Minimum Weight Design Research Articles

Size effect of lattice material and minimum weight design

The size effects of microstructure of lattice materials on structural analysis and minimum weight design are studied with extented multiscale finite element method (EMsFEM) in the paper. With the same volume of base material and configuration, the structural displacement and maximum axial stress of micro-rod of lattice structures with different sizes of microstructure are analyzed and compared. It is pointed out that different from the traditional mathematical homogenization method, EMsFEM is suitable for analyzing the structures which is constituted with lattice materials and composed of quantities of finite-sized micro-rods. The minimum weight design of structures composed of lattice material is studied with downscaling calculation of EMs-FEM under stress constraints of micro-rods. The optimal design results show that the weight of the structure increases with the decrease of the size of basic sub-unit cells. The paper presents a new approach for analysis and optimization of lattice materials in complex engineering constructions.

Automated optimal design of double-layer latticed domes using particle swarm optimization

Most of the conventional design methods of large-scale domes need deep engineering insight; furthermore, they hardly give the most economical solutions. Therefore, in this paper, a new practical design algorithm is presented to automate optimal geometry and sizing design of the latticed space domes through the idea of using parametric mathematical functions. Moreover, a simple approach is developed for the optimal sizing design of trusses with outsized number of elements. The robust technique of particle swarm optimization is employed to find the solution of the propounded optimization problem. Some numerical examples on the minimum weight design of several famous domes are provided to demonstrate the efficiency of the proposed design algorithm.

A sequential algorithm for minimum weight design of 2-D steel portal frames using Eurocode 3

A practical method to achieve the minimum weight design of 2D steel frames, built with European standard I-shaped crosssections, is hereby presented. The optimization methodology consists of an incremental iterative technique. It is based on the addition of lacking material by successive increasing of the size of the most stressed member. Second-order effects are considered in this approach. Eurocode 3 restrictions for both the Ultimate Limit States (ULS) and Serviceability Limit States (SLS) are also taken into account. The numerical procedure has been coded in MatLab. The proposed method gives, with reasonably small computing effort, a sound approach to the exact optimum solution. An illustrative example of applying this methodology for designing a steel portal frame is presented; besides, its results are validated for a classical benchmark problem.

Reliability-based analysis and design of steel frames with different supports

Purpose – The behaviours of four indeterminate frame-support combinations namely Type I (with fixed supports), Type II (with pinned supports), Type III (with fixed-pinned supports) and Type IV (with fixed-roller supports) frames under the exposure conditions and loads as existing on site were simulated. Two categories of these combinations (I and II) were studied namely single storey-single bay and multiple storey-single bay frames, as illustrated in the case studies treated. A procedure for determining the probability of failure at different sections along the frame types, the range between the probability of failure bounds and the reliability ratings of the frame types were developed based on the kinetic method of plastic moment analysis, minimum weight design method, piecewise method of moment analysis and first order-second moment (FOSM) methods. The analysis results of the Category I frames showed that the Type I frame was most reliable (with the lowest probability of failure range of 0.3269), while the Type II frame was least reliable (with the highest probability of failure range of 0.4918). These results were consistent with those of the Category II frames. The paper aims to discuss these issues. Design/methodology/approach – Collapse mechanisms were generated for four frame-support types and the corresponding plastic moments were determined using both the kinematic plastic analyses and minimum weight design methods. The members were designed and the plastic moments were distributed at sections of constant interval along the frame length to generate corresponding envelopes. A similar process was carried out to determine the elastic moment variables due to the loads. The reliability index and the corresponding probability of failure at each frame section were determined. Then, the probabilities of failure bounds for the frames were then compared to determine the most reliable. Findings – It was observed that there existed a wide margin between the elastic and plastic moments indicating that design of steel structures at the elastic limit does not take full advantage of its strength. Hence, the design can be carried out beyond the elastic limit and within the safety margin given in equation (3). However, the safety of the entire frame is assessed on the basis of range of values between the highest and the lowest probability of failure bounds. The lower this range is (not exceeding 0.5 or 50 per cent), the more reliable the frame is. Research limitations/implications – The equations developed in this study can only be directly applied to multi storey-single bay frames. However, the reliability-based analysis and design procedure developed can be extended to other types of frames. Practical implications – A practical approach for analysing steel frames with different supports with the overall goal of producing safe and economical designs has been developed and presented in this paper. Originality/value – The procedure adopted is very original and can be backed up by existing literature. The piecewise method for analysing moments at various sections along a frame is also innovative. The whole concept can be adopted to determine the reliability of other types of frames such as multiple bay-multistorey frames with different support types.

