Limit Design of a Full Reinforcement for a Circular Cutout in a Uniform Slab

1952 ◽  
Vol 19 (3) ◽  
pp. 397-401
Author(s):  
H. J. Weiss ◽  
W. Prager ◽  
P. G. Hodge
Keyword(s):  
Upper Bound ◽  
Plastic Material ◽  
Yield Criterion ◽  
Curved Beam ◽  
Shearing Stress ◽  
Concentric Ring ◽  
Perfectly Plastic ◽  
Circular Cutout

Abstract A thin square slab with a central circular cutout reinforced by a concentric ring is subjected to uniform tensions Tx and Ty on the exterior edges. It is desired to determine the dimensions of the reinforcement if the slab is not to collapse under any load which could be supported by a similar slab without any cutout or reinforcement. It is assumed that the slab and reinforcement are made of a perfectly plastic material which satisfies the Tresca yield criterion of maximum shearing stress, and that the dimensions of the reinforcement are such that it may reasonably be approximated by a curved beam. Under these assumptions, an upper bound on the necessary thickness of the reinforcement for any given radius is obtained. Certain practical limitations of the theory are discussed.

Three-Dimensional Analysis of Ice Sheet Indentation: Limit Analysis Solutions

1989 ◽  
Vol 111 (1) ◽  
pp. 63-69 ◽  
Author(s):  
D. G. Karr ◽  
J. C. Watson ◽  
M. HooFatt
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Plastic Material ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Upper Bound Theorem ◽  
Infinite Layer ◽  
Perfectly Plastic ◽  
Aspect Ratios

A method is presented for determining the collapse pressures of an ice sheet subjected to a uniformly distributed edge load by applying the upper-bound theorem of limit analysis. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. A quadratic anisotropic yield criterion is used to calculate the indentation pressures. The ice sheet consists of columnar ice and is assumed isotropic in the plane of the ice sheet. Upper-bound solutions are found by optimizing a three-dimensional discontinuous velocity field representing an assumed collapse pattern of the ice sheet. Solutions are based on various ratios of indentor width to ice thickness, thereby providing an envelope of indentation pressures over a range of aspect ratios, from conditions of plane strain to plane stress. Solutions are then compared with corresponding two and three-dimensional lower-bound analyses.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

On Friction of Ploughing by Rigid Asperities in the Presence of Straining—Upper Bound Method

1990 ◽  
Vol 112 (2) ◽  
pp. 324-329 ◽  
Author(s):  
A. Azarkhin ◽  
O. Richmond
Keyword(s):  
Finite Element ◽  
Friction Factor ◽  
Upper Bound ◽  
Plastic Material ◽  
High Accuracy ◽  
The Other ◽  
Periodic Array ◽  
Combined Loading ◽  
Upper Bound Method ◽  
Perfectly Plastic

Upper bound applications traditionally assume that a rigid/perfectly-plastic material moves by rigid blocks, creating discontinuities of velocity at the interfaces between the blocks. In the present version, the elements (blocks) are plastically deformable and there are no velocity discontinuities between adjacent sides. Since this modification incorporates major features of finite element representation employing arbitrary cells, it allows the use of many parameters for minimization, thus achieving high accuracy. On the other hand, it retains the advantage of upper bound techniques in that the incremental procedure for loading is not necessary, and the results for steady processes are obtained directly. Some energy statements for combined loading are derived and a technique for calculating the ploughing force is presented. Examples for a single fully embedded rigid pyramid and a periodic array of asperities ploughing through the rigid/perfectly plastic material in the presence of subsurface straining are given. The friction factor decreased as the rate of subsurface straining increased, as the pyramid angle of the asperities increased, and as the distance between asperities increased.

Dynamic Plastic Response of Circular Plates With Transverse Shear and Rotatory Inertia

1980 ◽  
Vol 47 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Norman Jones ◽  
J. Gomes de Oliveira
Keyword(s):  
Transverse Shear ◽  
Plastic Material ◽  
Yield Criterion ◽  
Circular Plates ◽  
Plastic Response ◽  
Governing Equations ◽  
Rotatory Inertia ◽  
Perfectly Plastic ◽  
Shear Effects ◽  
Transverse Shear Effects

The response of a simply supported circular plate made from a rigid perfectly plastic material and subjected to a uniformly distributed impulsive velocity is developed herein. Plastic yielding of the material is controlled by a yield criterion which retains the transverse shear force as well as bending moments and the influence of rotatory inertia is included in the governing equations. Various equations and numerical results are presented which may be used to assess the importance of transverse shear effects and rotatory inertia for this particular problem.

