Buckling Load Factor Research Articles

A method for the treatment of second order effects in plastically-designed steel frames

The susceptibility of steel frames to global second order effects, also referred to as sway effects, ‘P–Δ’ effects and global geometric nonlinearities, is traditionally assessed through the elastic buckling load amplifier αcr. For elastic analysis, EN 1993-1-1 and other international steel design standards state that second order effects may be neglected provided αcr is greater than or equal to 10. However, when plastic analysis is employed, yielding of the material degrades the stiffness of the structure, and hence a stricter requirement of αcr ≥ 15 is prescribed in EN 1993-1-1 for second order effects to be neglected. Use of a single limit of 15 for any structural system is however considered to be overly simplistic. A more consistent and accurate approach is to determine the degree of stiffness degradation and hence the increased susceptibility to second order effects on a frame-by-frame basis. A parametric analysis to assess the stability of steel frames in the plastic regime is presented herein. A series of frames with varying geometries and load cases has been assessed. Based on the findings, a proposal for the calculation of a modified elastic buckling load factor αcr,mod, which considers the reduction in stiffness following plasticity on a frame-by-frame basis, is presented.

A gradient boosting approach with diversity promoting measures for the ensemble of surrogates in engineering

Ensemble of surrogates has shown to be effective in the modeling of a variety of engineering problems, from aerospace to automotive and oil and gas industries, among many others. The ensemble performance though can be negatively affected by the lack of diversity (correlated errors) among the members of the ensemble, i.e., similar errors throughout the input space. During the last decade, ensemble research efforts in engineering have mostly focused on the so-called ensemble integration (combining prediction) phase with, for example, linear weighted averages of surrogate predictions based on performance (error) measures of both local and global natures. On the ensemble generation side (members of the ensemble), the emphasis has been on promoting diversity through the so-called heterogeneous ensembles, that is the use of different learners (surrogates), such as, linear regression, radial basis functions, kriging, support vector regression, and neural networks. Because of the lack of control on diversity in heterogeneous ensembles, potentially correlated error among the learners remains a critical issue. This paper presents an alternative approach based on homogeneous ensembles (single learning algorithm) that promotes diversity both implicitly and explicitly, by randomly sampling the training data and deterministically changing the data supplied to each surrogate model in the ensemble generation process. Specifically, it includes decision trees as learners, subsampling of the training set, and training on random selections of the input features, i.e., random subspace. The ensemble is sequentially constructed as an additive model where at each stage a simple surrogate is fit to the negative gradient of the loss function at the training data of the latest ensemble (gradient boosting). In addition, as a by-product of the modeling process, the proposed approach provides importance measures to preliminary rank input features. Statistically significant prediction improvements over heterogeneous ensembles were observed in a variety of well-known analytical test functions and industrial case studies in the areas of petroleum engineering-net present value of oil production in a mature reservoir and structural analysis-FSAE brake pedal von Mises stress and buckling load factor.

Topology optimization of functionally-graded lattice structures with buckling constraints

Lattice structures have been widely studied due to their advantage of low stiffness-to-weight ratio or sometimes auxetic properties. This paper presents a topology optimization method for structures with functionally-graded infill lattices with buckling constraints, which minimizes compliance while ensuring a prescribed level of structural stability against buckling failures. To realize topologically-optimized structures filled with functionally-graded lattices, Helmholtz PDE-filter with a variable radius is applied on the density field in Solid Isotropic Material with Penalization (SIMP) method. Buckling load factors based on the linear buckling analysis is employed as buckling constraints. Numerical examples show that proposed method can generate stiff structures comparable to the ones by the SIMP, with functionally-graded infill lattices that improve the structural stability by avoiding long, slender features under compression.

