EFFECT OF SUPPORT STIFFNESS ON STABILITY OF SHALLOW ARCHES

2010 ◽  
Vol 10 (05) ◽  
pp. 1099-1110 ◽  
Author(s):  
JIANGUO CAI ◽  
JIAN FENG

The nonlinear behavior and in-plane stability of parabolic shallow arches with elastic rotational supports are investigated. A central concentrated load is applied to create the compression in the supports. Nonlinear buckling analysis based on the virtual work formulation is carried out to obtain the critical load for both symmetric snap-through buckling and anti-symmetric bifurcation buckling. It is found that the effect of rotational stiffness of the elastic supports on the critical loads is significant. The critical load increases as either the initial stiffness coefficient α or the stiffening rate β increases. The effect of the stiffening rate β on the critical loads decreases, as the initial stiffness coefficient α increases. In addition, the influence of rotational stiffness on the bifurcation buckling is larger than that on the snap-through buckling. The limit of the geometric parameter λ between the bifurcation and snap-through buckling modes also increases with the increase in the stiffening rate β. In addition, the snap-through buckling mode governs the buckling of the arch with larger stiffening rates.

2016 ◽  
Vol 22 (12) ◽  
pp. 2240-2252 ◽  
Author(s):  
Jianguo Cai ◽  
Xiaowei Deng ◽  
Jian Feng

The behavior of a bistable strut for variable geometry structures was investigated in this paper. A three-hinged arch subjected to a central concentrated load was used to study the effect of symmetric imperfections on the behavior of the bistable strut. Based on a nonlinear strain–displacement relationship, the virtual work principle was adopted to establish both the pre-buckling and buckling nonlinear equilibrium equations for the symmetric snap-through buckling mode. Then the critical load for symmetric snap-through buckling was obtained. The results show that the axial force is in compression before the arch is buckled, but it becomes in tension after buckling. Thus, the previous formulas cannot be used for the analysis of post-buckling behavior of three-hinged shallow arches. Then, the principle of virtual work was also used to establish the post-buckling equilibrium equations of the arch in the horizontal and vertical directions as well as the static boundary conditions, which are very important for bistable struts.


2014 ◽  
Vol 989-994 ◽  
pp. 2859-2864
Author(s):  
Jing Zhang ◽  
Li Sui ◽  
Xu Hong Guo ◽  
Guo Hua Liu

Compression deformation will cause a micro-spring to buckle, and structural parameters, constraint conditions and structural forms of a micro-spring will affect its critical load and buckling mode. In order to study the influence on the micro-spring’s stability caused by structural forms and find a structure to improve its critical load in the end, this paper designs a new kind of parallel micro-springs, which consists of two same-structured S-shaped planar micro-springs. We have carried on eigenvalue buckling analysis on the parallel micro-spring by software ANSYS, and have gotten its six orders’ buckling mode. Because the critical load of the parallel micro-spring may change with the length of the beam connecting the two sub-springs, this paper studies the effect of the beam’s length on the parallel micro-spring’s critical loads and buckling mode. From comparing the analysis results between parallel micro-spring and single micro-spring with same stiffness, this paper concludes the stability’s degree of improvement.


1968 ◽  
Vol 35 (2) ◽  
pp. 289-296 ◽  
Author(s):  
N. C. Huang ◽  
W. Nachbar

Dynamic snap-through or dynamic buckling of imperfect viscoelastic shallow arches with hinged ends is considered under step loads of infinite duration. Attention is principally devoted to the influence both of small imperfections and of small amounts of damping, acting together, on the critical loads. For the problem considered, the Voigt model is used for viscoelasticity, the deflection is represented by the first two harmonic modes, and imperfections have the shape of the second (antisymmetric) mode. Results obtained by numerical integration of the differential equations show that the critical load exhibits a jump discontinuity in the limit for vanishing imperfection. Critical loads for slightly imperfect and elastic (inviscid) arches are slightly higher than those from the saddle-point formula of Hoff and Bruce [1, p. 276], confirming that the formula gives a lower bound on the critical load. However, critical loads for arches with slight imperfection and slight viscosity are considerably higher than for the slightly imperfect elastic arches. Another closed-form expression is shown to be in good agreement with these results. For finite amounts of viscosity, the critical loads tend rapidly to the values obtained for infinite viscosity, which are the same as the critical loads for quasi-static buckling. Apart from the jump discontinuity at zero, the critical load for any viscosity decreases continuously and monotonically with imperfection.


Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.


Author(s):  
M. Bateni ◽  
M. R. Eslami

This work presents a closed form investigation on the effect of temperature gradient on the buckling resistance of functionally graded material (FGM) shallow arches. The constituents are assumed to vary smoothly through the thickness of the arch according to the power law distribution and they are assumed to be temperature dependent. The arches subjected to the both uniform distributed radial load and central concentrated load and both boundary supports are supposed to be pinned. The temperature field is approximated by one-dimensional linear gradient through the thickness of the arch and the displacement field approximated by classical arches model. Also, Donnell type kinematics is utilized to extract the suitable strain-displacement relations for shallow arches. Adjacent equilibrium criterion is used to buckling analysis, and, critical bifurcation load is obtain in the complete presence of pre-buckling deformations. Results discloses the usefulness of using the FGM shallow arches in thermal environment because the temperature gradient enhances the buckling resistance of these structures when they are subjected to a lateral mechanical load.


2018 ◽  
Author(s):  
Paul A. Makar ◽  
Ayodeji Akingunola ◽  
Julian Aherne ◽  
Amanda S. Cole ◽  
Yayne-abeba Aklilu ◽  
...  

