• Journal of the Korean Society of Industry Convergence
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• v.13 no.2
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• pp.77-84
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• 2010

Recently, the concept of structural design against instability has been proposed in the chassis parts. The design considerations of lower control arm of chassis parts under the buckling and durability strengths are the general. More precisely, this paper considers a specific application and associated optimization problem for two strengths, where the design variables are the physical or geometric dimensions for skins and stiffeners. The objective is the minimization of the total weight, while optimization constrains involve reserve or improve factors for the buckling and durability strengths. The most important features are related to the numerical simulations for the estimation of buckling factor and their sensitivities by means of nonlinear and linear finite element analyses. The bucking and durability strength analyses, and the morping geometries are directly included in the optimization problem and the modified design is formulated. As a result, the optimal structure with stable behavior is obtained or increases the buckling and durability strengths of parts. Most of design problems for structures exposed to elastic instability can be formulated and solved.

• International Journal of Naval Architecture and Ocean Engineering
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• v.3 no.4
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• pp.274-285
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• 2011

The supercavitating vehicle is an underwater vehicle that is surrounded almost completely by a supercavity to reduce hydrodynamic drag substantially. Since the cruise speed of the vehicle is much higher than that of conventional submarines, the drag force is huge and a buckling may occur. The buckling phenomenon is analyzed in this study through static and dynamic approaches. Critical buckling load and pressure as well as buckling mode shapes are calculated using static buckling analysis and a stability map is obtained from dynamic buckling analysis. When the finite element method (FEM) is used for the buckling analysis, the solver requires a linear static solver and an eigenvalue solver. In this study, these two solvers are integrated and a consolidated buckling analysis module is constructed. Furthermore, Particle Swarm Optimization (PSO) algorithm is combined in the buckling analysis module to perform a design optimization computation of a simplified supercavitating vehicle. The simplified configuration includes cylindrical shell structure with three stiffeners. The target for the design optimization process is to minimize total weight while maintaining the given structure buckling-free.

• Advanced Composite Materials
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• v.18 no.1
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• pp.21-42
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• 2009

The vibration characteristics of post-buckled laminated composite doubly curved shells are investigated. The finite element method is used for the analysis of post-buckling and free vibration of post-buckled laminated shells. The geometric non-linear finite element model includes the general non-linear terms in the strain-displacement relationships. The shell geometry used in the present formulation is derived using an orthogonal curvilinear coordinate system. Based on the principle of virtual work the non-linear finite element equations are derived. Arc-length method is implemented to capture the load-displacement equilibrium curve. The vibration characteristics of post-buckled shell are performed using tangent stiffness obtained from the converged deflection. The code is first validated and then employed to generate numerical results. Parametric studies are performed to analyze the snapping and vibration characteristics. The relationship between loads and fundamental frequencies and between loads and the corresponding displacements are determined for various parameters such as thickness ratio and shallowness.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.221-238
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• 2014

A four-noded curved shell finite element for the geometrically non-linear analysis of beams curved in plan is introduced. The structure is conceived as a sequence of macro-elements (ME) having the form of transversal segments of identical topology where each slice is formed using a number of the curved shell elements which have 7 degrees of freedom (DOF) per node. A curved box-girder beam example is modelled using various meshes and linear analysis results are compared to the solutions of a well-known computer program SAP2000. Linear and non-linear analyses of the beam under increasing uniformly distributed loads are also carried out. In addition to box-girder beams, the proposed element can also be used in modelling open-section beams with curved or straight axes and circular plates under radial compression. Buckling loads of a circular plate example are obtained for coarse and successively refined meshes and results are compared with each other. The advantage of this element is that curved systems can be realistically modelled and satisfactory results can be obtained even by using coarse meshes.

• Structural Engineering and Mechanics
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• v.16 no.3
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• pp.259-274
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• 2003

In this paper, a novel numerical solution technique, the differential cubature method is employed to study the buckling problems of thick plates with arbitrary quadrilateral planforms and non-uniform boundary constraints based on the first order shear deformation theory. By using this method, the governing differential equations at each discrete point are transformed into sets of linear homogeneous algebraic equations. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Detailed formulation and implementation of this method are presented. The buckling parameters are calculated through solving a standard eigenvalue problem by subspace iterative method. Convergence and comparison studies are carried out to verify the reliability and accuracy of the numerical solutions. The applicability, efficiency, and simplicity of the present method are demonstrated through solving several sample plate buckling problems with various mixed boundary constraints. It is shown that the differential cubature method yields comparable numerical solutions with 2.77-times less degrees of freedom than the differential quadrature element method and 2-times less degrees of freedom than the energy method. Due to the lack of published solutions for buckling of thick rectangular plates with mixed edge conditions, the present solutions may serve as benchmark values for further studies in the future.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.1A
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• pp.1-7
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• 2011

This paper deals with buckling loads of the column with the constant surface area. The shape function of variable column depth is chosen as the linear taper. The ordinary differential equation governing buckled shapes of the column is derived based on the dynamic equilibrium equation of such column subjected to an axial load. Three kinds of end constraint of hinged-hinged, hinged-clamped and clamped-clamped are considered in numerical examples. Effects of the column parameters on buckling loads are extensively discussed. Especially, section ratios of the strongest column are calculated, under which the maximum, i.e. strongest, buckling loads are achieved. Also the buckled shapes are obtained for searching the nodal points where the inner transverse supports are simply installed to increase the buckling loads.

