One-Way Buckling of Circular Rings Confined Within a Rigid Boundary

1995 ◽  
Vol 117 (2) ◽  
pp. 162-169 ◽  
Author(s):  
C. Sun ◽  
W. J. D. Shaw ◽  
A. M. Vinogradov
Keyword(s):  
Critical Condition ◽  
Experimental Approach ◽  
Equilibrium Analysis ◽  
Initial Deflection ◽  
Rigid Boundary ◽  
Geometric Imperfections ◽  
Circular Rings ◽  
Initial Geometric Imperfections ◽  
The Stability ◽  
Theoretical Results

The stability of a ring confined by a rigid boundary, subjected to circumferential end loads, is investigated both theoretically and experimentally. The effect of initial geometric imperfections on the buckling load is determined by assuming an initial deflection configuration as a simple sine form and the critical condition was derived from equilibrium analysis. An experimental approach was designed to verify the analytical results. Comparison with other theoretical results are also made.

scholarly journals Numerical analysis of stability of the stiffened plates subjected aliquant critical loads

2020 ◽  
Vol 16 (1) ◽  
pp. 54-61
Author(s):  
Gaik A. Manuylov ◽  
Sergey B. Kositsyn ◽  
Irina E. Grudtsyna
Keyword(s):  
Numerical Analysis ◽  
Critical Loads ◽  
Geometric Nonlinearity ◽  
Compressive Load ◽  
Stiffened Plates ◽  
Geometric Imperfections ◽  
Initial Geometric Imperfections ◽  
Analysis Of Stability ◽  
The Stability

The aim of the work is to research the precritical and postcritical equilibrium of the stiffened plates subjected aliquant critical loads. Methods. The finiteelement complex MSC PATRAN - NASTRAN was used in the paper. To simulate the plates, flat four-node elements were used. Calculations taking into account geometric nonlinearity were carried out. The material of the shells was considered absolutely elastic. Results. A technique has been developed to study the stability of reinforced longitudinally compressed plates; the critical forces of the stiffened plates of various thicknesses had been calculated. Graphs of deflections dependences on the value of the compressive load had been constructed. The influence of initial geometric imperfections on the value of the critical loads for stiffened plates has been investigated.

scholarly journals Numerical modelingof a composite section element from thin-walled profiles taking into account the initial geometric imperfections

2020 ◽  
Vol 17 (1) ◽  
pp. 82-86
Author(s):  
D. A. Prostakishina ◽  
◽  
N. D. Korsun ◽  
Keyword(s):  
Bearing Capacity ◽  
Compressive Force ◽  
Stability Loss ◽  
Load Bearing Capacity ◽  
Geometric Imperfections ◽  
Load Bearing ◽  
Composite Section ◽  
Initial Geometric Imperfections ◽  
Thin Walled ◽  
The Stability

The article describes the process of numerical simulation of a composite symmetric section element made of thin-walled Sigma profiles operating under conditions of longitudinal compressive force with bending, taking into account the initial geometric imperfections. At numerical modeling, the main criterion of the load-bearing capacity exhaustion in case of eccentric compression is the stability loss in one of the forms. However, for thin-walled elements, the loss of local stability does not mean that the load-bearing capacity is completely exhausted, since the element continues to carry the load, but to a lesser extent. Therefore, simulation was carried out in two stages: initially, in the elastic formulation, the possible buckling modes were determined, afterwards, there was made calculation on the deformed pattern taking into account possible imperfections.

Effect of Initial Imperfections on the Instability of a Ring Confined in an Imperfect Rigid Boundary

1967 ◽  
Vol 34 (4) ◽  
pp. 979-984 ◽  
Author(s):  
L. L. Bucciarelli ◽  
T. H. H. Pian
Keyword(s):  
Limit Point ◽  
Stability Limit ◽  
Circular Ring ◽  
Load Level ◽  
Shallow Arch ◽  
Rigid Boundary ◽  
Initial Imperfections ◽  
Buckling Behavior ◽  
Initial Geometric Imperfections ◽  
The Stability

The stability of a radially constrained, complete, circular ring subjected to thermal stress and of a similarly restrained portion of a circular ring under circumferential end load is investigated. The effect of three types of initial geometric imperfections on the buckling behavior is determined. Results obtained, employing shallow arch approximations, show that this behavior depends on the assumed form of imperfection. In one case, no bifurcation or limit point exists at finite load level; in the second case, bifurcation and snap buckling may occur; in the third case, the system admits of a limit point. A design curve is proposed which can be used to estimate the stability limit of a circular ring exhibiting a certain “out-of-roundness.”