Nonlinear buckling of cylindrical steel silos with fabrication cracks

Large steel silos are typical kinds of thin-walled structures that are usually constructed with a vertical, circular form and are used as vessels for storing particulate granular solids in the industrial and agricultural sectors. In the present analyses, the buckling behaviours of circular steel silos with circumferential and meridional fabrication cracks are evaluated in accordance with Eurocodes EN1990, 1991, and 1993 [1–6]. A steel silo with a diameter of 10 m and a height of 24 m is used as an example silo. The finite element models of the steel silo cover a wide range of crack geometries: circumferential crack angles ranging from 10° to 60°, meridional crack lengths ranging from 0.5 m to 3.0 m, and various crack heights. The buckling equilibrium paths and buckling deformations are examined through a large number of numerical calculations. The effects of single circumferential crack, single meridional crack, multiple circumferential cracks, multiple meridional cracks and silo slenderness on the buckling behaviours of the silo structures are specifically addressed. The buckling modes of the silo structures with fabrication cracks are completely different from those of a geometrically perfect silo. Circumferential and meridional cracks have substantial influences on the buckling deformations, which occur mainly in the area around the crack. The most unfavourable crack height with respect to structural buckling is located in the lower position of the silo wall, and the buckling load factor increases with the decrease in crack length. Moreover, the cracks are more unfavourable to buckling behaviour of silo structures with larger slenderness than those with smaller slenderness.

Composite laminate design with strength and fatigue life optimization using Elite–Scout Genetic Algorithm (ESGA)

Genetic algorithm (GA)-based optimization is a common approach to deal with problems that have a large solution space. Composite laminate design is one such problem due to the substantial number of candidates that arise from the selection and stacking of lamina. Many authors have successfully demonstrated GA-based approach in stacking sequence optimization. A few of them extending it to as far as selecting the candidate lamina for the candidate laminate. However, a vast majority of the literature is limited to optimizing a single parameter such as Margin of Safety, Buckling Load Factor, etc., while neglecting other parameters or assigning ill-suited weights to obtain a unified fitness function. In this paper, we will be discussing a novel Elite–Scout Genetic Algorithm (ESGA) for multi-objective optimization which will result in the Pareto-optimal solution(s). The algorithm is based on the first multiple elitist selection method, integrated with the concept of a scout operator. ESGA incorporates a population dependent growing crossover rate, and decaying mutation rate. The growth and decay are modeled along the lines of the cooling schedule as found in simulated annealing (SA). This will ensure greater flexibility of the algorithm by accommodating better exploration of the solution space without deterring the convergence of the solution.

A framework for isogeometric‐analysis‐based optimization of wind turbine blade structures

AbstractEarly‐stage wind turbine blade design usually relies heavily on low‐fidelity structural models; high‐fidelity, finite‐element‐based structural analyses are reserved for later design stages because of their complex workflows and high computational expense. Yet, high‐fidelity structural analyses often provide design‐governing feedback such as buckling load factors. Mitigation of the issues of workflow complexity and computational expense would allow designers to utilize high‐fidelity feedback earlier, more easily, and more often in the design process. Thus, a blade analysis framework that employs isogeometric analysis (IGA), a simulation method that overcomes many of the aforementioned drawbacks associated with traditional finite element analysis (FEA), is presented. IGA directly utilizes the mathematical models generated by computer‐aided design (CAD) software, requiring less user interaction and no conversion of parametric geometries to finite element meshes. Furthermore, IGA tends to have superior per‐degree‐of‐freedom accuracy compared with traditional FEA. Issues unique to IGA in the context of wind turbine blade design, such as coupling of thin‐shell components, are addressed, and a design approach that combines reduced‐order aeroelastic analysis with IGA is outlined. Aeroelastic analysis is used to efficiently provide dynamic kinematic data for a wide range of wind load cases, while IGA is used to perform buckling analysis. The value of incorporating high‐fidelity analysis feedback into blade design is demonstrated through optimization of the NREL/SNL 5 MW wind turbine blade. A variety of potential designs are produced with reduced blade mass and material cost, and IGA‐based buckling analysis is shown to provide design‐governing constraint information.

Buckling analysis of functionally graded plates partially resting on elastic foundation using the differential quadrature element method

We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.

Optimal Formation Assessment of Multi-layered Ground Retrofit with Arch-Grid Units Considering Buckling Load Factor

This study presents an optimal shape generation method of local steel unit plates in arch-grid structures by using buckling load factor. ETABS software is utilized for a computational modeling of arch-grid to consider buckling analysis. According to the present optimal shape generation method, first, some shape types of a horizontal unit cell plate of arch-grid are assumed as initial designs. Second, they are analyzed through ETABS in terms of their buckling capacities. At the same time, appropriate vertical column bar sizes are achieved with respect to maximal stress of steel material and buckling load factor. Third, the generated arch-grid are combined to achieve optimal conditions of width and height of a given arch-grid structure, which shows the best structural feasibility to resist a given building. The arch-grid structure is extended by considering four different cases: a combined grid, an extended grid, a multi-story grid and a pyramid grid to verify the effectiveness of the present optimal shape generation method of steel arch-grid as numerical examples.

