An Improved Numerical Calculation Technique for Large Elastic-Plastic Transient Deformations of Thin Shells: Part 2—Evaluation and Applications

1971 ◽  
Vol 38 (2) ◽  
pp. 429-436 ◽  
Author(s):  
L. Morino ◽  
J. W. Leech ◽  
E. A. Witmer
Keyword(s):  
Numerical Calculation ◽  
Computational Efficiency ◽  
Large Deformations ◽  
Thin Shells ◽  
Theoretical Formulation ◽  
Elastic Plastic ◽  
Calculation Technique ◽  
Good Agreement

Based upon the theoretical formulation presented in Part 1 of this paper, improvements in accuracy and computational efficiency are realized. Comparisons of predictions with experimental transient large deformations and strains show good agreement.

An Improved Numerical Calculation Technique for Large Elastic-Plastic Transient Deformations of Thin Shells: Part 1—Background and Theoretical Formulation

1971 ◽  
Vol 38 (2) ◽  
pp. 423-428 ◽  
Author(s):  
L. Morino ◽  
J. W. Leech ◽  
E. A. Witmer
Keyword(s):  
Numerical Calculation ◽  
Finite Difference ◽  
Arbitrary Shape ◽  
Large Deflection ◽  
Dynamic Responses ◽  
Thin Shells ◽  
Theoretical Formulation ◽  
Transient Loading ◽  
Elastic Plastic ◽  
Calculation Technique

Recent improvements are reported in both the theoretical formulation and in the finite-difference treatment of the relations governing the large-deflection elastic-plastic dynamic responses of thin shells of arbitrary shape to transient loading.

Numerical calculation technique for large elastic-plastic transient deformations of thin shells.

AIAA Journal ◽  
1968 ◽  
Vol 6 (12) ◽  
pp. 2352-2359 ◽  
Author(s):  
JOHN W. LEECH ◽  
EMMETT A. WITMER ◽  
THEODORE H. H. PIAN
Keyword(s):  
Numerical Calculation ◽  
Thin Shells ◽  
Elastic Plastic ◽  
Calculation Technique

Bifurcation of Elastic-Plastic Circular Cylindrical Shells Under Internal Pressure

1979 ◽  
Vol 46 (4) ◽  
pp. 889-894 ◽  
Author(s):  
C.-C. Chu
Keyword(s):  
Internal Pressure ◽  
Critical Pressure ◽  
Separation Of Variables ◽  
Cylindrical Shells ◽  
Maximum Pressure ◽  
Thin Shells ◽  
The Finite Element Method ◽  
Elastic Plastic ◽  
Analytical Results ◽  
Good Agreement

The bifurcation of long elastic-plastic cylindrical shells subject to internal pressure is investigated. It is assumed that the end conditions are such that plane strain conditions prevail. For thin shells, simple approximate bifurcation criteria are obtained analytically. The finite-element method is then employed, in conjunction with separation of variables, to obtain the bifurcation conditions for cylindrical shells with arbitrary thickness to radius ratios. For sufficiently thin shells, the numerical and the analytical results are in good agreement for the critical pressure at bifurcation. The numerical and analytical results both indicate that, for sufficiently thin shells, a variety of bifurcation modes are available virtually simultaneously at this critical pressure. However, for thicker shells, the numerical results reveal that there is a single preferred bifurcation mode. The mode number associated with this preferred bifurcation mode depends on the thickness to radius ratio. The possibility of bifurcation occurring before the attainment of the maximum pressure is also explored. For the specific cases investigated here, bifurcation always occurs after the maximum pressure point.

Plastic Instability of Thin Shells Deformed by Rigid Punches and by Hydraulic Pressure

1973 ◽  
Vol 95 (1) ◽  
pp. 36-40 ◽  
Author(s):  
Bilgin Kaftanog˘lu
Keyword(s):  
Large Deformations ◽  
Initial Conditions ◽  
Plastic Anisotropy ◽  
Plastic Instability ◽  
Strain History ◽  
Thin Shells ◽  
Hydraulic Pressure ◽  
Varying Thickness ◽  
New Criterion ◽  
Hydraulic Bulging

A theory has been developed to provide a solution for axisymmetrical shells in the plastic range for large deformations up to fracture. It includes the effects of strain history, nonlinear strain-hardening characteristics of materials, plastic anisotropy in the thickness direction, prestrain, through-thickness stress, and boundary tractions. It is also possible to use nonuniform initial conditions such as varying thickness and varying prestrain. A numerical solution has been developed especially suitable for stretch forming by a rigid punch and for hydraulic bulging of shells or diaphragms. It can easily be modified for the deep-drawing problem. Different instability criteria have been studied. It was found that the conventional criteria would not yield satisfactory results. A new criterion called the “strain propagation” criterion gave satisfactory results in the prediction of the onset of fracture. It could expalin the fracture taking place at increasing or decreasing pressures in the hydraulic bulging problem.

scholarly journals Calculation of thin isotropic shells beyond the elastic limit by the method of elastic solutions

2018 ◽  
Vol 196 ◽  
pp. 01014 ◽  
Author(s):  
Avgustina Astakhova
Keyword(s):  
Elastic Limit ◽  
Physical Nonlinearity ◽  
Elasticity Tensor ◽  
Thin Shells ◽  
Equilibrium Equations ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Internal Forces

The paper focuses on the model of calculation of thin isotropic shells beyond the elastic limit. The determination of the stress-strain state of thin shells is based on the small elastic-plastic deformations theory and the elastic solutions method. In the present work the building of the solution based on the equilibrium equations and geometric relations of linear theory of thin shells in curved coordinate system α and β, and the relations between deformations and forces based on the Hirchhoff-Lave hypothesis and the small elastic-plastic deformations theory are presented. Internal forces tensor is presented in the form of its expansion to the elasticity tensor and the additional terms tensor expressed the physical nonlinearity of the problem. The functions expressed the physical nonlinearity of the material are determined. The relations that allow to determine the range of elastic-plastic deformations on the surface of the present shell and their changing in shell thickness are presented. The examples of the calculation demonstrate the convergence of elastic-plastic deformations method and the range of elastic-plastic deformations in thickness in the spherical shell. Spherical shells with the angle of half-life regarding 90 degree vertical symmetry axis under the action of equally distributed ring loads are observed.