Axisymmetric Elastoplasticity of a Temperature-Sensitive Functionally Graded Cylindrical Vessel

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Mojtaba Sadeghian ◽  
Hamid Ekhteraei Toussi
Keyword(s):  
Plastic Material ◽  
Yield Criterion ◽  
Small Deformation ◽  
Functionally Graded ◽  
Cylindrical Vessel ◽  
Linear Functions ◽  
Temperature Sensitive ◽  
Power Functions ◽  
Closed Form Solutions ◽  
Perfectly Plastic

Based on the small deformation theory and Tresca's yield criterion an axisymmetric, plane strain, elastoplastic, thermal stress analysis for a cylindrical vessel made of functionally graded elastic, perfectly plastic material is offered. Elastic modulus and yield strength coefficients are assumed to be power functions of radius and linear functions of temperature. A cylindrical vessel is taken to be composed of two or more nested fully elastic and perfectly plastic cylinders. By comparing the values of the deformation or stress components in the interfaces of the neighboring cylinders, a system of equations is formed. The interfacial boundary values of the fully elastic or perfectly plastic regions are obtained by simultaneous solution of the resulting interfacial consistency conditions. Having prepared the closed form solutions for the stress fields in purely elastic and purely plastic regions, the distribution of stress throughout the vessel can be obtained. Using this model, in some sample problems, the influences of temperature and pressure on the stress, strain, and plastic zone patterns are studied. The location of plastic zones is obtained for a class of material property compositions.

Limit Analysis of Ice Sheet Indentation

1983 ◽  
Vol 105 (3) ◽  
pp. 352-355 ◽  
Author(s):  
D. G. Karr ◽  
S. C. Das
Keyword(s):  
Limit Analysis ◽  
Plastic Material ◽  
Yield Criterion ◽  
Ice Sheet ◽  
Yield Function ◽  
Infinite Layer ◽  
Perfectly Plastic ◽  
Aspect Ratios ◽  
Yield Functions ◽  
Stress Ratios

The methods of plastic limit analysis are used to determine the indentation pressures of a flat rectangular punch on an ice sheet. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. Lower bounds are computed by application of the lower bound limit theorem. The suitability of basic yield functions are assessed based on their ability to predict failure at demonstrated ice failure stress ratios. The particular yield functions that are employed include the generalized Mohr-Coulomb (or Drucker-Prager) criterion, a modified Drucker-Prager criterion, as well as a parabolic yield criterion used previously in literature on this topic. A study of the effects on indentation pressure of varying ice strength parameters is presented. Limit analysis solutions are obtained for plane stress conditions, and thus the applicability of a particular yield function can be evaluated for a range of ice strengths for indentation problems involving high aspect ratios.

Numerical Simulation of the Installation and Extraction Process of Spudcan Foundations in Clay

2009 ◽  
Author(s):  
Jun Liu ◽  
Yuxia Hu
Keyword(s):  
Plastic Material ◽  
Yield Criterion ◽  
Strain Analysis ◽  
Small Strain ◽  
Extraction Process ◽  
Interface Roughness ◽  
Large Displacement ◽  
Centrifuge Model Test ◽  
Element Analysis ◽  
Perfectly Plastic

This paper presents results from large displacement finite element analysis for spudcan foundation penetrating into and extracting from normally consolidated (NC) clay. The soil was idealized as an elastic-perfectly plastic material obeying a Mohr-Coulomb yield criterion and the large displacement analysis was carried out using Remeshing and Interpolating Technique with Small Strain (RITSS) model to simulate the full installation and extraction process. The numerical results were compared with centrifuge model test data and existing analytical solutions. A full parametric study was undertaken to quantify the influence on spudcan extraction process from soil strength profile, foundation interface roughness and penetration depth. The extraction results showed that the normalized uplift resistance after spudcan installation was much lower than that from small strain analysis, and it was also lower than that of pre-embedded case. Thus it is necessary to apply RITSS method in spudcan extraction simulation after installation.

