An Analytical Framework for the Solution of Autofrettaged Tubes Under Constant Axial Strain Condition

2008 ◽  
Author(s):  
E. Hosseinian ◽  
G. H. Farrahi ◽  
M. R. Movahhedy
Keyword(s):  
Numerical Methods ◽  
Analytical Method ◽  
Numerical Solutions ◽  
Yield Criterion ◽  
Axial Strain ◽  
Material Model ◽  
Analytical Framework ◽  
Material Behavior ◽  
Perfectly Plastic ◽  
Special Cases

Autofrettage is a technique for introducing beneficial residual stresses into cylinders. Both analytical and numerical methods are used for analysis of the autofrettage process. Analytical methods have been presented only for special cases of autofrettage. In this work, an analytical framework for the solution of autofrettaged tubes with constant axial strain conditions is developed. Material behavior is assumed to be incompressible and two different quadratic polynomials are used for strain hardening in loading and unloading. Clearly, elastic-perfectly plastic and linear hardening materials are special cases of this general model. This material model is convenient for description of the behavior of a class of pressure vessel steels such as A723. The Bauschinger effect is assumed fixed and total deformation theory based upon von-Mises yield criterion is used. An explicit solution for the constant axial strain conditions and its special cases such as plane strain and closed-end conditions is obtained. For open-end condition for which axial force is zero the presented analytical method leads to a simple numerical solution. Finally, results of the new method are compared with those obtained from other analytical and numerical methods and excellent agreement is observed. Since the presented method is a general analytical method, it is believed that it could be used for validation of numerical solutions or analytical solutions for special loading cases.

An Analytical Framework for the Solution of Autofrettaged Tubes Under Constant Axial Strain Condition

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
E. Hosseinian ◽  
G. H. Farrahi ◽  
M. R. Movahhedy
Keyword(s):  
Numerical Methods ◽  
Analytical Method ◽  
Numerical Solutions ◽  
Yield Criterion ◽  
Axial Strain ◽  
Material Model ◽  
Analytical Framework ◽  
Material Behavior ◽  
Perfectly Plastic ◽  
Special Cases

Autofrettage is a technique for introducing beneficial residual stresses into cylinders. Both analytical and numerical methods are used for the analysis of the autofrettage process. Analytical methods have been presented only for special cases of autofrettage. In this work, an analytical framework for the solution of autofrettaged tubes with constant axial strain conditions is developed. Material behavior is assumed to be incompressible, and two different quadratic polynomials are used for strain hardening in loading and unloading. Clearly, elastic perfectly plastic and linear hardening materials are the special cases of this general model. This quadratic material model is convenient for the description of the behavior of a class of pressure vessel steels such as A723. The Bauschinger effect is assumed fixed, and the total deformation theory based on the von Mises yield criterion is used. An explicit solution for the constant axial strain conditions and its special cases such as plane strain and closed-end conditions is obtained. For an open-end condition, for which the axial force is zero, the presented analytical method leads to a simple numerical solution. Finally, results of the new method are compared with those obtained from other analytical and numerical methods, and excellent agreement is observed. Since the presented method is a general analytical method, it could be used for validation of numerical solutions or analytical solutions for special loading cases.

scholarly journals Simulation of three-dimensional rapid free-surface granular flow past different types of obstructions using the SPH method

2016 ◽  
Vol 62 (232) ◽  
pp. 335-347 ◽  
Author(s):  
AHMED M. ABDELRAZEK ◽  
ICHIRO KIMURA ◽  
YASUYUKI SHIMIZU
Keyword(s):  
Granular Flow ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Material Behavior ◽  
Sph Method ◽  
Perfectly Plastic ◽  
Depth Direction ◽  
Aspect Ratios ◽  
Flow Past ◽  
Different Types