A new laminates encoding scheme for the genetic algorithm-based optimization of stiffened composite panels

Purpose – The genetic algorithm (GA) technique is widely used for the optimization of stiffened composite panels. It is based on sequential execution of a number of specific operators, including the encoding of particular design variables. For instance, in the case of a stiffened composite panel, the design variables that need to be encoded are: the number of plies and their stacking sequences in the panel skin and stiffeners. This paper aims to present a novel, implicit, heuristic approach for encoding composite laminates and, through its use, demonstrates an improvement in the optimization process. Design/methodology/approach – The stiffened panel optimization has been formulated as a constrained discrete minimum-weight design problem. GAs, which use both new encoding schemes and those previously described in the literature, have been used to find near-optimal solutions to the formulated problem. The influence of the new encoding scheme on the searching capabilities of the GA has been investigated using comparative analysis of the optimization results. Findings – The new encoding scheme allows the definition of stacking sequences in composites using shorter symbolic representations as compared with standard encoding operators and, as a result of this, a reduction in the problem design space. According to numerical experiments performed in this work, this feature enables GA to obtain near-optimal designs using smaller population sizes than those required if standard encoding schemes are used. Originality/value – The approach to encoding laminates presented in this paper is based on the original heuristics. In the context of GA-based optimization of stiffened composite panels, the use of the new approach rather than the standard encoding technique can lead to a significant reduction in computational time employed.

Resizing Technique-Based Hybrid Genetic Algorithm for Optimal Drift Design of Multistory Steel Frame Buildings

Since genetic algorithm-based optimization methods are computationally expensive for practical use in the field of structural optimization, a resizing technique-based hybrid genetic algorithm for the drift design of multistory steel frame buildings is proposed to increase the convergence speed of genetic algorithms. To reduce the number of structural analyses required for the convergence, a genetic algorithm is combined with a resizing technique that is an efficient optimal technique to control the drift of buildings without the repetitive structural analysis. The resizing technique-based hybrid genetic algorithm proposed in this paper is applied to the minimum weight design of three steel frame buildings. To evaluate the performance of the algorithm, optimum weights, computational times, and generation numbers from the proposed algorithm are compared with those from a genetic algorithm. Based on the comparisons, it is concluded that the hybrid genetic algorithm shows clear improvements in convergence properties.

Two-phase genetic algorithm for size optimization of free-form steel space-frame roof structures

A two-phase GA approach is presented for minimum weight design of free-form steel space-frame roof structures consisting of discrete commercially available rectangular hollow structural sections (HSS). The new methodology is applied to two roof structures subjected to the AISC LRFD code and ASCE-10 snow, wind, and seismic loadings. They are two of the thirteen train stations making up the Ottawa Light Rail Transit (OLRT) system to be completed in Ottawa, Canada, in 2018. Both examples have a diamond grid pattern and their members are subjected to torsion in addition to bending and axial forces. The initial design in both cases is an actual design performed in a design office by the first author iteratively using general-purpose structural analysis software over a period of days. The optimum solutions obtained using the new methodology resulted in savings of 12% and 7% for the two examples. The advantages of the two-phase GA optimization algorithm presented in this paper are three fold: a) automation of the design process of a complicated and one-of-a-kind structure; b) relieving the designer of days of iterative design process; and c) achieving a lighter and therefore more economical design.

