• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1211-1221
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• 2002

A shape optimization of stiffener was conducted to increase buckling load or failure load with stiffened laminated composite panel of I-type under compression loading. Design variables are cap length, web length, and/or thickness under the constraint of volume constancy. The objective function is buckling load and failure load of post-buckling based on Tsai-Hill theory using ABAQUS 5.8 for analysis and Optimizer on Broydon-Fletcher Goldfarb-Sharno Method and Augmented Lagrange Multiplier Method. The effects of relative length of a web and a cap of stiffener on buckling load and failure load of post-buckling were investigated with the results of optimum design.

• Geomechanics and Engineering
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• v.31 no.3
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• pp.329-337
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• 2022

In this paper, the thermal post-buckling characteristics of functionally graded (FG) pipes with initial geometric imperfection are studied. Considering the influence of initial geometric defects, temperature and geometric nonlinearity, Euler-Lagrange principle is used to derive the nonlinear governing equations of the FG pipes. Considering three different boundary conditions, the two-step perturbation method is used to solve the nonlinear governing equations, and the expressions of thermal post-buckling responses are also obtained. Finally, the correctness of this paper is verified by numerical analyses, and the effects of initial geometric defects, functional graded index, elastic foundation, porosity, thickness of pipe and boundary conditions on thermal post-buckling response are analyzed. It is found that, bifurcation buckling exists for the pipes without initial geometric imperfection. In contrast, there is no bifurcation buckling phenomenon for the pipes with initial geometric imperfection. Meanwhile, the elastic stiffness can significantly improve thermal post-buckling load and thermal post-buckling strength. The larger the porosity, the greater the thermal buckling load and the thermal buckling strength.

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

• Steel and Composite Structures
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• v.52 no.1
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• pp.89-107
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• 2024

This article focuses on the static and dynamic analysis and optimization of an anisogrid lattice plate subjected to axial compressive load with simply supported boundary conditions. The lattice plate includes diagonal and transverse ribs and is modeled as an orthotropic plate with effective stiffness properties. The study employs the first-order shear deformation theory and the Ritz method with a Legendre approximation function. In the realm of optimization, the Non-dominated Sorting Genetic Algorithm-II is utilized as an evolutionary multi-objective algorithm to optimize. The research findings are validated through finite element analysis. Notably, this study addresses the less-explored areas of optimizing the geometric parameters of the plate by maximizing the buckling load and natural frequency while minimizing mass. Furthermore, this study attempts to fill the gap related to the analysis of the post-buckling behavior of lattice plates, which has been conspicuously overlooked in previous research. This has been accomplished by conducting nonlinear analyses and scrutinizing post-buckling diagrams of this type of lattice structure. The efficacy of the continuous methods for analyzing the natural frequency, buckling, and post-buckling of these lattice plates demonstrates that while a degree of accuracy is compromised, it provides a significant amount of computational efficiency.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.191-203
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• 2010

To investigate the critical buckling load and post-buckling behavior of an axially loaded pile entirely embedded in soil, the non-linear large deflection differential equation for a pinned pile, based on the Winkler-model and the discretionary distribution function of the foundation coefficient along pile shaft, was established by energy method. Assuming that the deflection function was a power series of some perturbation parameter according to the boundary condition and load in the pile, the non-linear large deflection differential equation was transformed to a series of linear differential equations by using perturbation approach. By taking the perturbation parameter at middle deflection, the higher-order asymptotic solution of load-deflection was then found. Effect of ratios of soil depth to pile length, and ratios of pile stiffness to soil stiffness on the critical buckling load and performance of piles (entirely embedded and partially embedded) after flexural buckling were analyzed. Results show that the buckling load capacity increases as the ratios of pile stiffness to soil stiffness increasing. The pile performance will be more stable when ratios of soil depth to pile length, and soil stiffness to pile stiffness decrease.

• Steel and Composite Structures
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• v.31 no.3
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• pp.243-259
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• 2019

This study deals with the nonlinear static analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) truncated conical shells subjected to axial load based on the classical shell theory. Detailed studies for both nonlinear buckling and post-buckling behavior of truncated conical shells. The truncated conical shells are reinforced by single-walled carbon nanotubes which alter according to linear functions of the shell thickness. The nonlinear equations are solved by both the Airy stress function and Galerkin method based on the classical shell theory. In numerical results, the influences of various types of distribution and volume fractions of carbon nanotubes, geometrical parameters, elastic foundations on the nonlinear buckling and post-buckling behavior of FG-CNTRC truncated conical shells are presented. The proposed results are validated by comparing with other authors.