ABSTRACTIn nature, when hazardous geophysical granular flows (e.g. a snow avalanche) impact on an obstacle as they stream down a slope, rapid changes in flow depth, direction and velocity will occur. It is important to understand how granular material flows around such obstacles in order to enhance the design of defense structures. In this study, a three dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) model is developed to simulate granular flow past different types of obstacles. The elastic–perfectly plastic model with implementation of the Mohr–Coulomb failure criterion is applied to simulate the material behavior, which describes the stress states of soil in the plastic flow regime. The model was validated by simulating the collapse of a 3-D column of sand with two different aspect ratios; the results showed that the SPH method is capable of simulating granular flow. The model is then applied to simulate the gravity-driven granular flow down an inclined surface obstructed by a group of columns with different spacing, a circular cylinder and a tetrahedral wedge. The numerical results are then compared with experimental results and two different numerical solutions. The good agreements obtained from these comparisons demonstrate that the SPH method may be a powerful method for simulating granular flow and can be extended to design protective structures.

Deflection of Clamped Plates by Two-Step Membrane Analogue

1955 ◽  
Vol 59 (533) ◽  
pp. 358-360 ◽  
Author(s):  
V. Cadambe ◽  
R. K. Kaul
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
General Solution ◽  
Fourth Order ◽  
Biharmonic Equation ◽  
Numerical Solutions ◽  
Thin Plates ◽  
Geometrical Shape ◽  
Marked Contrast ◽  
Special Cases

The Classical Kirchhofif–Love Theory for the deflection of thin plates leads to fourth order Lagrange's differential equation,D△4w — q = 0 for which a general solution is not always possible. Exact solutions are known so far only for a few special cases and, therefore, numerical solutions have often been tried. The advantage of numerical solution is that it can be applied easily to any plate plan form which is in marked contrast to the analytical method where, for mathematical reasons, definite restrictions have to be imposed on the geometrical shape of the plate. Among the various numerical methods, relaxation is the easiest, but when applied to solving a biharmonic equation, the process becomes extremely difficult and laborious as convergence is very slow and the unit relaxation operator cumbersome to deal with.

Analysis of thick-walled spherical shells subjected to external pressure: Elastoplastic and residual stress analysis

2019 ◽  
Vol 234 (1) ◽  
pp. 186-197
Author(s):  
Mohsen Kholdi ◽  
Abbas Loghman ◽  
Hossein Ashrafi ◽  
Mohammad Arefi
Keyword(s):  
Hydrostatic Pressure ◽  
Residual Stresses ◽  
Yield Criterion ◽  
External Pressure ◽  
Material Behavior ◽  
External Hydrostatic Pressure ◽  
Spherical Vessel ◽  
Tangential Stresses ◽  
Perfectly Plastic ◽  
Analytical Relations

When cylindrical and spherical vessels are subjected to the internal pressure, tensile tangential stresses are created throughout the thickness, the maximum of which are located at the inner surface of the vessels. To improve the performance of these vessels, autofrettage process has been devised to produce beneficial compressive residual stresses at the inner part of such vessels. The question arises whether the process such as autofrettage can be useful for vessels such as submarines or other thick walled tanks, which are used in deep sea waters and, therefore, subjected to high external hydrostatic pressure causing both radial and tangential stresses to be compressive across the thickness. On the other hand, is the residual stresses created by unloading from an external pressure beyond elastic limit beneficial and enhance their performances? In this study, elastoplastic and residual stresses in a thick-walled spherical vessel under external hydrostatic pressure has been investigated. The material behavior is considered to be elastic-perfectly plastic. Von Misses yield criterion is used to obtain initial yield point and for the ideal elastoplastic regime analytical relations are presented. It has been found that by applying external hydrostatic pressure yielding process will start from inside of the sphere. Finally after unloading, residual tensile stresses are created at the inner part of the vessel which is useful for the vessel. The residual stresses and the condition of reverse yielding is studied in this paper.