Bi-level optimization of laminated composite structures using particle swarm optimization algorithm

This paper presents an efficient bi-level optimization technique to obtain the optimal stacking sequence for symmetric composite structures. The proposed approach involves two levels of modeling and optimization. The first level of the optimization procedure is used to minimize the weight of the composite structure. At this level, lamination parameters and the number of plies of specified angles (0, ±45 and 90 degree) are design variables, buckling load factor is treated as a constraint, and the weight of the structure is to be minimized using continuous-discrete particle swarm optimization algorithm. Next, at the second level the location of each ply orientation through the thickness (i.e. the layup of the panel) is found. At the second level, optimum stacking sequence is sought to maximize the load bearing capacity of the structure with respect to the buckling. The proposed methodology is applied to two test cases. Results show that the approach improves the buckling load factor of the structure without any weight penalty.

Buckling design of large eccentrically filled steel silos

Large steel silos are typical kinds of thin-walled structure which are widely used for storing huge quantities of granular solids in industry and agriculture. In the present analyses, buckling design of circular steel silos subject to large eccentricity filling pressure is demonstrated in accordance with Eurocode: EN1990, 1991, 1993 . The finite element model is established by using the commercial general purpose computer package ANSYS. Five types of buckling analyses are carried out for the geometrically perfect and imperfect models, with and without the consideration of the material plasticity, which are designated as LBA, GNA, GMNA, GNIA, and GMNIA in EN 1993 Part 1–6.Buckling behavior of five example steel silos with capacity of 40,000 to 60,000m3 is investigated whose slenderness ranges from 1.89 to 0.46, comprising intermediate slender and squat silos widely applicable in practical engineering. The results show that the buckling deformations are nonsymmetrical and the GMNIA analysis gives out the least buckling load factor for all example silos from all proposed buckling analysis types, and the load displacement curves are highly nonlinear and predict a distinct maximum load followed by a descending path, in which the maximum load is taken as the critical buckling point λcr for the equilibrium path. The buckling mode in GMNIA analysis takes the form of the well-known elephant-foot deformation at the bottom part of the shell wall, combined with nonsymmetrical waves in meridional direction throughout the whole height of the silo wall due to the distribution of weld imperfection. The geometrical nonlinearity is beneficial while material nonlinearity is strong and detrimental to buckling behavior of example silos. The effect of weld imperfection is also harmful to buckling resistance of silo, which is more serious for relatively slender silos than squat silos. The buckling is mainly governed by the nonuniform distribution of the solid pressure other than other influential factors as the weld imperfection, geometrical and material nonlinearity, compared with the load case of symmetrical filling. The economical design of steel silos can be effectively measured by the economic index called the ratio of capacity to steel consumption (RCS). It is validated that the index RCS increases rapidly with the decrease of silo slenderness, and the storage efficiency of example silos is increased by about 2.1 times with the slenderness varying from 1.89 to 0.46. It also suggests that the eccentricity in filling of steel silo should be reduced as far as possible for improvement of buckling strength of structure under eccentric filling.

A multi-objective design optimization technique for weight and cost minimization of hybrid laminated composite structure by modified non-dominated sorting genetic algorithm

Laminated composite panels are presently being used in wider applications in automotive, aerospace, defence and civil type of industries. It has various advantages over conventional materials with superior specific stiffness & strength, fatigue and corrosion resistance with energy absorption feature comparing others. Optimal design of composite laminates regarding change in ply angles to increase the strength is obligatory to realize the complete potentiality of fibre reinforced particles/materials. The above epistemology is applied to the multi-objective design optimization technique of fibre-reinforced solid rocket motor composite cylindrical skirt of space vehicle is analyzed. In that solid rocket motor, a skirt is defined as a feasible component for weight diminution which leads to reduction of entire weight. Due to its significance, it is recommended to optimize the both weight and expense of the fibre reinforced composite (FRC) cylindrical shape skirt affected to overstressing strength and buckling strength at the combined conditions of aerodynamic torque and thrust in axial direction. In this paper, the failure principle of Tsai-wu is applied to determine the first ply catastrophe. Failure strength and Buckling strength of the skirt is depicts by using overstressing load level factor and buckling load factor. Various material combinations such as Graphite/Epoxy & Glass/Epoxy, have been used to find the optimal values. Laminated composite skirts are fabricated with glass-epoxy if cost is the criteria and graphite-epoxy if weight comes into an account

