• Steel and Composite Structures
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• v.45 no.3
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• pp.349-367
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• 2022

In this research, an approach combining a semi-analytical method and an analytical method is presented to investigate the static and dynamic post-buckling behavior of the sandwich functionally graded (FG) porous cylindrical shells exposed to external pressure. The sandwich cylindrical shell considered is composed of a viscoelastic core and two FG porous (FGP) face layers. The viscoelastic core is made of Kelvin-Voigt-type material. The material properties of the FG porous face layer are considered continuous through each face thickness according to a porosity coefficient and a volume fraction index. Two types of sandwich FG porous viscoelastic cylindrical shells named Type A and Type B are considered in the research. Type A shell has the porosity evenly distributed across the thickness direction, and Type B has the porosity unevenly distributes across the thickness direction. The FG face layers are considered in two cases: outside metal surface, inside ceramic surface (OMS-ICS), and inside metal surface, outside ceramic surface (IMS-OCS). According to Donnell shell theory, von-Karman equation, and Galerkin's method, a discretized nonlinear governing equation is derived for analyzing the behavior of the shells. The explicit expressions for static and dynamic critical buckling loading are thus developed. To study the dynamic buckling of the shells, the governing equation is examined via a numerical approach implementing the fourth-order Runge-Kutta method. With a procedure presented by Budiansky-Roth, the critical load for dynamic post-buckling is obtained. The effects of various parameters, such as material and geometrical parameters, on the post-buckling behaviors are investigated.

• Proceeding of KASS Symposium
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• 2005.05a
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• pp.154-160
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• 2005

The present study is concerned with the application of dynamic relaxation method in the investigation of the large deflection behavior of spatial structures. The dynamic relaxation do not require the computation or formulation of any tangent stiffness matrix. The convergence to the solution is achieved by using only vectorial quantities and no stiffness matrix is required in its overall assembled form. In an effort to evaluate the merits of the methods, extensive numerical studies were carried out on a number of selected structural systems. The advantages of using dynamic relaxation methods, in tracing the post-buckling behavior of spatial structures, are demonstrated.

• Advances in nano research
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• v.17 no.2
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• pp.95-107
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• 2024

In this article, the semi-analytical method was used to analyze the nonlinear dynamic stability and vibration analysis of sandwich shallow spherical shells (SSSS). The SSSS was considered as functionally graded carbon nanotube-reinforced composites (FG-CNTRC) with three new patterns of FG-CNTRC. The governing equation was obtained and discretized utilizing the Galerkin method by implementing the von Kármán-Donnell nonlinear strain-displacement relations. The nonlinear dynamic stability was analyzed by means of the fourth-order Runge-Kutta method. Then the Budiansky-Roth criterion was employed to obtain the critical load for the dynamic post-buckling. The approximate solution for the deflection was represented by suitable mode functions, which consisted of the three modes of transverse nonlinear oscillations, including one symmetrically and two asymmetrical mode shapes. The influences of various geometrical characteristics and material parameters were studied on the nonlinear dynamic stability and vibration response. The results showed that the order of layers had a significant influence on the amplitude of vibration and critical dynamic buckling load.

• Structural Engineering and Mechanics
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• v.37 no.5
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• pp.509-527
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• 2011

The paper investigates the dynamic buckling behaviour of a laminated composite stiffened cylindrical shell using the commercial finite element code ABAQUS. The numerical model of the composite shell is validated by static tests. In particular, the experimental collapse test is numerically simulated by a quasi static analysis carried out by both ABAQUS/Standard and ABAQUS/Explicit. The behaviour in the post-buckling field and the collapse load obtained by the analyses are close to the experimental data. The validated model is then used to study the dynamic buckling behaviour with ABAQUS/Explicit. The effects of the loading magnitude and of the loading duration are investigated, implementing in the analysis also first-ply failure criteria. It is observed that the dynamic buckling load is highly affected by the loading duration.

• 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.

