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.

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.

The Application of Limit Analysis to Punch-Indentation Problems

1953 ◽  
Vol 20 (4) ◽  
pp. 453-460
Author(s):  
R. T. Shield ◽  
D. C. Drucker
Keyword(s):  
Limit Analysis ◽  
Plane Surface ◽  
Plastic Material ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Flat Punch ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract Limit analysis is applied to obtain upper and lower bounds for the punch pressure in the indentation of the plane surface of an elastic-perfectly plastic material by a flat rigid punch. The two-dimensional flat punch and the three-dimensional flat square and rectangular punch problems are considered. The analysis assumes Tresca’s yield criterion of constant maximum shearing stress k, during plastic deformation. It is shown that the pressure required to produce indentation in the two-dimensional problem lies between 5k and (2 + π)k. The lower bound obtained for any rectangular punch is again 5k while the upper bound for a smooth punch lies between 5.71k for a square and (2 + π)k for a very long rectangle. A value of 5.36k is found for a ratio of length to breadth of 3. The limit pressure for a uniformly loaded area, as distinguished from an area loaded by a punch, is bracketed by 5k and (2 + π)k when the area is convex.

Yield Functions and Flow Rules for Porous Pressure-Dependent Strain-Hardening Polymeric Materials

1999 ◽  
Vol 67 (2) ◽  
pp. 288-297 ◽  
Author(s):  
J. H. Lee ◽  
J. Oung
Keyword(s):  
Closed Form ◽  
Strain Hardening ◽  
Upper Bound ◽  
Plastic Material ◽  
Yield Criterion ◽  
Polymeric Materials ◽  
Yield Function ◽  
Special Cases ◽  
Yield Functions ◽  
Spherical Voids

To characterize the response of progressively damaged glassy polymers due to the presence and evolution of voids, yield functions and flow rules were developed systematically for a pressure-dependent matrix following the modified von Mises criterion. A rigid-perfectly plastic material was first assumed. The upper bound method was used with a velocity field which has volume preserving and shape changing portions. Macroscopic yield criterion in analytical closed form was first obtained for spherical voids which is valid for all possible macroscopic strain rate fields. Macroscopic yield criteria in analytical closed form were then obtained for cylindrical voids for the special cases of axisymmetric and plane-strain modes of deformation. The upper-bound solutions were subsequently improved to better match analytical solutions for pure hydrostatic loading. Characteristics of the yield function as a function of pressure dependency and void fraction were studied in detail. Generalization of the model for spherical voids to include elasticity as well as strain hardening of the matrix was then obtained. An example for the uniaxial response of a progressively damaged material was then used to illustrate one possible application of the full set of constitutive equations. [S0021-8936(00)02902-0]

Limit analysis for plates: a simple loading problem involving a complex exact solution

1972 ◽  
Vol 272 (1228) ◽  
pp. 463-492 ◽  
Keyword(s):  
Exact Solutions ◽  
Limit Analysis ◽  
Yield Criterion ◽  
Point Load ◽  
Yield Line Theory ◽  
Perfectly Plastic ◽  
Aspect Ratios ◽  
Edge Conditions ◽  
Practical Standpoint ◽  
Line Theory

Known exact solutions in limit analysis for rigid perfectly plastic plates are relatively scarce and this has led Wood (1965) to question the soundness of the theory by suggesting that exact solutions may not exist even for apparently simple cases of loading, shape of plate and edge conditions. The alternative explanation for the scarcity is that simple problems may require rather complex exact solutions: this is exemplified in the solution now obtained for a central point load acting on a simply supported rectangular plate, with yielding governed by the square yield criterion. When the aspect ratio (length/breadth) of the rectangle lies in the range 1 to 2.25 approximately, the exact mechanism is relatively complex, involving regions of anticlastic curvature at the corners. From the practical standpoint, the known simple upper bounds of yield-line theory for this problem give the collapse load exactly for aspect ratios greater than about 2.25 and are in error by less than 4 % for smaller aspect ratios.

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.

Plastic Collapse of Orthotropic Plates

1982 ◽  
Vol 26 (04) ◽  
pp. 286-295
Author(s):  
John C. Christodoulides ◽  
Joao G. de Oliveira
Keyword(s):  
Limit Analysis ◽  
Lateral Pressure ◽  
Yield Criterion ◽  
Plastic Collapse ◽  
Orthotropic Plates ◽  
Perfectly Plastic ◽  
Technical Theory ◽  
Orthotropic Shells ◽  
Theory Of Shells

A yield criterion for thin orthotropic shells expressed in terms of generalized stresses is first derived. This yield criterion is based on the yield criterion proposed by Hill for anisotropic continua and it is consistent with all the assumptions usually adopted in the technical theory of shells. As an example of application of this criterion the collapse of perfectly plastic rectangular orthotropic plates subjected to a uniform lateral pressure is studied using the Theorems of Limit Analysis.

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 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.

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.

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