Semi-analytical skin buckling of curved orthotropic grid-stiffened shells

With the introduction of composite materials to industrial aerospace applications, the research for innovative panel stiffening methods has gained significant interest. Possible candidates are grid-stiffened structures comprising of parallel and intersecting stiffeners forming regular polygonal patterns of skin fields. Since these thin-walled structures are critical to buckling, the structural stability is one of the driving criteria for minimum weight design. The present study investigates the local skin buckling of grid-stiffened structures known as orthogrid, isogrid, diamond grid and kagome grid with a semi-analytical Ritz energy method based on sets of trigonometric shape functions. The influence of the aspect ratio (stiffener angle), curvature and material orthotropy is shown for uni- and biaxial in-plane compression and shear. A self-stiffening effect of the grid-stiffened structures due to interaction with adjacent skin fields is identified, significantly increasing the buckling resistance of such structures. The presented results and trends support preliminary design tasks and the verification of detailed finite element analyses.

Minimum weight design of beams against failure under uncertain loading by convex analysis

Under operational conditions, some loads acting on a beam are known (deterministic loads), but there usually exist other loads the magnitude and distribution of which are unpredictable (uncertain loads). If the uncertainty in the loading is not taken into account in the design, the likelihood of failure increases. In the present study beams are designed for minimum weight subject to maximum stress and buckling load criteria and under deterministic and uncertain transverse loads. The uncertain load, which is subject to a constraint on its L 2 norm, is determined to maximize the normal stress using a convex analysis. The location of the maximum stress is determined under the combination of deterministic and worst-case uncertain loads. The minimum weight design is obtained by determining the minimum cross-sectional area subject to stress and buckling load constraints. Results are given for a number of problem parameters including the axial load, elastic foundation modulus and uncertainty levels.

In-plane compression of hollow composite pyramidal lattice sandwich columns

Composite lattice structures can be regarded as hierarchical when trusses have their own structure (e.g. different stacking sequences are incorporated). In this study, hollow composite pyramidal lattice sandwich structures in end compression were analyzed, measured and evaluated with respect to the designable properties of sandwich cores, such as relative density and truss stacking sequence. Collapse mechanism charts were constructed for both component elements and sandwich columns to illustrate the influence of structural geometries and properties of composite pyramidal lattice cores on failure modes. Operative failure modes were identified and the analytical models were shown to be accurate when compared to the measured response. The minimum weight design for the hollow composite pyramidal lattice sandwich column in end compression was carried out and the structural efficiency was also discussed.

In-plane mechanical properties of elliptical cell honeycombs

The in-plane mechanical properties of honeycombs with hexagonally packed elliptical cells are first analyzed theoretically. The theoretical results can be expressed as the product of the mechanical properties of circular cell honeycombs and a cell-geometry coefficient which is a function of the ellipticity of cell walls. The theoretical expressions are then compared with the numerical results obtained from finite element analyses, and they agree well. It is found that the in-plane mechanical properties along the two principal directions of elliptical cell honeycombs are not the same, leading to an orthotropic mechanical behavior. The in-plane mechanical properties of elliptical cell honeycombs depend on the ellipticity of cell walls as well as their relative density. Moreover, a series of design maps for elliptical cell honeycombs with different relative densities and cell wall ellipticities are generated, and can be utilized as a tool in a minimum weight design to satisfy a set of prescribed in-plane mechanical properties.

Minimum Weight Design of Pre Engineered Steel Structures Using Built-up Sections and Cold Formed Sections

In the past few decades most of the efforts were made to achieve minimum weight of the steel structures by satisfying all the design requirements imposed by various latest building codes and this idea lead towards the concept of pre-engineered steel buildings (PEB). In current research work, minimum weight buildings are targeted with simple fabrication process and easy erection to have maximum structural efficiency. Minimum weight of structure is proportional to the minimum cost and hence lowers seismic and gravitational forces. To achieve above mentioned objectives and to verify the suitability and applicability of concept of PEB, a sample steel industrial building is first analyzed and designed by using conventional steel hot rolled sections and then by using pre-engineered tapered and cold formed sections. Results of analysis were compared in terms of weight and response of structures which clearly indicated that PEB structures are of less weight and structurally more efficient than conventional steel structures.

