Large Deflection of Circular Auxetic Membranes Under Uniform Load

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Teik-Cheng Lim
Keyword(s):  
Empirical Model ◽  
Poisson’S Ratio ◽  
Large Deflection ◽  
Radial Distance ◽  
Poisson's Ratio ◽  
Circular Membrane ◽  
Membrane Material ◽  
Uniform Load ◽  
Direct Computation ◽  
Semi Empirical

Currently, available results for the large deflection of circular isotropic membranes are valid for Poisson's ratio of 0.2, 0.3, and 0.4 only. This paper explores the deflection of circular membranes when the membrane material is auxetic, i.e., when they possess negative Poisson's ratio and compared against conventional ones. Due to the multistage calculations involved in the exact method, a generic semi-empirical model is proposed to facilitate convenient and direct computation of the membrane deflection as a function of the radial distance; additionally, a specific semi-empirical model is given to provide a more accurate maximum deflection. Comparison of deflection distributions verifies the validity of the semi-empirical model vis-à-vis the exact model. The deflection of circular membrane increases with the diminishing effect as the Poisson's ratio of the membrane material becomes more negative.

Surface Settlement of a Deep Elastic Stratum Whose Modulus Increases Linearly with Depth

1972 ◽  
Vol 9 (4) ◽  
pp. 467-476 ◽  
Author(s):  
P. T. Brown ◽  
R. E. Gibson
Keyword(s):  
Half Space ◽  
Elastic Material ◽  
Poisson’S Ratio ◽  
Surface Displacement ◽  
Vertical Surface ◽  
Surface Settlement ◽  
Poisson's Ratio ◽  
Uniform Load ◽  
Circular Area ◽  
Wide Range

An examination has been made of the behavior of a half space of elastic material of constant Poisson's ratio, whose Young's modulus increases linearly with depth, and which is subject to a strip or circle of uniform load. Poisson's ratio was considered in the range zero to one-half, and the surface modulus ranged from zero to the value corresponding to a homogeneous material.Numerical values are presented for vertical surface displacement due to a load uniformly distributed over a circular area for Poisson's ratio = 1/2, 1/3 and 0, and for a wide range of inhomogeneity.

scholarly journals Poisson's Ratio and Elastic Modulus of Honeycombs for a Large Deflection Model

2004 ◽  
Vol 70 (698) ◽  
pp. 1476-1483
Author(s):  
Hideyuki OHTAKI ◽  
Hui WAN ◽  
Sinya KOTOSAKA ◽  
Yasumi NAGASAKA
Keyword(s):  
Elastic Modulus ◽  
Poisson’S Ratio ◽  
Large Deflection ◽  
Poisson's Ratio

Effect of Poisson's ratio on bonded rubber blocks

1972 ◽  
Vol 7 (3) ◽  
pp. 236-242 ◽  
Author(s):  
B P Holownia
Keyword(s):  
Poisson’S Ratio ◽  
Circular Cross Section ◽  
Relaxation Method ◽  
Poisson's Ratio ◽  
Dynamic Relaxation ◽  
Stress Strain ◽  
A Value ◽  
Rubber Compounds ◽  
Dynamic Relaxation Method ◽  
Semi Empirical

A theoretical analysis of bonded rubber blocks with circular cross-section under axial compression is obtained by the use of dynamic-relaxation solutions of classical elastic stress-strain equations. The Poisson's ratio ν for rubber is close to 0.5 which causes difficulties in the analysis because the general stress-strain equations of elasticity contain terms such as ν E/(1 + ν)(1 − 2ν) which approaches infinity when ν approaches a value of 0.5. The range of ν considered varies between 0.45000 and 0.49990 which covers all the natural-rubber compounds used, including pure natural gum which has a ν value of 0.49989 (1)∗. It is shown that the stress distribution within the block is significantly affected by the value of ν and the shape of the block. When a block of material with ν ∼ 0.5, bonded to its end plates, is thin, the stress developed within the block is high and nearly equal in all three directions, which suggests a hydrostatic type of pressure. Such a pressure would confirm the finding in (2) and (3) based on a semi-empirical analysis. When the block is thick this effect is absent. The present paper confirms that these effects follow from the fundamental assumptions of classical elasticity. The investigation also confirms that the dynamic-relaxation method converges satisfactorily even when the Poisson's ratio is very close to the value of 0.5000.