Stability of roof trusses stiffened by trapezoidal sheeting and purlins

In the article linear buckling analysis of a set of steel trusses braced by purlins and trapezoidal sheeting are conducted. The buckling load factor due to the height of a corrugated sheeting profile is investigated in parametric studies. The minimal height of trapezoidal sheeting required for preventing the sheeting and chords of the trusses against the buckling is obtained. Two groups of models are considered: “axial” model as a simple one and “eccentric” model as a more complex one. In the second group of models, eccentricity between the top chord of the trusses and purlins is considered, by means of equivalent beam elements. The differences between models are indicated and the results are discussed.

Buckling load optimization of laminated plates resting on Pasternak foundation using TLBO

This paper deals with the maximization of the critical buckling load of simply supported antisymmetric angle-ply plates resting on Pasternak foundation subjected to compressive loads using teaching learning based optimization method (TLBO). The first order shear deformation theory is used to obtain governing equations of the laminated plate. In the present optimization problem, the objective function is to maximize the buckling load factor and the design variables are the fibre orientation angles in the layers. Computer programming is developed in the MATLAB environment to estimate optimum stacking sequences of laminated plates. A comparison also has been performed between the TLBO, genetic algorithm (GA) and differential evolution algorithm (DE). Some examples are solved to show the applicability and usefulness of the TLBO for maximizing the buckling load of the plate via finding optimum stacking sequences of the plate. Additionally, the influences of different number of layers, plate aspect ratios, foundation parameters and load ratios on the optimal solutions are investigated.

COMPARATIVE STUDY OF MONOCOQUE AND SEMIMONOCOQUE FLIGHT VEHICLE STRUCTURES UNDER STRUCTURAL AND THERMO-STRUCTURAL LOADS.

Analysis of monocoque and semi-monocoque cylindrical flight vehicle structures by using finite element method has been carried out. Shell elements are used for idealizing skin portions and end rings and beam elements are used for idealizing stiffeners. The behaviour of these structures is compared in terms of mass, deformation, stress and buckling under structural and thermo-structural loads to study the effect of number of longitudinal stiffeners. The study shows that semi-monocoque structures give higher factor of safety and buckling load factor when only structural loads (axial force and bending moment) are acting on them and the same structure give lesser factor of safety and buckling load factor when thermal loads (temperatures) and structural loads (axial force and bending moment) are acting on them in a combined manner. It is concluded that monocoque structures are best suitable under thermo-structural load environments.

An Adaptive Continuation Method for Topology Optimization of Continuum Structures Considering Buckling Constraints

This paper presents an adaptive continuation method for buckling topology optimization of continuum structures using the Solid Isotropic Material with Penalization (SIMP) model. For optimization problems of minimizing structural compliance subject to constraints on material volume and buckling load factors, it has been found that the conflict between the requirements for structural stiffness and stability may have an adverse impact on the performance of existing optimization algorithms. An automatic scheme for adjusting the penalization parameter is introduced to deal with this conflict and thus achieves better designs. Based on an investigation on the effect of the penalization parameter on design evolution during the optimization process, a rule is established to determine the appropriate penalization parameter values. Using this rule, an effective scheme is developed for determining the penalization parameter values such that the buckling constraints are appropriately considered throughout the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed method.

Global stability analysis of reinforced concrete buildings using the γ z coefficient

Abstract Global stability analysis is becoming increasingly important in the design of reinforced concrete buildings, especially in the slender ones, due its sensitivity to lateral displacement. The loss of stability is usually associated with the intensity of the second order effects and, in that sense, the gamma-z (γz) coefficient is an important evaluation parameter for this problem. This work aims to verify the γz efficiency as a global stability parameter based on the buckling load factors of the structures and their respective critical buckling modes. To this purpose, a comparative analysis is performed in several idealized structures, from which an approximate equation for calculating the critical load factor based on the γz coefficient is obtained. This equation was verified by numerical analysis of Finite Elements Method models of real reinforced concrete buildings. It was concluded that the proposed equation presents satisfying results within a certain range of γz.