The Upper Bound Approach to Plane Strain Problems Using Linear and Rotational Velocity Fields—Part II: Applications

1986 ◽  
Vol 108 (4) ◽  
pp. 307-316 ◽  
Author(s):  
Betzalel Avitzur ◽  
Waclaw Pachla
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Metal Cutting ◽  
Failure Modes ◽  
Plastic Material ◽  
Rotational Velocity ◽  
Optimization Procedure ◽  
Velocity Fields ◽  
Perfectly Plastic ◽  
Strip Drawing

Following Part I which investigated an upper bound approach to plane strain deformation of a rigid, perfectly plastic material, this Part II considers the same approach as applied to actual forming operations. The processes of drawing and extrusion, of metal cutting and of rolling are analyzed, and explicit equations are developed to calculate the surfaces of velocity discontinuity (shear boundaries), velocity discontinuities, and the upper bound on power for these processes. Both the simple, unielement velocity fields as well as the more complex multielement fields are explored. The upper bound solution is shown to be a function of the independent (input) and pseudoindependent (assumed) process parameters as minimized by an optimization procedure. Rules concerning the assumption of pseudoindependent parameters are presented and the optimization procedure is discussed. Final conclusions lead the way for the application of upper bound analyses to such industrial processes as sheet and strip drawing, extrusion, forging, rolling, leveling, ironing and machining, and to the investigation of such flow failure modes as central bursting, piping and end splitting (alligatoring).

Extension of the Upper Bound Method to Include Estimation of Stresses

1991 ◽  
Vol 58 (2) ◽  
pp. 493-498 ◽  
Author(s):  
A. Azarkhin ◽  
O. Richmond
Keyword(s):  
Plastic Deformation ◽  
Stress Field ◽  
Upper Bound ◽  
Plastic Material ◽  
Approximate Solutions ◽  
Incompressible Material ◽  
Bulk Deformation ◽  
Upper Bound Method ◽  
Convenient Tool ◽  
Perfectly Plastic

The upper bound method is a convenient tool for evaluating the rate of work in processes involving predominantly plastic deformation of rigid/perfectly plastic material. Since the rate of work for an incompressible material depends only on the deviator portion of the stress, the hydrostatic portion does not enter the formulation and the stress field is not determined. Here we show that this limitation can be overcome by adding a relatively simple postprocessing procedure. We then apply this technique to examples of rigid asperities penetrating a plastic material undergoing subsurface bulk deformation and compare our results with previous approximate solutions.

On the stability of supported excavations

1984 ◽  
Vol 21 (2) ◽  
pp. 338-348 ◽  
Author(s):  
A. M. Britto ◽  
O. Kusakabe
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Plastic Material ◽  
Cohesive Soil ◽  
Perfectly Plastic ◽  
Centrifuge Tests ◽  
Bentonite Slurry ◽  
Undrained Conditions ◽  
Elastic Perfectly Plastic ◽  
The Stability

Unsupported plane strain trenches and axisymmetric shafts cannot be excavated to great depths in a purely cohesive soil. Therefore, it is standard practice to provide some form of support. Timber supports with struts are conventional and quite common. Bentonite slurry support has become more popular in recent years especially in the construction of diaphragm walls. In this paper the effect of rigid lateral support and slurry support on the stability (mode of failure) for both plane strain and axisymmetric excavations are investigated under undrained conditions. When immediate failure is of interest in saturated clays the changes in the water content can be neglected and the soil can be treated as a [Formula: see text] material. For the purposes of the analyses presented here the lateral support is assumed to be rigid and the soil is idealized as an elastic perfectly plastic material with cohesion Cu. The results from upper bound calculations, finite element collapse analyses, and centrifuge tests are presented. The analogy between deep footing failure and base failure of excavation allows the solutions for the footing problem to be interpreted for trench excavations. It is found that slurry support is more effective than rigid lateral support for axisymmetric excavations. The slurry support reduces the amount of surface settlement and also stabilises the trench against base failure. For excavations with rigid lateral support the possibility of base failure is greatly increased. The results are presented in the form of stability charts. Keywords: limit analysis, slurry support, stability number, supported excavation, upper bound solution.

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