• Proceeding of KASS Symposium
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• 2006.05a
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• pp.58-65
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• 2006

The present study is concerned with the application of dynamic relaxation method in the investigation of the large deflection behavior of spatial structures. The dynamic relaxation do not require the computation or formulation of any tangent stiffness matrix. The convergence to the solution is achieved by using only vectorial quantities and no stiffness matrix is required in its overall assembled form. In an effort to evaluate the merits of the methods, extensive numerical studies were carried out on a number of selected structural systems. The advantages of using dynamic relaxation methods, in tracing the post-buckling behavior of spatial structures, are demonstrated.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.709-725
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• 2006

In this paper the buckling and post-buckling behavior of slender bars under self-weight are studied. In order to study the post-buckling behavior of the bar, a geometrically exact formulation for the non-linear analysis of uni-directional structural elements is presented, considering arbitrary load distribution and boundary conditions. From this formulation one obtains a set of first-order coupled nonlinear equations which, together with the boundary conditions at the bar ends, form a two-point boundary value problem. This problem is solved by the simultaneous use of the Runge-Kutta integration scheme and the Newton-Raphson method. By virtue of a continuation algorithm, accurate solutions can be obtained for a variety of stability problems exhibiting either limit point or bifurcational-type buckling. Using this formulation, a detailed parametric analysis is conducted in order to study the buckling and post-buckling behavior of slender bars under self-weight, including the influence of boundary conditions on the stability and large deflection behavior of the bar. In order to evaluate the quality and accuracy of the results, an experimental analysis was conducted considering a clamped-free thin-walled metal bar. As this kind of structure presents a high index of slenderness, its answers could be affected by the introduction of conventional sensors. In this paper, an experimental methodology was developed, allowing the measurement of static or dynamic displacements without making contact with the structure, using digital image processing techniques. The proposed experimental procedure can be used to a wide class of problems involving large deflections and deformations. The experimental buckling and post-buckling behavior compared favorably with the theoretical and numerical results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.175-182
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• 2005

The present study is concerned with the application of dynamic relaxation method in the investigation of the large deflection behavior of spatial structures. This numerical algorithm do not require the computation or formulation of any tangent stiffness matrix. The convergence to the solution is achieved by using only vectorial quantities and no stiffness matrix is required in its overall assembled form. In an effort to evaluate the merits of the methods, extensive numerical studies were carried out on a number of selected structural systems. The advantages of using dynamic relaxation methods, in tracing the post-buckling behavior of spatial structures, are demonstrated.

• Earthquakes and Structures
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• v.16 no.5
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• pp.589-599
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• 2019

Conventional buckling restrained braces used in concentrically braced frames are expected to yield in both tension and compression without major degradation of capacity under severe seismic ground motions. One of the weakness points of a standard buckling restrained braced frame is the low post-yield stiffness and thus large residual deformation under moderate to severe ground motions. This phenomenon can be attributed to low post-yield stiffness of core member in a BRB. This paper introduces a multi-core buckling restrained brace. The multi-core term arises from the use of more than one core component with different steel materials, including high-performance steel (HPS-70W) and stainless steel (304L) with high strain hardening properties. Nonlinear dynamic time history analyses were conducted on variety of diagonally braced frames with different heights, in order to compare the seismic performance of regular and multi-core buckling restrained braced frames. The results exhibited that the proposed multi-core buckling restrained braces reduce inter-story and especially residual drift demands in BRBFs. In addition, the results of seismic fragility analysis designated that the probability of exceedance of residual drifts in multi-core buckling restrained braced frames is significantly lower in comparison to standard BRBFs.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.67-75
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• 1990

A geometrically nonlinear analysis procedure including the damping effects is presented for the investigation of the dynamic post-divergence and post-flutter behavior of a non-conservative system. The dynamic nonlinear analysis of plane frame structure subjected to conservative and non-conservative forces is carried out by solving the equations of motion using Newmark method. Numerical results are presented to demonstrate the effects of the internal and external damping forces in the conservative and non-conservative systems.