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.

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.

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.

Passive earth-pressure coefficients by upper-bound numerical limit analysis

2011 ◽  
Vol 48 (5) ◽  
pp. 767-780 ◽  
Author(s):  
Armando N. Antão ◽  
Teresa G. Santana ◽  
Mário Vicente da Silva ◽  
Nuno M. da Costa Guerra
Keyword(s):  
Upper Bound ◽  
Limit Analysis ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Earth Pressure ◽  
Wall Friction ◽  
Passive Earth Pressure ◽  
Upper Bound Theorem ◽  
Pressure Coefficients ◽  
Bound Theorem

A three-dimensional (3D) numerical implementation of the limit analysis upper-bound theorem is used to determine passive horizontal earth-pressure coefficients. An extension technique allowing determination of the 3D passive earth pressures for any width-to-height ratios greater than 7 is presented. The horizontal passive earth-pressure coefficients are presented and compared with solutions published previously. Results of the ratio between the 3D and two-dimensional horizontal passive earth-pressure coefficients are shown and found to be almost independent of the soil-to-wall friction ratio. A simple equation is proposed for calculating this passive earth-pressure ratio.

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.

scholarly journals A bubble-enhanced quadrilateral finite element for estimation bearing capacity factors of strip footing

2021 ◽  
Vol 15 (2) ◽  
pp. 77-89
Author(s):  
Vo Minh Thien
Keyword(s):  
Finite Element ◽  
Bearing Capacity ◽  
Upper Bound ◽  
Limit Analysis ◽  
Optimization Problems ◽  
Plastic Material ◽  
Strip Footing ◽  
Flow Rule ◽  
Upper Bound Theorem ◽  
Quadrilateral Finite Element

In this paper, a computational approach using a combination of the upper bound theorem and the bubble-enhanced quadrilateral finite element (FEM-Qi6) is proposed to evaluate bearing capacity factors of strip footing in cohesive-frictional soil. The new element is built based on the quadrilateral element (Q4) by adding a pair of internal nodes to solve the volumetric locking phenomenon. In the upper bound finite element limit analysis, the soil behaviour is described as a perfectly plastic material and obeys associated plastic flow rule following the Mohr-Coulomb failure criterion. The discrete limit analysis problem can be formulated in the form of the well-known second-order cone programming to utilize the interior-point method efficiently. The bearing capacity factors of strip footing and failure mechanisms in both rough and smooth interfaces are obtained directly from solving the optimization problems and presented in design tables and charts for engineers to use. To demonstrate the accuracy of the proposed method, the results of bearing capacity factors using FEM-Qi6 were compared with those available in the literature. Keywords: limit analysis; bearing capacity factors; strip footing; SOCP; FEM-Qi6.

Three-Dimensional Analysis of Ice Sheet Indentation: Lower-Bound Solutions

1988 ◽  
Vol 110 (1) ◽  
pp. 81-86 ◽  
Author(s):  
D. G. Karr
Keyword(s):  
Lower Bound ◽  
Sea Ice ◽  
Plane Strain ◽  
Plane Stress ◽  
Limit Analysis ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Plastic Limit ◽  
Aspect Ratios ◽  
Plastic Limit Analysis

The methods of plastic limit analysis are used to determine the indentation pressures of a flat rigid punch on a columnar ice sheet. The ice sheet is idealized as a semi-infinite layer of elastic-perfectly plastic material. Representative strength parameters of columnar sea ice are used to define anisotropic yield criteria for the ice sheet. The anisotropic yield criteria reflect the variations in mechanical properties caused by the horizontal orientation of the c-axis of sea ice in the columnar zone. Numerical results are obtained by applying the lower-bound theorem of plastic limit analysis. A three-dimensional stress field is optimized for a given ice condition for various indentor sizes. The effects of varying the aspect ratio (defined as the ratio of indentor width to ice thickness) are then addressed. A comparison of results for intermediate aspect ratios to results for extremely high (plane stress) and extremely low (plane strain) aspect ratios is presented. It is found that the transition from plane stress to plane strain is governed by the tensile strength of the ice medium.

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.

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