Reliability-based and deterministic design optimization of a FSAE brake pedal: a risk allocation analysis

While probabilistic designs can translate into significant weight savings through better risk allocation, deterministic design optimization remains widely used in industry. To promote the use of probabilistic designs among engineering students and practitioners, this work solves reliability based design optimization (RBDO) and deterministic design optimization (DDO) models of a FSAE brake pedal with multiple failure modes (stress and buckling) with their relative performance evaluated through a risk allocation analysis. The problems of interest were systematically solved through the following steps: i) topology optimization to specify the brake-pedal shape, ii) numerical 3D brake-pedal modeling under uncertainty for stress and buckling analysis, iii) mass (M), maximum von Mises stress (Smax) and buckling load factor (fbuck) surrogate modeling, iv) global sensitivity analysis and surrogate model selection, and v) surrogate-based RBDO and DDO with risk allocation analysis. Results show that when compared to DDO with alternative safety factors, for the same probability of system failure, the RBDO brake pedal designs were significantly lighter and more robust (less mass variability).

Parametric Study of Integral Buckle Arrestors Design of Submarine Pipeline System in Masela Block

A pipe collapse or local buckling is one of catastrophic failures that might be occurred in a submarine pipeline system due to a high external hydrostatic pressure. A preliminary survey of pipeline on the selected route shows that the pipeline will pass through a 5,309ft of depth. Buckle arrestors are necessary to be installed along a critical location of pipeline to prevent buckle propagation and catastrophic failure. The purposes of this study was to examine the effect of geometry variation, such as (i) pipe thickness, (ii) ratio of buckle arrestor thickness to pipe thickness, (iii) buckle arrestor length, and (iv) pipe diameter, of the integral buckle arrestor system to a buckling load factor. The study was conducted by numerical simulations using ANSYS™. Nominal Pipe Sizes of 28”, 30” and 32” with API 5L grade X60 materials were used in the simulation. The simulation was validated using experimental data of previous study and DNV-OS-F101. Based on this study, the buckle load factor was significantly influenced by the pipe thickness and the pipe diameter. The other two factors generate a slight change on the buckle load factor. For selected NPS of 28” with 1.2” thickness of pipeline, we hypothesize that the integral buckle arrestor with 30” length and 3.6” thickness can be used to prevent buckling propagation.

A Study on Structural Design and Test of Micro Scale Composite Material Blade for Wind Turbine

The purpose of the present study is to design a micro scale composite wind turbine blade. The blade airfoil of FFA-W3-211 was selected to meet Korean weather condition. The skin-spar-foam sandwich type structure was adopted for improving buckling and vibration damping characteristics. The design loads were determined at wind speed of 25m/s, and the structural analysis was performed to confirm safety and stability from strength, buckling and natural frequency using the finite element analysis method. The prototype was manufactured using the hand-lay up method and it was experimentally tested using the three point concentrated loading method. In order to evaluate the design results, it was compared with experimental results. According to comparison results, the estimated results such as compressible stress, max tip deflection, natural frequency and buckling load factor were well agreed with the experimental results.

Application of linear buckling sensitivity analysis to economic design of cylindrical steel silos composed of corrugated sheets and columns

Abstract The paper deals with global stability of steel cylindrical silos composed of corrugated walls and vertical columns with loads imposed by a bulk solid following Eurocode 1. The optimum silo design with respect to the steel weight was based on a sensitivity analysis method. The changes of silo column profiles at each design step were performed by means of influence lines for the buckling load factor due to the unit column bending stiffness variation. The corrugated walls were simulated as an equivalent orthotropic shell and vertical thin-walled columns as beam elements. The results were compared with the Eurocode 3 approach and verified by FE results of linear buckling and non-linear analyses with geometric non-linearity carried out with the commercial finite element code ABAQUS for a 3D shell model of a perfect silo. The proposed procedure allowed for a rational silo design with an economic material use. Some recommendations for the silo optimum design were elaborated.