Minimum Structural Weight Research Articles

Multiple cardinality constraints and automatic member grouping in the optimal design of steel framed structures

For structural optimization problems, such as the weight minimization of steel framed structures, the sizing design variables are often defined as the cross-sectional areas of the members, which are to be chosen from commercially available tables such as those provided by the American Institute of Steel Construction. Alternatively, the cross-section dimensions, bf, tf, d and tw (which may be discrete or continuous) can be defined independently for each profile. This paper discusses the structural optimization problem of framed structures involving sizing design variables where a special genetic algorithm encoding is proposed in order to establish a strategy to discover ideal member grouping of members. Advantages in fabrication, checking, assembling, and welding, which are usually not explicitly included in the cost function, are thus expected. The adaptive penalty method (APM) previously developed by the authors is applied to enforce all other mechanical constraints considered in the structural optimization problems discussed in this paper.

Buckling Optimization of Wood Composite Columns with Variable Cross-Sectional Area: A Comparison between two Tree Species

The minimization of structural weight and the maximization of critical buckling load are problems that have been addressed many times. The problem of maximizing the buckling load of a wood composite column of given volume, length and material is studied. Tadjbakhsh and Keller were the first to obtain an optimum solution analytically for the case of clamped-clamped case. Unimodal solutions obtained by Tadjbaksh-Keller are not optimal because they buckle by the modes with discontinuities of the slope corresponding to the lower critical load. This leads to taking into account bimodal formulation of the optimization problem. Olhoff-Rasmussen (1977) first discovered that the unimodal solution given for the clamped by Tadjbaksh-Keller (1962) is incorrect. The optimal columns must be considered from the point of view of practical design. In this paper, it will be shown that bimodal solution is not practical and optimal since in points of minimum thickness crush occurred but not buckling. This leads to the necessity of both stability and crush formulation of the optimization problem. The present contribution of this paper is that crush is taken into account in the formulation of column optimization problem allowing for bimodal optimum solution. To test the accuracy of our new optimization column with clamped ends, experimental data were compared to numerical analysis using ANSYS. Both necessary and sufficient optimality conditions are derived. One important conclusion of this paper is that our new optimal solution is in agreement with results obtained by numerical analysis and by experiments.

Weight minimization of trusses with genetic algorithm

This study is concerned with encoding types such as value encoding and binary encoding for continuous and discrete optimization with a GA, which is coded in FORTRAN and considers stress and displacement constraints, in view of weight minimization of truss structures. Moreover, when continuous optimization is performed, the challenge of huge search space due to the effort of considering continuous set of design variables is overcame by a mechanism introduced as restricted range approach (RRA) in this study. In comparison with the literature, it is concluded that the program developed in this study can be effectively used in the weight minimization of truss structures. It is also came to the conclusion that value encoding overcomes the adverse effects of Hamming-cliff, and that value encoding requires less computer memory and time, never destroys the fit chromosome.

Multi-objective optimization of ring stiffened cylindrical shells using a genetic algorithm

In this paper, the genetic algorithm (GA) method is used for the multi-objective optimization of ring stiffened cylindrical shells. The objective functions seek the maximum fundamental frequency and minimum structural weight of the shell subjected to four constraints including the fundamental frequency, the structural weight, the axial buckling load, and the radial buckling load. The optimization process contains six design variables including the shell thickness, the number of stiffeners, the width and height of stiffeners, the stiffeners eccentricity distribution order, and the stiffeners spacing distribution order. The real coding scheme is used for representing the solution string, while the generation number-based adaptive penalty function is applied for penalizing infeasible solutions. In analytical solution, the Ritz method is applied and the stiffeners are treated as discrete elements. Some examples of simply supported cylindrical shells with nonuniform eccentricity distribution and nonuniform rings spacing distribution are provided to demonstrate the optimality of the solution obtained by the GA technique. The effects of objective weighting coefficients and bounding values of the design variables on the optimum solution are studied for various cases. The results show that the optimal solution can vary with the weighting coefficients significantly. It is also found that extreme reduction and augmentation in turn in the structural weight and fundamental frequency can be simultaneously achieved by selecting suitable stiffeners’ geometrical parameters and distributions. Furthermore, the bounding values of the design variables have great effects on the optimum results.

