark problems from literature.

Find the Optimum Shape Design of Externally Pressurized Torispherical Dome Ends Based on Buckling Pressure by Using Imperialist Competitive Algorithm and Genetic Algorithm

In this paper, we used the Imperialist Competitive Algorithm (ICA) and Genetic Algorithm (GA) to find the minimum weight design of torispherical dome ends under external pressure load. According to fabrication and strength of material requirements, a group of compromised counters are selected and studied. Based on ASME Section VIII and BS5500 pressure vessel codes, a reasonable buckling pressure limit is proposed. Four-centered ellipse method is quite effective in designing and constructing the dome structure and it is used here to construct the torispherical dome ends. Two different size torispherical dome end models are selected and studied. Imperialist competitive algorithm is found to be very efficient and easy to use for the applications.

The Karush–Kuhn–Tucker optimality conditions in minimum weight design of elastic rotating disks with variable thickness and density

The Karush–Kuhn–Tucker optimality conditions in minimum weight design of elastic rotating disks with variable thickness and density

Reliability-based Minimum Weight Design of Mechanism Specified Frames Considering Randomness of Yield Strength

Reliability-based Minimum Weight Design of Mechanism Specified Frames Considering Randomness of Yield Strength

Optimum Design of Composite Sandwich Structures Subjected to Combined Torsion and Bending Loads

This research is motivated by the increase use of composite sandwich structures in a wide range of industries such as automotive, aerospace and civil infrastructure. To maximise stiffness at minimum weight, the paper develops a minimum weight optimization method for sandwich structure under combined torsion and bending loads. We first extend the minimum-weight design of sandwich structures under bending load to the case of torsional deformation and then present optimum solutions for the combined requirements of both bending and torsional stiffness. Three design cases are identified for a sandwich structure required to meet multiple design constraints of torsion and bending stiffness. The optimum solutions for all three cases are derived. To illustrate the newly developed optimum design solutions, numerical examples are presented for sandwich structures made of either isotropic face skins or orthotropic composite face skins.

건조비를 고려한 LPG 운반선 화물창의 최적설계에 관한 연구

Generally in order to reduce the steel weight of stiffened plate, stiffener spaces tend to be narrow and the plate gets thin. However, it will involve more fabrication cost because it can lead to the increase of welding length and the number of structural members. In the yard, the design which is able to reduce the total fabrication cost is needed, although it requires more steel weight. The purpose of this study is to find optimum stiffener spaces to minimize the fabrication cost for the cargo tank of LPG Carriers. Global optimization methods such as ES(Evolution Strategy) and GA(Genetic Algorithm) are introduced to find a global optimum solution and the sum of steel material cost and labor cost is selected as main objective function. Convergence degree of both methods in according to the size of searching population is examined and an efficient size is investigated. In order to verify the necessity of the optimum design based on the cost, minimum weight design and minimum cost design are carried out.

Optimum design of steel frames using a multiple-deme GA with improved reproduction operators

In this paper, the performance of the genetic algorithm is improved by introducing some new crossover and mutation operators. The new operators are incorporated into a multiple-deme genetic algorithm in which population is divided into subpopulations and communication between different demes is established through migration of individuals, enhancing diversity and resulting in better solutions. This algorithm is applied to the minimum weight design of steel frames subjected to actual strength and ductility constraints of AISC–ASD specifications as well as other serviceability and constructability constraints. The efficiency of the proposed method is demonstrated through optimising two benchmark problems including a three-bay, three-storey steel frame and a five-bay, 22-storey special steel frame. Significant improvements in the optimum solutions are obtained with reduced number of finite element analyses, resulting in less computational effort.

초기인장력을 받은 그리드 구조물의 최적설계

In this study, micro genetic algorithm is used to find an optimum cross section of grid structures with pretension. Design optimization of trusses consists of arriving at optimum sizes of cross-section and prestressing force parameters, when weight of the truss is minimum, satisfying a set of specified constraints. The present approach is verified by ten-bar truss example showing good agreements with previous results. Features of the proposed method, which help in modeling and application to optimal design of pretensioned truss structures, are demonstrated by solving a problem of seventy two bar truss structures. The minimum weight design of seventy two bar truss is performed for various magnitudes of pretension and optimal prestressing forces are also found for various configurations of pretensioned truss structures.