• Journal of Korean Society of Steel Construction
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• v.15 no.3
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• pp.313-320
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• 2003

The governing equation of the post-buckling of shear-deformable uniform columns under a combined load consisting of a uniformly distributed axial load and a concentrated load at a free end was derived and the post-buckling analysis was investigated by using differential transformation. The loads were obtained for various end-slopes. The results obtained by the present method agree well with published results. In this paper, the differential transformation method was illustrated through its application to the non-linear differential equation of the post-buckling. It is expected that applications of the method to more challenging problems will are expected follow in future to ensue.

• Architectural research
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• v.8 no.1
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• pp.47-56
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• 2006

In this research, the analysis of post-buckling behavior of tapered columns has been performed under a combined load of uniformly distributed axial load along the length and concentric axial load at free end by solving the nonlinear differential equation with the differential transformation technique. The buckling load at various slopes at free end of column is calculated and the results of the analysis using the differential transformation technique is verified with those of previous studies. It is also shown through the results that the buckling load of sinusoidal tapered columns is largest, the linear is second largest, and the parabolic is small in the all ranges of slopes at free end and the deflection of parabolic tapered columns in the x coordinates is largest, the sinusoidal is second largest, and the linear is smallest in the range of slope 0 to 140 degrees at free end. However, when the range of the slope is 160 to 176 degrees at the free end, the deflection of sinusoidal tapered columns in the x coordinates is largest, the linear is second largest, and the parabolic is smallest. In addition, for the linear tapered column, the buckling load increases along with the flexural stiffness ratio. Also, for the parabolic and the sinusoidal tapered column, the buckling loads increase and decrease as the flexural ratios increase in the range of flexural stiffness ratio n = 1.0 to n = 2.0. Through this research, it is verified that the differential transformation technique can be applied to solve the nonlinear differential equation problems, such as analysis of post-buckling behavior of tapered columns. It is also expected that the differential transformation technique apply to various more complicated problems in future.

• Advances in nano research
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• v.7 no.6
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• pp.405-417
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• 2019

This research is devoted to study post-buckling analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) micro plate with cut out subjected to magnetic field and resting on elastic medium. The basic formulation of plate is based on first order shear deformation theory (FSDT) and the material properties of FG-CNTRCs are presumed to be changed through the thickness direction, and are assumed based on rule of mixture; moreover, nonlocal Eringen's theory is applied to consider the size-dependent effect. It is considered that the system is embedded in elastic medium and subjected to longitudinal magnetic field. Energy approach, domain decomposition and Rayleigh-Ritz methods in conjunction with Newton-Raphson iterative technique are employed to trace the post-buckling paths of FG-CNTRC micro cut out plate. The influence of some important parameters such as small scale effect, cut out dimension, different types of FG distributions of CNTs, volume fraction of CNTs, aspect ratio of plate, magnitude of magnetic field, elastic medium and biaxial load on the post-buckling behavior of system are calculated. With respect to results, it is concluded that the aspect ratio and length of square cut out have negative effect on post-buckling response of micro composite plate. Furthermore, existence of CNTs in system causes improvement in the post-buckling behavior of plate and different distributions of CNTs in plate have diverse response. Meanwhile, nonlocal parameter and biaxial compression load on the plate has negative effect on post-buckling response. In addition, imposing magnetic field increases the post-buckling load of the microstructure.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.935-940
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• 2006

Numerical methods are developed for solving the elastica and buckling load of cantilever column with constant volume, subjected to a compressive end load. The linear, parabolic and sinusoidal tapers with the regular polygon cross-sections are considered, whose material volume and span length are always held constant. The differential equations governing the elastica of buckled column are derived. The Runge-Kutta method is used to integrate the differential equations, and the Regula-Falsi method is used to determine the horizontal deflection at free end and the buckling load, respectively. The numerical methods developed herein for computing the elastica and the buckling loads of the columns are found to be efficient and reliable.