The Interaction between Sustainable Structures and Architectural Form of Tall Buildings

Energy efficient building design is becoming increasingly important as we think more about energy conservation and environment. In such a context, structure has to assume its place and directly contribute to the building's overall energy conservation strategy. This paper, which is an extension of previous work by the first author, focuses on the interaction between structural efficiency and architectural form of tall buildings. In doing so, the paper attempts to show that efficient structures are sustainable, and that efficiency, defined here as minimum structural weight in conjunction with economical construction, is in the core of structural design. This paper highlights some examples of sustainable structures, illustrating the interaction between architectural form, structural efficiency, and energy efficiency. It also presents a methodological interactive design process which builds on previous work by the authors[1]. This time, the design process is developed to accommodate structural efficiency crit...

Development and validation of a numerical topology optimization scheme for two and three dimensional structures

A novel finite element topology optimization procedure is presented based on the application of probability density and cumulative distribution functions. The procedure utilizes a family of Beta functions with constant probability mean which provide a smooth transition from a uniform to a bi-modal density distribution while conserving constant mean density and therefore constant mass. Validation of the method is demonstrated for several well-known two-dimensional minimum-weight structures. A general minimum-weight cylindrical structural layout for the support of any combination of axial and torsional loading has been developed to provide a test case for three dimensional numerical topological optimization. It is observed that this solution presents a challenge, especially for cases where the axial load is significantly larger than the torsional loading. For these cases, slender members are an essential part of the optimal topology.

PROPOSAL OF AN ENHANCED GENETIC ALGORITHM FOR THE OPTIMUM DESIGN OF STEEL STRUCTURAL PLANE FRAMES

This paper presents an enhanced genetic algorithm with a randomized line search technique to improve the convergence and accuracy ratio. The presented technique is the simple one-dimensional search in which design variable axes are selected randomly as the search direction. The presented algorithms are applied to the discrete sectional optimization problems to achieve the minimum structural weight and the minimum structural cost of the 3-story and 5-story steel structural plane frames. The numerical results obtained by the presented algorithm are compared with those obtained by the conventional genetic algorithm to check the effectiveness.

Structural optimization with limited number of element properties

This note investigates the weight lost of a structure that presents a limited number of cross-sections for its members. A combined genetic algorithm-gradient approach is used to obtain the minimum weight structure for various numbers of cross-sections. The problem is investigated for the well known ten-bar truss structure. Results show that decreasing the number of cross-sections from nine to four has a small impact on the weight of approximately 5.3%.

A coupled finite element genetic algorithm technique for optimum design of steel conical tanks

Steel conical tanks having an upper cylindrical section and supported by a reinforced concrete shaft are widely used for water containment in elevated tanks. During the past few decades, a number of conical tanks have failed as a result of buckling of the steel vessel due to inadequate selection of the shell thickness. In the current study a powerful numerical tool that couples a non-linear finite element model and a genetic algorithm optimization technique is developed specifically for the analysis and design of steel conical tanks. The developed numerical tool is capable of selecting the set of design variables which satisfies the structure safety requirements while achieving a minimum structure weight and consequently minimum cost.

Adaptive volume constraint algorithm for stress limit-based topology optimization

Homogenization or density-based topology optimization methods work by distributing a fixed amount of material to the most effective areas of the design domain so as to create an optimal structural configuration that meets the minimum compliance criteria. These topology optimization methods generally cannot control the maximum stress levels of the structure; therefore, the smoothened optimum structure is not guaranteed to be ready for immediate use. This can be because it is either unsafe if the maximum stress at this structure exceeds the strength limit, or over designed if the maximum stress is far below the stress limit. Difficult and complex shape optimization must then be done to obtain a minimum-weight structure that meets the maximum stress constraint. This paper proposes an adaptive volume constraint (AVC) algorithm, a heuristic approach, in place of traditional topology optimization methods so that the maximum stress in the optimal structural configuration will be below the predefined stress limit and the smoothened structure will be directly applicable. In order to test the applicability and robustness of the AVC algorithm, topology optimization using both a traditional fixed volume constraint and an AVC are tested on a number of configuration design problems. To further illustrate the usefulness of the AVC algorithm, shape optimizations at the maximum stress constraint are also conducted on the smooth structural models by both optimization approaches on an identical problem set.