Topology optimization for the seismic design of truss-like structures

A practical optimization method is applied to design nonlinear truss-like structures subjected to seismic excitation. To achieve minimum weight design, inefficient material is gradually shifted from strong parts to weak parts of a structure until a state of uniform deformation prevails. By considering different truss structures, effects of seismic excitation, target ductility and buckling of the compression members on optimum topology are investigated. It is shown that the proposed method could lead to 60% less structural weight compared to optimization methods based on elastic behavior and equivalent static loads, and is efficient at controlling performance parameters under a design earthquake.

Minimum-Weight Sandwich Structure Optimum Design Subjected to Torsional Loading

As one of the most valued structural engineering innovations developed by the composites industry, sandwich structures are now used extensively in automotive, aerospace and civil infrastructure due to the main advantage of lightweight. This paper develops a minimum weight optimization method for sandwich structure subjected to torsion load. The design process are identified for a sandwich structure required to meet the design constraint of torsion stiffness. The optimum solutions show that at optimum design the core weight accounts for 66.7% of the whole sandwich structure. To illustrate the newly developed optimum design solutions, numerical examples are presented for sandwich structures made of either isotropic face skins or orthotropic composite face skins. Agreement between the theoretical analysis and the examples results is good.

Structural design optimization of racing motor boat based on nonlinear finite element analysis

Since 1980's, optimum design techniques for ship structural design have been developed to the preliminary design which aims at minimum weight or minimum cost design of mid-ship section based on analytic structural analysis. But the optimum structural design researches about the application for the detail design of local structure based on FEA have been still insufficient. This paper presents optimization technique for the detail design of a racing motor boat. To improve the performance and reduce the damage of a real existing racing boat, direct structural analyses; static and non-linear transient dynamic analyses, were carried out to check the constraints of minimum weight design. As a result, it is shown that the optimum structural design of a racing boat has to be focused on reducing impulse response from pitching motion than static response because the dynamic effect is more dominant. Optimum design algorithm based on nonlinear finite element analysis for a racing motor boat was developed and coded to ANSYS, and its applicability for actual structural design was verifed.

Minimum weight design of fiber-reinforced laminated composite structures with maximum stress and Tsai-Wu failure criteria

In this article, a minimum weight design of carbon/epoxy laminates is carried out using genetic algorithms. New failure envelopes have been developed by the combination of two commonly used phenomenological failure criteria, namely Maximum Stress (MS) and Tsai—Wu (TW) are used to obtain the minimum weight of the laminate. These failure envelopes are the most conservative failure envelope (MCFE) and the least conservative failure envelope (LCFE). Uniaxial and biaxial loading conditions are considered for the study and the differences in the optimal weight of the laminate are compared for the MCFE and LCFE. The MCFE can be used for design of critical load-carrying composites, while the LCFE could be used for the design of composite structures where weight reduction is much more important than safety such as unmanned air vehicles.

Coefficient Distribution Method for Minimum Weight Design of Large-Span Determinate Trusses

The minimum weight design method of large-span statically determinate trusses satisfying the displacement constraint is studied. The displacement calculation formula is provided, and the critical condition of minimum weight design satisfying the condition of allowed displacement is educed using Cauchy inequality. The distribution coefficient, which is used to obtain the minimum weight design, is defined and the coefficient distribution method is proposed. An engineering example is analyzed using the coefficient distribution method above, and the compared results are discussed. Study results show that the proposed method, coefficient distribution method, is correct，reliable and effective.