The Annular Membrane Under Axial Load

1981 ◽  
Vol 48 (4) ◽  
pp. 975-976 ◽  
Author(s):  
D. J. Allman ◽  
E. H. Mansfield
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Poisson’S Ratio ◽  
Axial Load ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Poisson's Ratio ◽  
Annular Membrane

An exact solution is given of the nonlinear differential equations for the large deflection behavior of an initially unstressed annular membrane under axial load for the case of Poisson’s ratio equal to one third.

The Model for Calculating Elastic Modulus and Poisson's Ratio of Coal Body

2013 ◽  
Vol 6 (1) ◽  
pp. 36-43 ◽  
Author(s):  
Ai Chi ◽  
Li Yuwei
Keyword(s):  
Elastic Modulus ◽  
Poisson’S Ratio ◽  
Fractured Rock ◽  
Rock Block ◽  
Poisson's Ratio ◽  
Linear Elastic ◽  
Study Results ◽  
The Face ◽  
Block Face ◽  
Coal Rock

Coal body is a type of fractured rock mass in which lots of cleat fractures developed. Its mechanical properties vary with the parametric variation of coal rock block, face cleat and butt cleat. Based on the linear elastic theory and displacement equivalent principle and simplifying the face cleat and butt cleat as multi-bank penetrating and intermittent cracks, the model was established to calculate the elastic modulus and Poisson's ratio of coal body combined with cleat. By analyzing the model, it also obtained the influence of the parameter variation of coal rock block, face cleat and butt cleat on the elastic modulus and Poisson's ratio of the coal body. Study results showed that the connectivity rate of butt cleat and the distance between face cleats had a weak influence on elastic modulus of coal body. When the inclination of face cleat was 90°, the elastic modulus of coal body reached the maximal value and it equaled to the elastic modulus of coal rock block. When the inclination of face cleat was 0°, the elastic modulus of coal body was exclusively dependent on the elastic modulus of coal rock block, the normal stiffness of face cleat and the distance between them. When the distance between butt cleats or the connectivity rate of butt cleat was fixed, the Poisson's ratio of the coal body initially increased and then decreased with increasing of the face cleat inclination.

scholarly journals A Hybrid Artificial Intelligence Model to Predict the Elastic Behavior of Sandstone Rocks

2019 ◽  
Vol 11 (19) ◽  
pp. 5283 ◽  
Author(s):  
Gowida ◽  
Moussa ◽  
Elkatatny ◽  
Ali
Keyword(s):  
Poisson’S Ratio ◽  
Accurate Determination ◽  
Oil And Gas Industry ◽  
Poisson's Ratio ◽  
Elastic Behavior ◽  
Percentage Error ◽  
Ann Model ◽  
Field Development ◽  
Well Completion

Rock mechanical properties play a key role in the optimization process of engineering practices in the oil and gas industry so that better field development decisions can be made. Estimation of these properties is central in well placement, drilling programs, and well completion design. The elastic behavior of rocks can be studied by determining two main parameters: Young’s modulus and Poisson’s ratio. Accurate determination of the Poisson’s ratio helps to estimate the in-situ horizontal stresses and in turn, avoid many critical problems which interrupt drilling operations, such as pipe sticking and wellbore instability issues. Accurate Poisson’s ratio values can be experimentally determined using retrieved core samples under simulated in-situ downhole conditions. However, this technique is time-consuming and economically ineffective, requiring the development of a more effective technique. This study has developed a new generalized model to estimate static Poisson’s ratio values of sandstone rocks using a supervised artificial neural network (ANN). The developed ANN model uses well log data such as bulk density and sonic log as the input parameters to target static Poisson’s ratio values as outputs. Subsequently, the developed ANN model was transformed into a more practical and easier to use white-box mode using an ANN-based empirical equation. Core data (692 data points) and their corresponding petrophysical data were used to train and test the ANN model. The self-adaptive differential evolution (SADE) algorithm was used to fine-tune the parameters of the ANN model to obtain the most accurate results in terms of the highest correlation coefficient (R) and the lowest mean absolute percentage error (MAPE). The results obtained from the optimized ANN model show an excellent agreement with the laboratory measured static Poisson’s ratio, confirming the high accuracy of the developed model. A comparison of the developed ANN-based empirical correlation with the previously developed approaches demonstrates the superiority of the developed correlation in predicting static Poisson’s ratio values with the highest R and the lowest MAPE. The developed correlation performs in a manner far superior to other approaches when validated against unseen field data. The developed ANN-based mathematical model can be used as a robust tool to estimate static Poisson’s ratio without the need to run the ANN model.

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