Ramberg–Osgood material behavior expression and large deflections of Euler beams

2020 ◽  
pp. 108128652093236
Author(s):  
Ronald J Giardina ◽  
Dongming Wei
Keyword(s):  
Cross Sections ◽  
Nonlinear Behavior ◽  
Material Model ◽  
Material Behavior ◽  
Combined Loading ◽  
Elastic Behavior ◽  
Large Deflections ◽  
Euler Beam ◽  
Special Cases ◽  
Material Behaviors

Several assumptions are commonly made throughout the literature with regard to the mechanical expression of material behavior under a Ramberg–Osgood material model; specifically, the negligible effects of nonlinearity on the elastic behavior of the material. These assumptions do not reflect the complicated nonlinearity implied by the Ramberg–Osgood expression, which can lead to significant differences in the member model response from the true material behavior curve. With the proposed approach, new explicit results for Ramberg–Osgood materials are achieved without relying on these assumptions of material and model expression. The only assumptions present within the proposed model are the standard mechanical assumptions of an Euler beam. A general nonlinear moment–curvature relationship for monotone material behaviors is constructed. Large deflections of cantilever Euler beams with rectangular cross-sections under a combined loading are modeled. Numerical validation of this new method against results already given in the literature for the special cases of linear and power-law material behaviors are provided. An analysis is presented for three common material behavior relationships, with a focus on how these relationships are expressed through the deflection of members under the application of force within the model; this analysis clearly demonstrates that the sub-yield nonlinear behavior of the Ramberg–Osgood expression can be significant. The distinctions between material behavior expression demonstrated in this analysis have been long overlooked within the literature. This work addresses a gap between the modeling of Ramberg–Osgood material behaviors and the implementation of that model in mechanics.

Elastic–Brittle–Plastic Analysis of Double-Layered Combined Thick-Walled Cylinder Under Internal Pressure

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Qian Zhu ◽  
Junhai Zhao ◽  
Changguang Zhang ◽  
Yan Li ◽  
Su Wang
Keyword(s):  
Internal Pressure ◽  
Principal Stress ◽  
Yield Criterion ◽  
Engineering Application ◽  
Strength Criterion ◽  
Intermediate Principal Stress ◽  
Material Behavior ◽  
Strength Theory ◽  
Special Cases ◽  
Walled Cylinder

The elastic–brittle–plastic unified solutions of limit internal pressure are presented for double-layered combined thick-walled cylinder by the triple-shear unified strength criterion. The unified solutions obtained in this paper are especially versatile that can take into account of material brittle softening and intermediate principal stress quantitatively. The conventional existing elastic-perfectly plastic solutions, based on the Tresca yield criterion, Mises yield criterion, or twin-shear strength theory, can be categorized as special cases of the present unified solutions which can overcome their shortages. Parametric studies were carried out to evaluate the influences of various factors such as brittle softening parameter, strength theory parameter, cohesion, internal friction angle, and intermediate principal stress coefficient on the unified solutions. It is shown that proper choices of failure criterion, material behavior model, and brittle softening are significant in combined cylinder design. The new solutions can be naturally degraded to the existing formula and agree well with the results of the prevailing failure criteria. It is concluded that the unified solutions have an important practical value for the optimum design and engineering application of combined thick-walled cylinder.

An Analytical Solution of Residual Stresses for Shrink-Fit Two-Layer Cylinders After Autofrettage Based on Actual Material Behavior

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Yuan Gexia ◽  
Liu Hongzhao
Keyword(s):  
Residual Stress ◽  
Stress Distribution ◽  
Analytical Solution ◽  
Analytical Method ◽  
Numerical Solutions ◽  
Residual Stress Distribution ◽  
Material Behavior ◽  
Layer Compound ◽  
Shrink Fitting ◽  
Shrink Fit

To enhance the pressure capacity and the life of a pressure vessel, different processes such as shrink-fit and autofrettage are usually employed. For autofrettaged and shrink-fit multilayer cylinders, numerical solutions for determining the residual stress distribution have been reported. However, few studies about the analytical method are available. In this study, an analytical solution was presented for shrink-fit two-layer cylinders after autofrettage based on the actual tensile-compressive stress–strain curve of material. The new analytical method accurately predicted a residual stress distribution, and it could be used to design two-layer compound cylinders. In this method, unloading and shrink-fitting were considered as a simultaneous operation for an inner cylinder, allowing for a simple and accurate analysis. Some significant factors were taken into account, including the nonlinear behavior of an original autofrettaged inner layer in the shrink-fitting process and a material’s different unloading behavior at different maximum tensile affects back-yielding. The results of the proposed method were in excellent agreement with the results from the simulation performed by ansys. The results indicated that an increased shrink-fit pressure expanded the back-yielding zone of the inner cylinders, and did not affect the back-yielding zone of the outer cylinders. The optimum percentages overstrain depend on the working pressure when the shrink-fit pressure, cylinder size, and material are defined, and inner and outer cylinders have different optimum percentages overstrain.