Structural design optimization of racing motor boat based on nonlinear finite element analysis

Since 1980's, optimum design techniques for ship structural design have been developed to the preliminary design which aims at minimum weight or minimum cost design of mid-ship section based on analytic structural analysis. But the optimum structural design researches about the application for the detail design of local structure based on FEA have been still insufficient. This paper presents optimization technique for the detail design of a racing motor boat. To improve the performance and reduce the damage of a real existing racing boat, direct structural analyses; static and non-linear transient dynamic analyses, were carried out to check the constraints of minimum weight design. As a result, it is shown that the optimum structural design of a racing boat has to be focused on reducing impulse response from pitching motion than static response because the dynamic effect is more dominant. Optimum design algorithm based on nonlinear finite element analysis for a racing motor boat was developed and coded to ANSYS, and its applicability for actual structural design was verifed.

Structural Synthesis by Method of Centers in Force Formulation under Size and Stress Constraints

ABSTRACTThis paper studies a novel approach to optimize trusses and truss-like structures for minimum weight design. It is based on the force method of analysis which is incorporated inside the optimization routine. The design variables in force formulation are the member cross sectional areas and the redundant forces in each load condition. The optimization method used is the method of center points using the inscribed hyperspheres to the feasible-usable design space. By incorporating the analysis step as part of the optimization problem, a separate structural solution phase, which is necessary in all other methods, is avoided resulting in large computational savings. In this article the simplest form of structuresi.e.trusses are treated to illustrate the efficacy of the method. Stress limits on the members as well as limitations on their sizes, and linking among them, under several load conditions have been considered. Combination of the method of center points and force formulation results in a viable routine for structural optimization. Comparison of the example results with those obtained by others clearly shows the effectiveness and novelty of the proposed method.

Maximum stiffness and minimum weight optimization of laminated composite beams using continuous fiber angles

This paper deals with identification of optimal fiber orientations and laminate thicknesses in maximum stiffness and minimum weight design of laminated composite beams. The structural response is evaluated using beam finite elements which correctly account for the influence of the fiber orientation and cross section geometry. The resulting finite element matrices are significantly smaller than those obtained using equivalent finite element models. This modeling approach is therefore an attractive alternative in computationally intensive applications at the conceptual design stage where the focus is on the global structural response. An optimization strategy is presented which aims at enabling the use of fiber angles as continuous design variables albeit the problems may have many local minima. A sequence of closely related problems with an increasing number of design variables is treated. The design found for a problem in the sequence is projected to generate the starting point for the next problem in the sequence. Numerical results are presented for cantilever beams with different geometries and load cases. The results indicate that the devised strategy is well suited for finding optimal fiber orientations and laminate thicknesses in the design of slender laminated composite structures.

On the solution of the three forces problem and its application in optimal designing of a class of symmetric plane frameworks of least weight

Two problems of minimum weight design of plane trusses are dealt with. The first problem concerns construction of the lightest fully stressed truss subject to three self-equilibrated forces applied at three given points. This problem has been solved analytically by H.S.Y. Chan in 1966. This analytical solution is re-derived in the present paper. It compares favourably with new numerical solutions found here by the method developed recently by the first author. The solution to the three forces problem paves the way to half-analytical as well as numerical solutions to the problem of minimum weight design of plane symmetric frameworks transmitting two symmetrically located vertical forces to two fixed supports lying along the line linking the points of application of the forces.

An Enhanced Binary Particle Swarm Optimization for Structural Topology Optimization

Particle swarm optimization (PSO), a heuristic optimization method, has been successfully applied in solving many optimization problems in real-value search space. The original binary particle swarm optimization (BPSO) uses the concept of bit flipping of the binary string to convert the velocity from a real code into a binary code. However, the conversion process cannot be reversed, and it is difficult to extend this framework to solve certain discrete optimization problems. An enhanced binary particle swarm algorithm is proposed in this study based on pure binary bit-string frameworks to deal with structural topology optimization problems. Further, two enhancement strategies, stress-based strategy and pair-switched strategy, were developed to improve the performance of the proposed algorithm for topology optimization of structure. The results of experimental cases demonstrated in this study show that the proposed enhanced binary particle swarm optimization (EBPSO) with two developed strategies is an efficient population-based approach for finding the optimal design for structural topology optimization problems of minimum compliance design and minimum weight design.