Plastic Deformations of a Free Ring Under Concentrated Dynamic Loading

1955 ◽  
Vol 22 (4) ◽  
pp. 523-529
Author(s):  
R. H. Owens ◽  
P. S. Symonds
Keyword(s):  
Dynamic Loading ◽  
Arbitrary Shape ◽  
Time Dependent ◽  
Plastic Behavior ◽  
Plastic Strains ◽  
Plastic Deformations ◽  
Free Ring ◽  
Thin Ring ◽  
Special Case ◽  
Elastic Strains

Abstract A concentrated time-dependent force acts on an unsupported thin ring along a diameter. The problem considered in this paper is to determine the deformations of the ring when the force magnitudes are such that plastic strains large compared with elastic strains occur. By neglecting elastic strains and assuming ideally plastic behavior, approximations to the final deformations of the ring are obtained. The analysis is developed for force pulses of arbitrary shape, but numerical results are obtained only in the special case of a rectangular force pulse. A criterion is stated for conditions when this type of analysis can be expected to provide satisfactory results.

scholarly journals Large deformations of a cylindrical tube with prestressed coatings

2019 ◽  
Vol 484 (5) ◽  
pp. 547-549
Author(s):  
Yu. N. Kulchin ◽  
V. E. Ragozina ◽  
O. V. Dudko
Keyword(s):  
Shock Waves ◽  
Large Deformations ◽  
Cylindrical Tube ◽  
Plastic Strains ◽  
Rotation Tensor ◽  
Plastic Deformations ◽  
Incompressible Materials ◽  
Isotropic Media ◽  
Elastic Loading ◽  
Elastic Shock

General theoretical relations for calculating the redistribution of the preliminary irreversible strain field during unloading or elastic loading of a medium are obtained for the nonlinear multiplicative gradient model of large elastic-plastic deformations. It is shown that the dynamics of elastic shock waves does not depend directly on the previously accumulated plastic strains. A formula for the plastic-strain rotation tensor is obtained. It is shown that rigid rotation of plastic strains under elastic shock waves can be jump-like. All results are obtained for the general case of model relations of isotropic media and are valid for both compressible and incompressible materials.

Influence of Rock Plastic Behavior on the Wellbore Stability

2021 ◽  
Author(s):  
Elena Grishko ◽  
Aboozar Garavand ◽  
Alexey Cheremisin
Keyword(s):  
Failure Criteria ◽  
Wellbore Stability ◽  
Standard Approach ◽  
Plastic Behavior ◽  
Element Formulation ◽  
Geomechanical Model ◽  
Plastic Properties ◽  
Plastic Deformations ◽  
3D Geomechanical Model

Abstract Currently, the standard approach to building a geomechanical model for analyzing wellbore stability involves taking into account only elastic deformations. This approach has shown its inconsistency in the design and drilling of wells passing through rocks with pronounced plastic properties. Such rocks are characterized by the fact that when the loads acting on them change, they demonstrate not only elastic, but also plastic (irreversible) deformations. Plastic deformations have an additional impact on the distribution of stresses in the rock of the near-wellbore zone on a qualitative and quantitative level. Since plastic deformations are not taken into account in the standard approach, in this case the results of the wellbore stability analysis are based on incorrectly calculated stresses acting in the rock. As a result, it can lead to misinterpretation of the model for analysis, suboptimal choice of trajectory, incorrect calculation of safe mud window and an incorrectly selected set of measures to reduce the risks of instability. The aim of this work is to demonstrate the advantages of the developed 3D elasto-plastic program for calculating the wellbore stability in comparison with the standard elastic method used in petroleum geomechanics. The central core of the work is the process of initialization of the elasto-plastic model according to the data of core tests and the subsequent validation of experimental and numerical loading curves. The developed 3D program is based on a modified Drucker-Prager model and implemented in a finite element formulation. 3D geomechanical model of wellbore stability allows describing deformation processes in the near-wellbore zone and includes the developed failure criteria. The paper shows a special approach to the determination of the mud window based on well logging data and core tests by taking into account the plastic behavior of rocks. An important result of this study is the determination of the possibility of expanding the mud window when taking into account the plastic criterion of rock failure.

A general time-dependent invariant for and integrability of the quadratic system

1994 ◽  
Vol 444 (1922) ◽  
pp. 643-650 ◽  
Keyword(s):  
Direct Method ◽  
First Integral ◽  
Quadratic System ◽  
Time Dependent ◽  
Polynomial Invariant ◽  
Polynomial Invariants ◽  
Linear Polynomial ◽  
A Direct Method ◽  
Special Case ◽  
General Time

We derive a general time-dependent invariant (first integral) for the quadratic system (QS) that requires only one condition on the coefficients of the QS. The general invariant could yield asymptotic behaviour of phase-space trajectories. With more conditions imposed on the coefficients, the general invariant reduces to polynomial form and is equivalent to polynomial invariants found using a direct method. For the special case of a linear polynomial invariant where one of the variables is analytically invertible, the solution of the QS is reduced to a quadrature.