Engineering Knowledge-Based Variance-Reduction Simulation and G-Dominance for Structural Frame Robust Optimization

This paper proposes the incorporation of engineering knowledge through both (a) advanced state-of-the-art preference handling decision-making tools integrated in multiobjective evolutionary algorithms and (b) engineering knowledge-based variance-reduction simulation as enhancing tools for the robust optimum design of structural frames taking uncertainties into consideration in the design variables. The simultaneous minimization of the constrained weight (adding structural weight and average distribution of constraint violations) on the one hand and the standard deviation of the distribution of constraint violation on the other are handled with multiobjective optimization-based evolutionary computation in two different multiobjective algorithms. The optimum design values of the deterministic structural problem in question are proposed as a reference point (the aspiration level) in reference-point-based evolutionary multiobjective algorithms (here g-dominance is used). Results including S-metric statistics in a structural frame test case with uncertain loads show considerable reductions in computational costs without harming the nondominated front quality, obtaining a design set that makes it possible to select minimum weight and maximum robustness optimum designs.

Tailoring of composite cantilever beam for maximum stiffness and minimum weight

As the natural resources goes on decreasing now a days and to meet the needs of natural resources conservation, energy economy most of the manufacturers and their sub contractors are attempting to reduce the weight of the members in recent years. In this approach they are searching for low cost, high strength to weight ratio materials. Substituting composite structures for conventional metallic structures has many advantages because of higher specific stiffness and strength of composite materials. Composite materials have the major advantage of high strength to weight ratio with continuously decreasing travel of cost in addition to other advantages like excellent corrosive resistance, superior torsional buckling and fatigue strength and high specific strain energy storage capacity. The present work aims at the suitability of composite materials usage, by the identification of optimal fiber orientation stacking sequence and tailoring for laminate thickness/width for maximum stiffness and minimum weight design of laminated composite beam. The structural response is evaluated from conventional metallic structure with optimization techniques for maximizing stiffness and minimum weight. These metallic optimum values are extended initially to composite beam to maintain strength with the developed of optimization algorithm. Later with topology optimization and by tailoring cross-sections algorithm of the beam is evaluated with optimal fiber orientations and stacking sequence to maintain strength as in additional advantage of less weight for composites. Tailoring is done based on gradual decrement in cross-section over the length in both thickness and width direction. Numerical results are presented for cantilever beam with different geometries showing the maximizing stiffness and with minimum weight. The results indicate that the devised strategy is well suited for finding optimal fiber orientations and laminate thickness/width in the tailoring design of slender laminated composite structure.

Optimum Unbraced Length Ratios of Slender Steel Sections

To get minimum weight design of steel structures, selection of suitable steel section for design of a steel member is always been a point of great interest from a designer's point of view. Because of thin flanges and webs slender sections are lighter as compared to compact and non-compact sections. Aim of this research study is to determine the optimum unbraced length of slender steel sections under bending and compression effects. Required objectives are achieved by selecting a wide range of steel sections having non compact to slender webs and flanges. After making a careful selection of different steel sections, each steel section is analyzed under compression and bending for a given unbraced length of steel member and optimum values of flange and web slenderness are determined. Same procedure is repeated for all selected steel sections for different unbraced length ratios. Results have determined the optimum values of flange and web slenderness which can lead towards the minimum weight and cost of steel structures.

Conservative Failure Criteria for Optimal Design of Composite Structures Including Effect of Shear Loading

A minimum weight design of laminated composite structures is carried out for different loading conditions and failure criteria using genetic algorithm. The phenomenological maximum stress (MS) and Tsai-Wu (TW) criteria and the micro-mechanism-based failure mechanism based (FMB) failure criteria are considered. A new failure envelope called the Most Conservative Failure Envelope (MCFE) is proposed by combining the three failure envelopes based on the lowest absolute values of the strengths predicted. The effect of shear loading on the MCFE is investigated. The interaction between the loading conditions, failure criteria, and strength-based optimal design is brought out.