Analysis and optimization of laminated composite circular cylindrical shell subjected to compressive axial and transverse transient dynamic loads

Optimization is one of the important stages in the design process. In this paper the genetic algorithms method is applied for weight and transient dynamic response and two constraints including critical buckling loads and principle strains optimization of laminated composite cylindrical shells. The multi-objective function seeks the minimum structural weight and transient dynamic response. Nine design variables including material properties (fibre and matrix), volume fraction of fibre, fibre orientation and thickness of each layer are considered. In analytical solution, vibration of composite circular cylindrical shells are investigated based on the first-order shear deformation shell theory. The boundary conditions are assumed to be fully simply support. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. An example of simply supported laminated composite cylindrical shells is given to demonstrate the optimality of the solution obtained by the genetic algorithms technique. Results are shown that the weight coefficient of multi-objective function and the type of the constraints have considerable effect on the optimum weight and dynamic response.

Structural weight minimization of high speed vehicle-passenger catamaran by genetic algorithm

Structural weight minimization of high speed vehicle-passenger catamaran by genetic algorithmReduction of hull structural weight is the most important aim in the design of many ship types. But the ability of designers to produce optimal designs of ship structures is severely limited by the calculation techniques available for this task. Complete definition of the optimal structural design requires formulation of size-topology-shape-material optimization task unifying optimization problems from four areas and effective solution of the problem. So far a significant progress towards solution of this problem has not been achieved. In other hand in recent years attempts have been made to apply genetic algorithm (GA) optimization techniques to design of ship structures. An objective of the paper was to create a computer code and investigate a possibility of simultaneous optimization of both topology and scantlings of structural elements of large spacial sections of ships using GA. In the paper GA is applied to solve the problem of structural weight minimisation of a high speed vehicle-passenger catamaran with several design variables as dimensions of the plate thickness, longitudinal stiffeners and transverse frames and spacing between longitudinals and transversal members. Results of numerical experiments obtained using the code are presented. They shows that

Design and Modelling of Selective Reinforcements for Integral Aircraft Structures

A numerical simulation is presented in this paper on the performance of crack retarders bonded to integral metallic structures. The work is described in two main parts. First, a novel modeling approach employing the finite element method has been developed for simulating the various failure mechanisms of a bonded structure and for predicting fatigue crack growth life. Crack growth in the substrate and the substrate/strap interface disbond failure aremodeledintheframeworkoflinearelasticfracturemechanics.Acomputercodeinterfacingwiththecommercial package MSC NASTRAN has been developed and validated by experimental tests. Second, the effectiveness of differentstrapconfigurationsoncrackgrowthretardationhasbeenmodeled;theseincludedifferentstrapmaterials, strap dimensions, and their locations on the substrate. The research has included two substrate materials and four strap materials, and at this stage the specimens were cured at room temperature. Strap stiffness and adhesive toughness are found to be the most influential parameters in designing crack retarders. A design tool has been developedbasedonthe numericalsimulationto achieveoptimalcrackretarderdesigninterms ofprescribedfatigue life target and minimum structural weight added by the bonded reinforcement.

Optimum topological design of simply supported composite stiffened panels via genetic algorithms

In the present paper the topological optimal design of isotropic/orthotropic thin structures performed via genetic algorithms is shown. Examples involving structural weight minimization under compressive load or buckling load maximization are presented. A modified finite strip method was developed and used to analyze parametric structures arranged in form of plates or stiffened panels with almost arbitrary cross-section shapes. Specific design variables were defined to assure a robust control over geometrical and topological features. In particular, a semi-analytical formulation for the determination of eigenvalues and eigenvectors was adopted in order to reduce computational efforts requested by the optimization task. A mesh-independent solver, involving a reduced number of degrees of freedom, was implemented and interfaced with a genetic optimizer for the purpose. The optimization procedure was based on a specific bit-masking oriented genetic algorithm, able to handle in parallel different genetic operators expressly conceived to process with proper metrics discrete and continuous design variables. As preliminary example, the buckling load maximization of a metallic plate with an arbitrary grid-shaped cross-section is described first. Then a topological optimization concerning the weight minimization of a composite stiffened panel subject to constraint about buckling load is illustrated and discussed in detail about parametric model definition and genetic procedure.

