• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.1 s.244
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• pp.76-83
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• 2006

This paper addresses the method for the shape design sensitivity analysis of the buckling load in the continuous elastic body. The sensitivity formula for critical load is analytically derived and expressed in terms of shape variation, based on the continuum formulation of the stability problem. Though the buckling problem is more efficiently solved by the structural elements such as beam and shell, the elastic solids are considered in this paper because the solid elements can be used in general for any kind of structures whether they are thick or thin. The initial stress and buckling analysis is carried out by the commercial analysis code ANSYS. The sensitivity is computed by using the mathematical package MATLAB using the results of ANSYS. Several problems including straight and curved beams under compressive load, ring under pressure load, thin-walled section and bottle shaped column are chosen to illustrate the efficiency of the presented method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.841-846
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• 2006

This paper addresses the method for the shape design sensitivity analysis of the buckling load in the continuous elastic body. The sensitivity formula for critical load is analytically derived and expressed in terms of shape variation, based on the continuum formulation of the stability problem. Though the buckling problem is more efficiently solved by the structural elements such as beam and shell, the elastic solids are considered in this paper because the solid elements can be used in general for any kind of structures whether they are thick or thin. The initial stress and buckling analysis is carried out by the commercial analysis code ANSYS. The sensitivity is computed by using the mathematical package MATLAB using the results of ANSYS. Several problems including straight and curved beams under compressive load, ring under pressure load, thin-walled section are chosen to illustrate the efficiency of the presented method.

• Transactions of the Korean Society of Pressure Vessels and Piping
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• v.19 no.2
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• pp.140-145
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• 2023

When performing stress analysis for a nozzle in nuclear power plants, the nozzle loads should be determined conservatively. Existing stress analysis report of 3-D nozzle loads in nuclear power plants often provide only load magnitude not the sign (direction). Since calculated stress distribution depends on load direction, determining critical load directions for conservative stress analysis is crucial. In this study, an efficient method for determining critical load directions in nozzle loads is proposed. In the proposed method, stresses are firstly calculated using elastic finite element (FE) analysis for the uni-axial load in each direction. Then stress distributions for the multi-axial loads are analytically calculated using the principle of superposition. The calculated stress values are verified by comparing with FE analysis results under multi-axial loading. By using this method, the complex task of determining conservative load directions can be simplified.

• Structural Engineering and Mechanics
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• v.10 no.1
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• pp.67-79
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• 2000

Critical loads and load-carrying capacities for steel scaffolds used as shoring systems were compared using computational and experimental methods in Part I of this paper. In that paper, a simple 2-D model was established for use in evaluating the structural behavior of scaffold-shoring systems. This 2-D model was derived using an incremental finite element analysis (FEA) of a typical complete scaffold-shoring system. Although the simplified model is only two-dimensional, it predicts the critical loads and failure modes of the complete system. The objective of this paper is to present a closed-form solution to the 2-D model. To simplify the analysis, a simpler model was first established to replace the 2-D model. Then, a closed-form solution for the critical loads and failure modes based on this simplified model were derived using a bifurcation (eigenvalue) approach to the elastic-buckling problem. In this closed-form equation, the critical loads are shown to be function of the number of stories, material properties, and section properties of the scaffolds. The critical loads and failure modes obtained from the analytical (closed-form) solution were compared with the results from the 2-D model. The comparisons show that the critical loads from the analytical solution (simplified model) closely match the results from the more complex model, and that the predicted failure modes are nearly identical.

• Structural Engineering and Mechanics
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• v.90 no.4
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• pp.391-401
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• 2024

The present study focuses on the effect of extension-bending coupling on the elastic stability (buckling) of laminated composite plates. These plates will be loaded under uni-axial or bi-axial in-plane mechanical loads, especially in the orthotropic or anti-symmetric cross-angle cases. The main objective is to find a limit where we can approximate the elastic stability behavior of angularly crossed anti-symmetric plates by the simple behavior of specially orthotropic plates. The contribution of my present study is to predict the explicit effect of extension-flexion coupling on the elastic stability of this type of panel. Critically, a parametric study is carried out, involving the search for the critical buckling load as a function of deformation mode, aspect ratio, plate anisotropy ratio and finally the study of the effect of lamination angle and number of layers on the contribution of extension-flexure coupling in terms of plate buckling stability. We use first-order shear deformation theory (FSDT) with a correction factor of 5/6. Simply supported conditions along the four boundaries are adopted where we can develop closed-form analytical solutions obtained by a Navier development.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.291-298
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• 2001