scholarly journals Plastic failure zone characteristics and stability control technology of roadway in the fault area under non-uniformly high geostress: A case study from Yuandian Coal Mine in Northern Anhui Province, China

2020 ◽  
Vol 12 (1) ◽  
pp. 406-424 ◽  
Author(s):  
Yaoguang Huang ◽  
Aining Zhao ◽  
Tianjun Zhang ◽  
Weibin Guo
Keyword(s):  
Numerical Methods ◽  
Numerical Solutions ◽  
Stress Test ◽  
Pressure Coefficient ◽  
Stability Control ◽  
Failure Zone ◽  
Plastic Failure ◽  
Comparison Results ◽  
High Geostress ◽  
The Difference

AbstractIn order to explore the effective support method for deep broken roadway, based on the in situ stress test results, the analytical and numerical solutions of the stress and the range of plastic failure zone (PFZ) in a circular roadway subjected to non-uniform loads were obtained using analytical and finite difference numerical methods based on the elastoplastic theory, respectively. Their comparison results show that the analytical and numerical methods are correct and reasonable. Furthermore, the high geostress causes the stress and range of PFZ in roadway roof and floor to increase sharply while those in roadway ribs decrease. Moreover, the greater the difference of horizontal geostress in different horizontal directions is, the larger the range of PFZ in roadway roof and floor is. The shape of PFZ in roadway varies with the ratio of horizontal lateral pressure coefficient in x-direction and y-direction. Finally, according to the distribution characteristics of PFZ and range of PFZ under the non-uniformly high geostress, this paper has proposed a combined support scheme, and refined and optimized supporting parameters. The field monitoring results prove that the roadway deformation and fracture have been effectively controlled. The research results of this paper can provide theoretical foundation as well as technical reference for the stability control of deep broken roadway under non-uniformly high geostress.

Actual Problems of the Safety and Reliability of the NPP Structures in Slovakia

2017 ◽  
Vol 738 ◽  
pp. 261-272 ◽  
Author(s):  
Juraj Kralik
Keyword(s):  
Risk Assessment ◽  
Numerical Methods ◽  
Probabilistic Analysis ◽  
Material Model ◽  
Safety Level ◽  
Concrete Cracking ◽  
The World ◽  
Safety And Reliability ◽  
Long Time ◽  
Calculated Model

The last accidents of the NPP in Chernobyl and Fukushima give us the new inspiration to verify the safety level of the NPP structures. This paper presents the new requirements to test of the safety and reliability of the NPP structures due to the last accidents in the world. The risk assessment to verify of the safety and reliability of the NPP structures based on probabilistic and nonlinear analysis is presented. The uncertainties of the loads level (long-time temperature and dead loads), the material model (concrete cracking and crushing, behaviour of the reinforcement and liner), degradation effects and other influences following from the inaccuracy of the calculated model and numerical methods were taken into account in the LHS method. The results of the deterministic and probabilistic analysis of the NPP structures are presented.

A Viscoelastic Correspondence Principle for Plane Membranes Subjected to Lateral Pressure

1983 ◽  
Vol 50 (4a) ◽  
pp. 740-742 ◽  
Author(s):  
B. Stora˚kers
Keyword(s):  
Time Dependence ◽  
Viscoelastic Material ◽  
Lateral Pressure ◽  
Correspondence Principle ◽  
Material Model ◽  
Material Behavior ◽  
Linear Elastic Material ◽  
First Order ◽  
Linear Elastic ◽  
Consistent Approximation

The classical Fo¨ppl equations, governing the deflection of plane membranes, constitute the first-order consistent approximation in the case of linear elastic material behavior. It is shown that despite the static and kinematic nonlinearities present, for arbitrary load histories a correspondence principle for viscoelastic material behavior exists if all relevant relaxation moduli are of uniform time dependence. Application of the principle is illustrated by means of a popular material model.

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