• Journal of Mechanical Science and Technology
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• v.17 no.1
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• pp.85-96
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• 2003

In the present investigation, the nonlinear dynamic buckling of a curved plate subjected to sinusoidal loading is examined. By the theoretical analyses, a highly nonlinear snap-through motion of a clamped-free-clamped-free plate and its effect on the overall vibration response are investigated. The problem is reduced to that of a single degree of freedom system with the Rayleigh-Ritz procedure. The resulting nonlinear governing equation is solved using Runge-Kutta (RK-4) numerical integration method. The snap-through boundaries, which vary with different damping coefficient and linear circular frequency of the flat plate are studied and given in terms of force and displacement. The relationships between static and dynamic responses at the start of a snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. 1) small oscillation about the buckled position-softening spring type motion, 2) chaotic motion of intermittent snap-through, and 3) large oscillation of continuous snap-through motion crossing the two buckled positions-hardening spring type. The responses of buckled plate were found to be greatly affected by the snap-through motion. Therefore, better understanding of the snap-through motion is needed to predict the full dynamic response of a curved plate.

• Computational Structural Engineering
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• v.9 no.3
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• pp.107-114
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• 1996

The performance for the algorithm of the arc length method has been examined in terms of the choice of the tangential stiffness matrix through the analysis for the snap buckling phenomenon of the arch beam. The curved beam element with 2 nodes including shear effect has been formed by strain element technique and then it has been used in this nonlinear analysis. Snap-through characteristics has been examined with respect to the ratios of the arch beam length to hight.

• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.13-22
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• 2024

The nonlinear snap-through buckling of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) curved tubes is analytically investigated in this research. It is assumed that the FG-CNTRC curved tube is supported on a three-parameter nonlinear elastic foundation and is subjected to the uniformly distributed pressure and thermal loads. Properties of the curved nanocomposite tube are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite tube are temperature-dependent. The governing equations of the curved tube are obtained using a higher-order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the tube. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved tube. Equations of motion are solved using the two-step perturbation technique for nanocomposite curved tubes which are simply-supported and clamped. Closed-form expressions are provided to estimate the snap-buckling resistance of FG-CNTRC curved pipes rested on nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of the distribution pattern and volume fraction of CNTs, thermal field, foundation stiffnesses, and geometrical parameters on the instability of the curved nanocomposite tube.

• Structural Engineering and Mechanics
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• v.32 no.4
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• pp.501-516
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• 2009

This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on Kirchhoff's rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance ($10^{-5}$). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.3
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• pp.168-174
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• 2012

This paper presents a bending propagating actuation using SMA (Shape Memory Alloy) spring for an effective shape transition of a flytrap-inspired soft morphing structure. The flytrap-inspired soft morphing structure is made from unsymmetric CFRP (Carbon Fiber Reinforced Prepreg) structure which shows bi-stability and snap-through phenomenon. For a thin and large curved bistable CFRP structure, SMA spring is more acceptable than SMA wire and piezoelectric actuator which used in previous investigations. A bending propagating actuation is proposed which can induce snap-through of the bi-stable CFRP structure effectively. From this research, effective shape transition of soft morphing structure is possible.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.277-284
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• 2003

One of important problem, in large space structure, is to overcome the self-weight of roof structure. This problem can be solved with using tension members effectively. Thus the rapid progress of hybrid structure, that makes effective use of the means of settling, has a good effect on realizing the large space. These systems of hybrid structure have the advantages of light weight and its own internal redundancy, but are occurred unstable phenomenon such as bifurcation or snap-through buckling, when the load level is come to the critical point. Among the hybrid structure, cable dome is shown the strong nonlinearity of unstable phenomenon in accordance with the external force. Therefore, the purpose of this study is to analyze and verify comparatively the unstable phenomenon of the Geiger and Flower type cable dome structures under axismmetric load.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.2
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• pp.481-487
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• 1996

A snapping-beam microswitch has been designed, fabricated and tested. From a design analysis, necessary and sufficient conditions for a snap-through switching fouction have been derived for a clamped shallow beam. The necessary condition has resulted in a geometric relation, in which the ratio of beam thickness to initial beam deflection plays a key role in the snapping ability. The sufficient condition for the snapping action has been obtained as a function of the inertia force due to applied acceleration, and the electrostatic force, adjustable by an inter-electrode voltage. For experimental investigations, a set of microbeams of silicon dioxide/$P^+$silicon bimorphs have been fabricated. Geometric size and mechanical behavior of each material film have been measured from on-chip test structures. Estimated and measured characteristics of the fabricated devices are compared.

• Steel and Composite Structures
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• v.27 no.1
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• pp.13-25
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• 2018

The main objective of this study is to develop a dual approach for geometrically nonlinear finite element analysis of plane truss structures. The geometric nonlinearity is considered using the Total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to displacement-type constraints. The proposed method can fully trace the whole equilibrium path of geometrically nonlinear plane truss structures not only before the limit point but also after it. No stiffness matrix is used in the main approach and the solution is acquired only based on the direct classical stress-strain formulations. As a result, produced errors caused by linearization and approximation of the main equilibrium equation will be eliminated. The suggested algorithm can predict both pre- and post-buckling behavior of the steel plane truss structures as well as any arbitrary point of equilibrium path. In addition, an equilibrium path with multiple limit points and snap-back phenomenon can be followed in this approach. To demonstrate the accuracy, efficiency and robustness of the proposed procedure, numerical results of the suggested approach are compared with theoretical solution, modified arc-length method, and those of reported in the literature.

• Journal of Korean Association for Spatial Structures
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• v.3 no.1 s.7
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• pp.87-97
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• 2003

The structural system that discreterized from continuous shells is frequently used to make a large space structures. As well these structures show the unstable phenomena when a load level over the limit load, and snap-through and bifurcation are most well known of it. For the collapse mechanism, rise-span ratio, element stiffness and load mode are main factor, which it give an effect to unstable behavior. In our real situation, most structures have semi-rigid joint that has middle characteristic between pin and rigid joint. So the knowledge of semi-rigid joint is very important problem of stable large space structure. And the instability phenemena of framed space structures show a strong non-linearity and very sensitive behavior according to the joint rigidity For this reason In this study, we are investigating to unstable problem of framed structure with semi-rigidity and to grasp the nonlinear instability behavior that make the fundamental collapse mechanism of the large space frame structures with semi-rigid joint, by proposed the numerical analysis method. Using the incremental stiffness matrix in chapter 2, we study instability of space structures.

• Journal of Korean Association for Spatial Structures
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• v.4 no.3 s.13
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• pp.65-75
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• 2004

A shell structure, having a curvature with a curved surface, is an extremely efficient mechanical creation regard to the external load. A basic structural resistance mechanism is the structural system, which is resisted the out-of-plane direction load by in-plane forces using the structure's curvature. Therefore, it has a merit to make thin and lightweight large spacial structures using minimum materials. Among the large spare structural system, the rapid development of the membrane structures, cable structures and the hybrid structures are watched recently. But, this kind of structural system shows the unstable phenomenon by snap-through or bifurcation according to the shape of structure, and the understanding of the collapse mechanism by this phenomenon is very important to the design process. In this study, I investigated the unstable characteristics of the Geiger-type, Zetlin-type and flower-type hybrid cable dome structures, which is the lightweight hybrid structures using compression and tension elements continuously, according to the difference of structural system.