The Stochastic Imperfection Method of Sheet Space Structure Based on Truncated Univariate Normal Distributions

2014 ◽  
Vol 937 ◽  
pp. 707-711
Author(s):  
Tian Jiao Jin ◽  
Xiao Ming Guo
Keyword(s):  
Space Structure ◽  
Acceptance Rate ◽  
Space Structures ◽  
Design Code ◽  
Geometric Imperfections ◽  
Spherical Coordinate ◽  
Normal Distributions ◽  
Truncated Normal ◽  
Initial Geometric Imperfections ◽  
The Stability

The initial geometric imperfections is a key issue of the stability analysis of sheet space structures. A new described method of the initial geometric imperfections which is located in local spherical coordinate system is given, and the random imperfection variable is assumed to follow a truncated univariate normal distribution (TUVN). A well working envelope function for TUVN is chosen, and the acceptance rate is high for constrained region of the design code. The method provided in the paper is called spherical truncated normal stochastic imperfection method (STNS). The results of consistent mode imperfections method, traditional stochastic imperfection method and STNS method are compared, by which some conclusions that are useful for the design and the study of sheet space structures are obtained.

Application of Modified Consistent Mode Imperfection Method in Stability Analysis of Single-Layer Reticulated Shells

2013 ◽  
Vol 477-478 ◽  
pp. 744-748 ◽  
Author(s):  
Sheng He ◽  
Jian Cai ◽  
Qi Qi Liu
Keyword(s):  
Stability Analysis ◽  
Single Layer ◽  
Buckling Load ◽  
Structure Stability ◽  
Geometric Imperfections ◽  
Stability Performance ◽  
Mode Method ◽  
Initial Geometric Imperfections ◽  
The Stability ◽  
Reticulated Shell Structure

Based on the probability reliability theory, this paper proposes a modified consistent mode imperfection method, which fits the integral stability analysis of single-layer reticulated shells with the initial geometric imperfections. Nearly 1000 elasto-plastic load-deflection overall processes of four different rise-to-span ratio for Kiewitt-8 single-layer reticulated shells are analyzed by using the random imperfection mode method, the consistent mode imperfection method and the modified consistent mode imperfection method respectively. The study shows that the random imperfection mode method can assess the influence of initial geometric imperfections on structure stability more scientifically, but the calculation is quite large. By using the consistent mode imperfection method, the buckling load is not sure to be the most unfavorable, and the degree of reliability couldnt be ensured effectively. The modified consistent mode imperfection method can gain the buckling load which meets the requirement of probability reliability with less calculation. It can also assess the stability performance of single-layer reticulated shell structure more reasonably and safely.

scholarly journals Some aspects of consideration of initial imperfections in the calculations of stability of thin-walled elements of open profile

2021 ◽  
pp. 122-128
Author(s):  
Ivan Okhten ◽  
Olha Lukianchenko
Keyword(s):  
Middle Surface ◽  
Stability Loss ◽  
Critical Force ◽  
The Finite Element Method ◽  
Geometric Imperfections ◽  
Initial Imperfections ◽  
General Stability ◽  
Initial Geometric Imperfections ◽  
Linear And Nonlinear ◽  
The Stability

Performed analysis of the initial geometric imperfections influence on the stability of the open C-shaped bars. Test tasks were solved in MSC Nastran, which is based on the finite element method. Imperfections are given in different formulations: the general stability loss of an ideal bar, of wavy bulging of walls and shelves, of deplanation of a bar. To model imperfections, has been developed a program which for the formation of new coordinates of the nodes of the "deformed" model, the components of a vector similar to the form of stability loss are added to the corresponding coordinates of the middle surface of the bar. In this way, you can set initial imperfections in the forms of stability loss of the bar with different amplitude. Researches made with different values of the imperfection amplitude and eccentricity of applied efforts. All tasks are performed in linear and nonlinear staging. The conclusion is made regarding the influence of initial imperfections form and imperfection amplitude on the critical force in nonlinear calculations. It was found that the most affected are imperfections, which are given in the form of total loss of stability. It was revealed the influence of the imperfection amplitude on the magnitude of the critical force for such imperfections. The influence of imperfections amplitude given in the form of wavy bulging walls and in the form of deplanations is not affected on the value of the critical force.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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