When the compression members have the variable cross sections along their member axes, the determination of the elastic critical loads by classical methods becomes impossible and if possible involves complicated calculation only to obtain the approximate values of critical load. In this paper the elastic critical load coefficients of the tapered members with simply supported ends were determined by finite element method. And then the results were represented by simple algebraic equations of two parameters, a( =taper parameter) and m ( = sectional property parameter). One the basis of algebraic equations, the equivalent moment of inertia concept originally proposed by Bleich for a spesific case, are extended to the general cases.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.3
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• pp.865-873
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• 2013

This paper proposes a theoretical solution of elastic critical buckling load of infinitely long pipelines with non-uniform thickness under external pressure. The non-uniform cross section of pipelines can be considered as corroded or stiffened pipelines so that this paper can be a fundamental research of pipelines that are essential technology for offshore industries. The theoretical solution of pipelines with non-uniform thickness is derived with an assumption that a cylindrical shell under external pressure can be considered as a simple ring. The eigenfunctions are derived to obtain the critical buckling load. The reduced thickness and the reduced range are considered as variables in parametric analysis. The finite element analysis is performed to verify the theoretical solutions and the results of the analytic method and the finite element method are in good agreement.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.244-251
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• 2002

The purpose of this paper is to investigate the stability of tapered columns with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass of rotatory inertia with translational elastic support at the other end. The column model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered columns subjected to a subtangential follower force is solved numerically using the corresponding boundary conditions. And the bisection method is used to calculate the critical divergence/flutter load. After having verified the results of the present study, the frequency and critical divergence/flutter load are presented as functions of various nondimensional system parameters.

• Structural Engineering and Mechanics
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• v.49 no.2
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• pp.273-283
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• 2014

According to deformation features of pre-twisted bar, its elastic bending and torsion buckling equation is developed in the paper. The equation indicates that the bending buckling deformations in two main bending directions are coupled with each other, bending and twist buckling deformations are coupled with each other as well. However, for pre-twisted bar with dual-axis symmetry cross-section, bending buckling deformations are independent to the twist buckling deformation. The research indicates that the elastic torsion buckling load is not related to the pre-twisted angle, and equals to the torsion buckling load of the straight bar. Finite element analysis to pre-twisted bar with different pre-twisted angle is performed, the prediction shows that the assumption of a plane elastic bending buckling deformation curve proposed in previous literature (Shadnam and Abbasnia 2002) may not be accurate, and the curve deviates more from a plane with increasing of the pre-twisting angle. Finally, the parameters analysis is carried out to obtain the relationships between elastic bending buckling critical capacity, the effect of different pre-twisted angles and bending rigidity ratios are studied. The numerical results show that the existence of the pre-twisted angle leads to "resistance" effect of the stronger axis on buckling deformation, and enhances the elastic bending buckling critical capacity. It is noted that the "resistance" is getting stronger and the elastic buckling capacity is higher as the cross section bending rigidity ratio increases.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.169-184
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• 2006

A close form solution of the maximum deflection for cracked columns with rectangular cross-sections was developed and thus the elastic buckling behavior and ultimate bearing capacity were studied analytically. First, taking into account the effect of the crack in the potential energy of elastic systems, a trigonometric series solution for the elastic deflection equation of an arbitrary crack position was derived by use of the Rayleigh-Ritz energy method and an analytical expression of the maximum deflection was obtained. By comparison with the rotational spring model (Okamura et al. 1969) and the equivalent stiffness method (Sinha et al. 2002), the advantages of the present solution are that there are few assumed conditions and the effect of axial compression on crack closure was considered. Second, based on the above solutions, the equilibrium paths of the elastic buckling were analytically described for cracked columns subjected to both axial and eccentric compressive load. Finally, as examples, the influence of crack depth, load eccentricity and column slenderness on the elastic buckling behavior was investigated in the case of a rectangular column with a single-edge crack. The relationship of the load capacity of the column with respect to crack depth and eccentricity or slenderness was also illustrated. The analytical and numerical results from the examples show that there are three kinds of collapse mechanisms for the various states of cracking, eccentricity and slenderness. These are the bifurcation for axial compression, the limit point instability for the condition of the deeper crack and lighter eccentricity and the fracture for higher eccentricity. As a result, the conception of critical transition eccentricity $(e/h)_c$, from limit-point buckling to fracture failure, was proposed and the critical values of $(e/h)_c$ were numerically determined for various eccentricities, crack depths and slenderness.