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

• Journal of Korean Society of Steel Construction
• /
• v.17 no.5 s.78
• /
• pp.627-636
• /
• 2005

The analysis and design procedure of intermediate support strut for the innovative prestressed scaffolding (IPS) system was presented in this paper. The stability check of intermediate support strut is required as the behavior of the strut system is similar to that of the built-up column. The computer analysis model of the support strut was constructed for in-plane and out-of-plane buckling analysis, and the design of the support strut was performed. Using the eigenvalue for the buckling load and the member forces of support strut under design earth pressure, the effective buckling length was estimated. The allowable axial and bending stresses were calculated considering the effective buckling length. The combined stresses due to these axial forces and bending moment were estimated to be satisfied the safety condition of the intermediate support strut.

• Structural Engineering and Mechanics
• /
• v.40 no.6
• /
• pp.783-800
• /
• 2011

This paper addresses the finite strip formulations for the stability analysis of viscoelastic composite plates with variable thickness in the transverse direction, which are subjected to in-plane forces. While the finite strip method is fairly well-known in the buckling analysis, hitherto its direct application to the buckling of viscoelastic composite plates with variable thickness has not been investigated. The equations governing the stiffness and the geometry matrices of the composite plate are solved in the time domain using both the higher-order shear deformation theory and the method of effective moduli. These matrices are then assembled so that the global stiffness and geometry matrices of a moderately thick rectangular plate are formed which lead to an eigenvalue problem that is solved to determine the magnitude of critical buckling load for the viscoelastic plate. The accuracy of the proposed model is verified against the results which have been reported elsewhere whilst a comprehensive parametric study is presented to show the effects of viscoelasticity parameters, boundary conditions as well as combined bending and compression loads on the critical buckling load of thin and moderately thick viscoelastic composite plates.

• Steel and Composite Structures
• /
• v.18 no.2
• /
• pp.425-442
• /
• 2015

This paper addresses theoretically the bending and buckling behaviors of size-dependent nanobeams made of functionally graded materials (FGMs) including the thickness stretching effect. The size-dependent FGM nanobeam is investigated on the basis of the nonlocal continuum model. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a sinusoidal variation of all displacements through the thickness without using shear correction factor. The material properties of FGM nanobeams are assumed to vary through the thickness according to a power law. The governing equations and the related boundary conditions are derived using the principal of minimum total potential energy. A Navier-type solution is developed for simply-supported boundary conditions, and exact expressions are proposed for the deflections and the buckling load. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and stability responses of the FGM nanobeam are discussed in detail. The study is relevant to nanotechnology deployment in for example aircraft structures.

• Steel and Composite Structures
• /
• v.23 no.6
• /
• pp.647-656
• /
• 2017

This paper presents an experimental study on the behaviour of steel beams with different types of web openings. Steel beams with web openings became progressively more accepted as a well-organized structural form in steel construction since their existence. Their complicated design and profiling method provides better flexibility in beam proportioning for strength, depth, size and location of holes. The objective of this study is to carry out the experiments on steel beams with different types of web openings and performed non-linear finite element (FE) analysis of the beams that were considered in the experimental study in order to determine their ultimate load capacity and failure modes for comparison. Ten full scale models of steel beam with web openings have been tested in the experimental investigation. The finite element method has been used to predict their entire response to increasing values of external loading until they lose their load carrying capacity. FE model of each specimen that is utilized in the experimental studies is carried out. These models are used to simulate the experimental work to verify test results and to investigate the nonlinear behaviour of failure modes such as local buckling, lateral torsional buckling, web-post buckling, shear buckling and Vierendeel bending of beams.

• Steel and Composite Structures
• /
• v.25 no.3
• /
• pp.257-270
• /
• 2017

In this article, an efficient and simple refined theory is proposed for buckling analysis of functionally graded plates by using a new displacement field which includes undetermined integral variables. This theory contains only four unknowns, with is even less than the first shear deformation theory (FSDT). Governing equations are obtained from the principle of virtual works. The closed-form solutions of rectangular plates are determined. Comparison studies are carried out to check the validity of obtained results. The influences of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are examined and discussed.

• International journal of steel structures
• /
• v.18 no.4
• /
• pp.1440-1463
• /
• 2018

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

• Journal of Korean Society of Steel Construction
• /
• v.16 no.1 s.68
• /
• pp.51-60
• /
• 2004

The stress analysis of cold-formed channel section steel beams under transverse load was conducted. The local buckling effect was included in the analysis using effective area concept. The proposed analytical model is capable of predicting accurate normal stress in the beam due to various behaviors including biaxial bending and warping. It was found to be appropriate for predicting stresses as well as deflection in the beam. A finite element model was developed to solve the analytical model.

• Journal of the Korean Society for Precision Engineering
• /
• v.19 no.6
• /
• pp.104-108
• /
• 2002

Sandwich plate structure is widely used in various fields of industry due to its excellent strength and stiffness compared with weight. In this paper, the mechanical behavior of sandwich plate structure with honeycomb core considering buckling is investigated in detail. The focus of the analysis is to evaluate strength and stiffness of the plate structure with critical stress, natural frequency, and mode shapes. The results of this investigation are obtained from detailed finite element analysis for various parameters, such as length, height ratio, and thickness ratio of honeycomb core.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.29 no.3
• /
• pp.153-162
• /
• 1987

A numerical procedure for the analysis of slender arch buckling problems for uniform dead weight is presented in this paper. Such loading changes in the arch profile. The problem is nonlinear. The numerical procedure is limited to an inextensible analysis and to elastic behavior. Based upon a numerical integration technique developed by Newmark for straight beams, a large deflection bending analysis is combined with small deflection buckling routines to formulate the numerical procedure. The numerical procedure is composed of a combination of the numerical integration and successive approximations procedure. The results obtained in this study are as follows : 1.The critical loads obtained in this study coincide with the results by Austin so that the algorithm developed in this study is verified. 2.The numerical results are converged with good precision when the half arch is divided into 10 segments in both Prime and Quadratic section. 3.The critical loads are decreased as the ratios of rise versus span are increased. 4.The critical loads are increased as the moments of inertia at the ends are increased. 5.The critical loads of Prime section are larger than that of Quadratic section under the same profile conditions.