Assessment of Materials for Fuselage Panels Considering Fatigue Behavior

Minimum-weight designs are frequently too costly to manufacture, whereas less expensive and easy to fabricate and assemble designs are often much heavier. The most efficient design on the basis of both cost and weight often lies between these two extremes. The current trend in structural materials selection consists of the extensive use of composite materials in the airframe. Composite materials have high specific strength, are less prone to fatigue crack initiation and provide enhanced flexibility for structural optimization compared to the aluminum alloys. On the other hand, aluminum alloys display higher toughness and better damage tolerance in the presence of defects. A simple methodology for the weight assessment based on the specific weight for different damage scenarios for an exemplary, simplified fuselage panel, will be presented, in order to quantify the savings under different conditions. The results show that the composites have advantages over the aluminum alloys, although due to low ductility, in parts that are exposed to external damages the aluminum alloys can have better performance due to the better damage tolerant properties.

Minimum weight design of helically and hoop wound toroidal hydrogen storage tanks with variable slippage coefficients

AbstractThis article determines the optimal winding parameters for helically and hoop overwound toroidal hydrogen storage tanks, based on the application of variable slippage coefficients. First, an optimality condition between helical winding angle and hoop‐to‐helical thickness ratio is derived from the minimum strain energy density criterion. The winding angle distributions are then obtained with the aid of the optimality condition, taking into account the shell thickness variation along the meridional direction. The general criteria for fiber trajectory stability on a torus are presented, and the relationship for the slippage coefficient and the helical winding angle is formulated according to the windability and manufacturability. The helical winding angle and thickness at the equator are considered as design variables, whereas the minimum weight acts as the objective function. A design example with a toroidal hydrogen storage tank is outlined to demonstrate the favorable performance of the present method. The results show that the present method using variable slippage coefficients leads to a better distribution of the fiber stress in the toroidal shell and an efficient utilization of the laminate strength. The obtained winding parameters can thus be regarded as optimal for filament‐wound toroidal hydrogen storage tanks. POLYM. COMPOS., 2012. © 2012 Society of Plastics Engineers

OPTIMAL DESIGN OF SANDWICH BEAMS WITH LIGHTWEIGHT CORES IN THREE-POINT BENDING

Being widely used in engineering, the optimization of sandwich beams to achieve greater stiffness-to-weight ratio is of great research interest. In this paper, the optimization process was carried to obtain minimum weight designs in three-point bending based on prescribed stiffness index. Results indicate that honeycomb-cored sandwich beams possess smaller minimum weight index in comparison with metal foam-cored beams. In addition, failure mechanisms of the optimized designs were also investigated to reveal that the sandwich-cored beams were more prone to face wrinkling than metal foam-cored beams. In the optimization process, five different core topologies and four different parent materials were investigated under a given load index. It was found for low prescribed load values where bending is dominant, unidirectional lattice composite sandwich beams bear loads more efficiently than steel cored beams. However, the primary mode of failure for high prescribed load index is core shear, thus implying no significant advantage in lattice composite sandwich beams over other materials. Comparing the different materials, that laminate lattice composite sandwich beams possess the best bending performance for varying levels of prescribed load index, making it suitable for applications in the aerospace field.

Optimum design of geometrically non-linear steel frames using artificial bee colony algorithm

An artificial bee colony (ABC) algorithm is developed for the optimum design of geometrically non-linear steel frames. The ABC is a new swarm intelligence method which simulates the intelligent foraging behaviour of honeybee swarm for solving the optimization problems. Minimum weight design of steel frames is aimed under the strength, displacement and size constraints. The geometric non-linearity of the frame members is taken into account in the optimum design algorithm. The performance of the ABC algorithm is tested on three steel frames taken from literature. The results obtained from the design examples demonstrate that the ABC algorithm could find better designs than other meta-heuristic optimization algorithms in shorter time.