A computational procedure for response statistics-based optimization of stochastic non-linear FE-models

An approach for an efficient solution of response statistics-based optimization problems of non-linear FE systems under stochastic loading is presented. A sequential approximate optimization approach, where approximate stochastic analyses are used during portions of the optimization process, is implemented in the proposed formulation. In this approach, analytical approximations of the performance functions in terms of the design variables are considered during the optimization process. The analytical approximations are constructed by combining a mixed linearization approach with a stochastic response sensitivity analysis. The state of the system is defined in terms of the statistical second-moment characteristics of the structural response. The stochastic loading and the response of the system are represented by an orthogonal series expansion of the corresponding covariance matrices. In particular, a truncated Karhunen–Loève (K–L) expansion is applied. The system of non-linear equations is replaced by a statistical equivalent linear system. The evaluation of the K–L vectors is carried out by an efficient procedure that combines local linearization, modal analysis and static response of higher structural modes. An illustrative example is presented that shows the efficiency of the proposed methodology: it considers a building finite element model enforced with non-linear hysteretic devices and subject to a stochastic ground acceleration. Two types of problems are considered: a minimum structural weight design problem and an optimal non-linear device design problem.

A technique for optimally designing fibre-reinforced laminated structures for minimum weight with manufacturing uncertainties accounted for

A methodology to design symmetrically laminated fibre-reinforced structures under transverse loads for minimum weight, with manufacturing uncertainty in the ply angle, is described. The ply angle and the ply thickness are the design variables, and the Tsai-Wu failure criteria is the design constraint implemented. It is assumed that the probability of any tolerance value occurring within the tolerance band, compared with any other, is equal, and thus the approach is a worst-case scenario approach. The finite element method, based on Mindlin plate and shell theory, is implemented, and thus effects like bending-twisting coupling are accounted for. The Golden Section method is used as the search algorithm, but the methodology is flexible enough to allow any appropriate finite element formulation, search algorithm and failure criterion to be substituted. In order to demonstrate the procedure, laminated plates with varying aspect ratios and boundary conditions are optimally designed and compared.

Weight Optimization of Composite Flat and Curved Wings Satisfying Both Flutter and Divergence Constrains

Aeroelastic tailoring studies using effective computational method with genetic algorithm have been conducted to find an optimized lamination set which give minimum structural weight. The efficient and robust computational system for the flutter optimization has been developed using the coupled computational method based on the micro genetic algorithm. It is shown that the wing structural weight with both divergence and flutter constrains can be significantly reduced using composite materials with proper optimum lamination compared to the case of isotropic wing model.

Structural Weight Optimization of Frames Using Tabu Search. I: Optimization Procedure

A class of search techniques, heuristic search methods, and their suitability for structural optimization are considered for discrete optimization problems. The tabu search method is selected for application to structural weight optimization of skeleton structures. The search method is first tested to find the minima of a function in a nonlinear nonconvex optimization mathematical problem, and an algorithm is developed. Further, a computer program is developed that uses tabu search for weight minimization of two-dimensional framed structures. The program, written in the FORTRAN computer language, performs search, structural analysis, and structural design in an iterative procedure. The program is used to optimize the weight of three previously designed frames including three-story/three-bay, nine-story/five-bay, and 20-story/five-bay steel moment resisting frames. The program demonstrated its capability of optimizing the weight of these medium size frames in a reasonable amount of time without requiring engineer interference during the search. The structural weights for the three frames are reduced by an average of 23.4% from their original design weight.

Rank‐based ant colony algorithms for truss weight minimization with discrete variables

AbstractOne variant of the ant colony optimization (ACO) metaheuristic, known as rank‐based ant system (RBAS), is proposed for weight minimization of structures involving discrete design variables. Stress and displacements constraints are handled using a penalty technique, and the structural analysis is performed by the finite element method.Results obtained for several discrete weight minimization problems show that the RBAS algorithm implemented is effective and competitive when compared with results found by genetic algorithms and another RBAS variant. Copyright © 2006 John Wiley & Sons, Ltd.

Seismic Design Optimization of Steel Building Frameworks

This paper presents a multicriteria optimization method for the performance-based seismic design of steel building frameworks under (equivalent static) seismic loading. Minimizing structural cost (interpreted as structural weight) is taken as one objective. The other objective concerns minimizing earthquake damage which, since uniform postelastic ductility demand over all stories generally avoids local weak-story collapse, is interpreted as providing a uniform interstory drift distribution over the height of the building. That is, the overall objective for the design of a building framework is to have minimum structural weight and uniform plastic ductility demand while, at the same time, meeting displacement and strength constraints corresponding to the various performance levels. Explicit forms of the objective functions and constraints in terms of member sizing variables are formulated to enable computer solution for the optimization model. The concepts are illustrated for three-story and nine-story steel building frame examples.