Development and verification of a numerical model for the analysis of geosynthetic-reinforced soil segmental walls under working stress conditions

2005 ◽  
Vol 42 (4) ◽  
pp. 1066-1085 ◽  
Author(s):  
Kianoosh Hatami ◽  
Richard J Bathurst
Keyword(s):  
Numerical Model ◽  
Constitutive Models ◽  
Reinforced Soil ◽  
Stress Conditions ◽  
Soil Reinforcement ◽  
Lagrangian Analysis ◽  
Elastic Plastic ◽  
Geosynthetic Reinforced Soil ◽  
Working Stress ◽  
Good Agreement

The paper describes a numerical model that was developed to simulate the response of three instrumented, full-scale, geosynthetic-reinforced soil walls under working stress conditions. The walls were constructed with a fascia column of solid modular concrete units and clean, uniform sand backfill on a rigid foundation. The soil reinforcement comprised different arrangements of a weak biaxial polypropylene geogrid reinforcement material. The properties of backfill material, the method of construction, the wall geometry, and the boundary conditions were otherwise nominally the same for each structure. The performance of the test walls up to the end of construction was simulated with the finite-difference-based Fast Lagrangian Analysis of Continua (FLAC) program. The paper describes FLAC program implementation, material properties, constitutive models for component materials, and predicted results for the model walls. The results predicted with the use of nonlinear elastic-plastic models for the backfill soil and reinforcement layers are shown to be in good agreement with measured toe boundary forces, vertical foundation pressures, facing displacements, connection loads, and reinforcement strains. Numerical results using a linear elastic-plastic model for the soil also gave good agreement with measured wall displacements and boundary toe forces but gave a poorer prediction of the distribution of strain in the reinforcement layers.Key words: numerical modelling, retaining walls, reinforced soil, geosynthetics, FLAC.

scholarly journals A novel rapid method of purely elastic solution correction to estimate multiaxial elastic-plastic behaviour

2019 ◽  
Vol 6 (3) ◽  
pp. 269-283
Author(s):  
Nicolas Antoni
Keyword(s):  
Three Dimensional ◽  
Elastic Solution ◽  
Upper And Lower Bounds ◽  
Efficient Design ◽  
Effective Parameters ◽  
Relative Deviation ◽  
Elastic Plastic ◽  
Plastic Behaviour ◽  
A New Technique ◽  
Good Agreement

Abstract In structural analysis, it is of paramount importance to assess the level of plasticity a structure may experience under monotonic or cyclic loading as this may have a significant impact, particularly in fatigue analysis for singular areas. For efficient design analyses, it is often searched for a compromise in accuracy that consists in correcting a purely elastic analysis, generally simpler and faster to obtain compared to a full non-linear Finite Element (FE) analysis involving elastic-plastic behaviour, to estimate the actual elastic-plastic solution. There exists a great number of correction techniques in the literature among which the most famous and commonly used are Neuber and ESED energy-based methods. Nonetheless, both of them are known to provide respectively upper and lower bounds of the exact solution in most cases, with a relative deviation depending on the level of multiaxiality and on the amount of stress redistribution due to yielding. The new methodology presented in this paper is based on the well-known multiaxial Radial Return Method (RRM) revisited using effective parameters approach. By essence, it is fast and can be applied either to analytical elastic problems or to more complex three-dimensional elastic FE analyses. The accuracy of the proposed method is assessed by direct comparison with results from Neuber and ESED methods on various examples. It is also shown for each of them that this new method is very good agreement with the exact elastic-plastic solution. Highlights A new technique of purely elastic solution correction is presented and evaluated. The proposed method relies on the modification of Return Radial Method (RRM) considering effective parameters in lieu of initial elastic tensor. The obtained equation preserves the simplicity and efficiency of other well-known energy-based methods such as Neuber and ESED. It is shown on several examples that the proposed technique is in very good agreement with the exact or FE elastic-plastic solution, with very low relative deviation.

scholarly journals Plastic deformations in the ring spherical shells

2018 ◽  
Vol 251 ◽  
pp. 04060
Author(s):  
Avgustina Astakhova
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Thin Shells ◽  
Stress Dependence ◽  
Strain Intensity ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Linear Hardening ◽  
Elastic Plastic ◽  
Development Area

In the present work the results of the study of plastic deformations distribution in the thickness in ring spherical shells are presented. Resolving differential equations system is based on the Hirchhoff-Lave hypothesis, linear thin shells theory and small elastic-plastic deformations theory. The studying of the development area of plastic deformations in shells thickness are performed with using the results of the elastic solutions method. The basic relations of elastic solutions method that allow to determine the distribution areas of plastic deformations in shells thickness and along the generatrix are presented. The diagram of intense stress dependence from the strain intensity with linear hardening is received. The numerical solution is performed by orthogonal run method. Long and short spherical shells under the operation of three evenly distributed ring loads are observed. The shells have a tough jamming along the contour at the bottom and at the top. Dependency between tension intensity and deformations intensity is accepted for the case of a material linear hardening. Area of plastic deformations in shells thickness for three kinds of ring spherical shells are shown. The results for the loads differed by the value in twice are presented.

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