Large Elastic-Plastic Deformation Analysis of Rectangular Plates

2002 ◽  
Author(s):  
Reza Naghdabadi ◽  
Mohsen Shahi
Keyword(s):  
Lateral Displacement ◽  
Deformation Analysis ◽  
Plastic Behavior ◽  
Rectangular Plates ◽  
Computationally Efficient ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Various Boundary Conditions ◽  
Method Of Solution ◽  
Suitable Combination

The purpose of this paper is to find a fast and simple solution for the large deformation of rectangular plates considering elastic-plastic behavior. This analysis contains material and geometric nonlinearities. For geometric nonlinearity the concept of load analogy is used. In this method the effect of nonlinear terms of lateral displacement is considered as suitable combination of additional fictitious lateral load, edge moment and in-plane forces acting on the plate. Variable Material Property (V.M.P.) method has been used for analysis of material nonlinearity. In this method, the basic relations maintain the form of stress-strain elastic formula, while material properties are modified to take into account the path-dependency involved in elastic-plastic deformations. Therefore, the solution of a von-Karman plate enduring large elastic-plastic deformations is reduced to that of an equivalent elastic plate undergoing small deformations. The method of solution employed in this study is computationally efficient and can easily be used for various boundary conditions and loadings.

A CLOSED-FORM SOLUTION OF THE EVOLUTION OPERATOR IN TWO-LEVEL SYSTEMS

1994 ◽  
Vol 08 (08n09) ◽  
pp. 505-508 ◽  
Author(s):  
XIAN-GENG ZHAO
Keyword(s):  
Closed Form ◽  
Lie Algebra ◽  
Evolution Operator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Dependent ◽  
Arbitrary Time ◽  
Two Level Systems ◽  
Special Case

It is demonstrated by using the technique of Lie algebra SU(2) that the problem of two-level systems described by arbitrary time-dependent Hamiltonians can be solved exactly. A closed-form solution of the evolution operator is presented, from which the results for any special case can be deduced.

Solution of Non-Fourier Temperature Field in a Hollow Sphere under Harmonic Boundary Condition

2015 ◽  
Vol 772 ◽  
pp. 197-203 ◽  
Author(s):  
Amin Bahrami ◽  
Siamak Hosseinzadeh ◽  
Ramin Ghasemiasl ◽  
Morteza Radmanesh
Keyword(s):  
Heat Flux ◽  
Temperature Field ◽  
Hollow Sphere ◽  
Separation Of Variables ◽  
Time Dependent ◽  
Separation Of Variables Method ◽  
Method Of Solution ◽  
Duhamel Integral ◽  
Special Case ◽  
General Time

Analytical solution of the axisymmetric two-dimensional non-Fourier temperature field within a hollow sphere is investigated considering Cattaneo-Vernotte constitutive equation with general time-dependent heat flux. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The method of solution is the standard separation of variables method. Duhamel integral is used for applying the time-dependent boundary conditions. The presented solution is applied to special case of harmonic heat flux on outer surface.

scholarly journals WAVE SCATTERING BY PERMEABLE AND IMPERMEABLE BREAKWATER OF ARBITRARY SHAPE

1974 ◽  
Vol 1 (14) ◽  
pp. 110
Author(s):  
Takeshi Ijima ◽  
Chung Ren Chou ◽  
Yasu Yumura
Keyword(s):  
Arbitrary Shape ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Theoretical Method ◽  
Floating Body ◽  
Wave Forces ◽  
Method Of Calculation ◽  
Wave Channel ◽  
Method Of Solution ◽  
Special Case

This paper deals with a theoretical method of calculation of the fluid motion, when a sinusoidal plane wave incidents to a permeable breakwater of arbitrary shape at constant water depth and shows that the problem for impermeable breakwater is solved as a special case of this method. The method described here is the extension of the author's method of solution for two-dimensional permeable breakwater by the method of continuation of velocity potentials for two different fluid regions into three-dimensional problems by means of Green functions. Here, the analytical process of calculation is presented and as representative examples, wave height distributions and wave forces around an isolated elliptic- and rectangular breakwater are calculated and compared with experiments in wave channel. The principle of this method is also applied to the analysis of submerged and semi-immersed fixed cylinder and the motions of floating body of arbitrary.

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