• Steel and Composite Structures
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• v.28 no.2
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• pp.251-266
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• 2018

Compared to conventional flat web I-beams, the prediction of shear buckling stress of corrugated web steel beams (CWSBs) is not straightforward. But the CWSBs combined advantages of lightweight large spans with low-depth high load-bearing capacities justify dealing with such difficulties. This work investigates experimentally and analytically the shear strength of trapezoidal CWSBs. A set of large scale CWSBs are manufactured and tested to failure in shear. The results are compared with widely accepted CWSBs shear strength prediction models. Confirmed by the experimental results, the linear buckling analyses of trapezoidal corrugated webs demonstrated that the local shear buckling occurs only in the flat plane folds of the web, while the global shear buckling occurs over multiple folds of the web. New analytical prediction model accounting for the interaction between the local and global shear buckling of CWSBs is proposed. Experimental results from the current work and previous studies are compared with the proposed analytical prediction model. The predictions of the proposed model are significantly better than all other studied models. In light of the dispersion of test data, accuracy, consistency, and economical aspects of the prediction models, the authors recommend their proposed model for the design of CWSBs over the rest of the models.

• Steel and Composite Structures
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• v.34 no.2
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• pp.241-260
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• 2020

This article presented a comprehensive model to study static buckling stability and associated mode-shapes of higher shear deformation theories of sandwich laminated composite beam under the compression of varying axial load function. Four higher order shear deformation beam theories are considered in formulation and analysis. So, the model can consider the influence of both thick and thin beams without needing to shear correction factor. The compression force can be described through axial direction by uniform constant, linear and parabolic distribution functions. The Hamilton's principle is exploited to derive equilibrium governing equations of unified sandwich laminated beams. The governing equilibrium differential equations are transformed to algebraic system of equations by using numerical differential quadrature method (DQM). The system of equations is solved as an eigenvalue problem to get critical buckling loads and their corresponding mode-shapes. The stability of DQM in determining of buckling loads of sandwich structure is performed. The validation studies are achieved and the obtained results are matched with those. Parametric studies are presented to figure out effects of in-plane load type, sandwich thickness, fiber orientation and boundary conditions on buckling loads and mode-shapes. The present model is important in designing process of aircraft, naval structural components, and naval structural when non-uniform in-plane compressive loading is dominated.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.383-397
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• 2019

More than one longitudinal web stiffener may be economical in the design of plate girders that have considerably high width-to-thickness ratio of webs. In this study, the bend-buckling strength of relatively deep webs with two horizontal lines of flat plate-shaped single-sided stiffeners was numerically investigated. Linear eigenvalue buckling analyses were conducted for specially selected hypothetical models of stiffened web panels, in which top and bottom junctions of a web with flanges were assumed to have simply supported boundary conditions. Major parameters in the analyses were the locations of two longitudinal stiffeners, stress ratios in the web, slenderness ratios and aspect ratios of web panels. Based on the application of assumptions on the combined locations of the two longitudinal web stiffeners, simplified equations were proposed for the bend-buckling coefficients and compared to the case of one longitudinal stiffener. It was found that bend-buckling coefficients can be doubled by adopting two longitudinal stiffeners instead of one longitudinal stiffener. For practical design purposes, additional equations were proposed for the required bending rigidity of the longitudinal stiffeners arranged in two horizontal lines on a web.

• Journal of Korean Society of Steel Construction
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• v.23 no.6
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• pp.679-690
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• 2011

Since the elastic buckling problem of the plate has been studied both experimentally and theoretically, the buckling loads with various boundary conditions and loads can be easily determined. Currently, flange and web design specifications are based on the buckling stress and the post-buckling strength and include a safety-factor. Therefore, this study extended suchresearch to the linear buckling theory with ideal conditions and to the ultimate state with post-buckling. The current specifications are based on elastic buckling stress; and therefore, further research on the ultimate behavior of the plate is required. The ultimate strength design concept, which allows finite deflection, is used in this studyto maximize the post-buckling strength in a steel box. An empirical equation, which provides the ultimate strength of the steel box due to the change in the slenderness and optimum rigidity, are suggested based on the experiment results. Moreover, the appropriateness of the current design specifications was analyzed and discussed.