Abstract. Estimates of potential harmful effects to ecosystems in the Canadian provinces of Alberta and Saskatchewan due to acidifying deposition were calculated, using a one year simulation of a high resolution implementation of the Global Environmental Multiscale – Modelling Air-quality and Chemistry (GEM-MACH) model, and estimates of aquatic and terrestrial ecosystem critical loads. The model simulation was evaluated against two different sources of deposition data; total deposition in precipitation and total deposition to snowpack in the vicinity of the Athabasca oil sands. The model captured much of the variability of observed ions in wet deposition in precipitation (observed versus model sulphur, nitrogen and base cation R2 values of 0.90, 0.76 and 0.72, respectively), while being biased high for sulphur deposition, and low for nitrogen and base cations (slopes 2.2, 0.89 and 0.40, respectively). Aircraft-observation-based estimates of fugitive dust emissions, shown to be a factor of ten higher than reported values (Zhang et al., 2017), were used to estimate the impact of increased levels of fugitive dust on model results. Model comparisons to open snowpack observations were shown to be biased high, but in reasonable agreement for sulphur deposition when observations were corrected to account for throughfall in needleleaf forests. The model-observation relationships for precipitation deposition data, along with the expected effects of increased (unreported) base cation emissions, were used to provide a simple observation-based correction to model deposition fields. Base cation deposition was estimated using published observations of base cation fractions in surface collected particles (Wang et al., 2015). Both original and observation-corrected model estimates of sulphur, nitrogen and base cation deposition were used in conjunction with critical load data created using the NEG-ECP (2001) and CLRTAP (2004, 2016, 2017) protocols for critical loads, using variations on the Simple Mass Balance model for forest and terrestrial ecosystems, and the Steady State Water Chemistry and the First-order Acidity Balance models for aquatic ecosystems. Potential ecosystem damage at 2013/14 emissions and deposition levels was predicted for regions within each of the ecosystem critical load datasets examined here. The spatial extent of the regions in exceedance of critical loads varied between 1 × 104 and 3.3 × 105 km2, for the more conservative observation-corrected estimates of deposition, with the variation dependant on the ecosystem and critical load protocol. The larger estimates (for aquatic ecosystems) represent a substantial fraction of the area of the provinces examined. Base cation deposition was shown to have a neutralizing effect on acidifying deposition, and the use of the aircraft and precipitation observation-based corrections to base cation deposition resulted in reasonable agreement with snowpack data collected in the oil sands area. However, critical load exceedances calculated using both observations and observation-corrected deposition suggest that the neutralization effect is limited in spatial extent, decreasing rapidly with distance from emissions sources, due to the rapid deposition of emitted primary particles dust particles as a function of their size.


Mechanika ◽  
2020 ◽  
Vol 26 (5) ◽  
Author(s):  
Kai QIN ◽  
Jingyuan LI ◽  
Mengsha LIU ◽  
Jinsan JU

The dynamic in-plane instability process of extreme point type for pin-ended arches when a central radial load applied suddenly with infinite duration is analyzed with finite element method in this study. The state of arch can be determined by the crown’s vertical displacement varied with time and the critical load can be obtained by repeating trial-calculation. When the arch structure reaches the dynamically stable critical state, the kinetic energy of the structure is very small or even zero. The dynamic critical load of elastic arch calculated with the theoretical analysis method which is based on energy principle is proved accuracy enough by comparing with the finite element calculation results and the percentage of the differences between them are no more than 4.5 %. The maximal elastic strain energy is certain for the elastic-plastic arch in certain geometry under both a sudden load and static load. The maximal elastic strain energy in static calculation can be used in determining the state of the elastic-plastic arch under dynamic sudden loads applied and this method is more accurate which errors won’t exceed 3.5 %. The accuracy of dynamic critical load calculation method for elastic arch is verified by numerical calculation in this study, and based on the characteristic of elastic strain energy in critical state, a method for determining the stability of elastic-plastic arch is presented.


2000 ◽  
Vol 4 (1) ◽  
pp. 125-140 ◽  
Author(s):  
C. Curtis ◽  
T. Allott ◽  
J. Hall ◽  
R. Harriman ◽  
R. Helliwell ◽  
...  

Abstract. The critical loads approach is widely used within Europe to assess the impacts of acid deposition on terrestrial and freshwater ecosystems. Recent work in Great Britain has focused on the national application of the First-order Acidity Balance (FAB) model to a freshwaters dataset of 1470 lake and stream water chemistry samples from sites across Britain which were selected to represent the most sensitive water bodies in their corresponding 10 km grid square. A ``Critical Load Function" generated for each site is compared with the deposition load of S and N at the time of water chemistry sampling. The model predicts that when catchment processes reach steady-state with these deposition levels, increases in nitrate leaching will depress acid neutralizing capacity (ANC) below the critical threshold of 0 μeql-1 at more than a quarter of the sites sampled, i.e. the critical load of acid deposition is exceeded at these sites. The critical load exceedances are generally found in upland regions of high deposition where acidification has been previously recognised, but critical loads in large areas of western Scotland are also exceeded where little biological evidence of acidification has yet been found. There is a regional variation in the deposition reduction requirements for protection of the sampled sites. The FAB model indicates that in Scotland, most of the sampled sites could be protected by sufficiently large reductions in S deposition alone. In the English and Welsh uplands, both S and N deposition must be reduced to protect the sites. Current international commitments to reduce S deposition throughout Europe will therefore be insufficient to protect the most sensitive freshwaters in England and Wales. Keywords: critical loads; acidification; nitrate; FAB model; acid deposition


1984 ◽  
Vol 51 (3) ◽  
pp. 531-535 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson

In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.


Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.


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