Anwendungsbeispiele zu einem Henckyschen Satz über das plastische Gleichgewicht

Prandtl, L.

doi:10.1002/zamm.19230030601

Cited by 181 publications

(62 citation statements)

References 2 publications

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“…Equation (3.4. 19) shows that the characteristics of the velocity field coincide with the families of slip lines. This is to be expectad from th?…”

Section: A)+mentioning

confidence: 77%

A Quasi-Static Theory of Soil-Structure Interaction

Bedesem¹,

Das²,

Robinson³

1964

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This study treats the effect of the interaction between underground structures and the surrounding soil in reducin6 the loads transmitted to the structure, the so-called "arching" phenomenon.A continuum theory of soils proposed by G. A. Geniev is applied to a quasi-static, plane-stradn problem of arching. The basic partial differential equations are shown to form a hyperbolic set and are solved by the method of characteristics.Consistent stress and velocity fields are obtained.Comparison with available experimental results shows that the Geniev theory underestimates the surface pressure required for failure of an underground structure in relatively dense granular soils.The source of this difficulty is explained and an atnrovimate method of overcoming it is presented.

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“…Equation (3.4. 19) shows that the characteristics of the velocity field coincide with the families of slip lines. This is to be expectad from th?…”

Section: A)+mentioning

confidence: 77%

A Quasi-Static Theory of Soil-Structure Interaction

Bedesem¹,

Das²,

Robinson³

1964

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“…They then extended the field to the right by a small-arc numerical process. They found that the field rapidly approached an asymptotic configuration in which successive slip-lines have the sam e shape ; this is the well-known cycloidal slip-lin e field of Frontard (I g22) and Prandtl ( 1923). The approach is accompanied by discontinuities of diminishing strength; discontinuities propaga ting along the slip-lin es are a ll owed by the h yperbolic natureof the equations, but they are very severely damped at each reflex ion a t th e plates.…”

Section: ~ ~mentioning

confidence: 83%

Plasticity Solution for a Glacier Snout

Nye

1967

J. Glaciol.

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ABSTRACT. The flow near the end of a glacier in a steady state is in vestigated b y using a theoreti ca l model : a plasti c-r ig id materia l with a constant fl ow stress resting on a rough horizontal bed. Starting from a n a ppropria tely chosen slip-lin e far from the end , th e slip-lin e field is constru cted numeri call y a nd continued to th e end of the g lacier. T he field ra pidl y settles down to a form independ ent of t he precise sta rting conditions. I n the region of sma ll surface slope it agrees w ith the approx imate a na lyt ica l solution reported ea rl ier (Nye, 195 1) . To avo id a breakdown in the meth od it is found necessary to modify the bed b y a trivia l amount over th e final 3 m. In prac tice the ice can lose con tact with the bed very near the end, a nd the effect of th is on the so lu tion is discussed.The velocity field is computed for a uniform a bl a ti on-rate. Other distributions of a bla tion-ra te could be accomm odated , but there a ppears to be a cri tica l g rad ient of a bl ation-rate beyond wh ich th e slip-lin e fi eld fail s. R EsUME . Solution de plasticite pour la langue terminale d'un glacier. L 'ecou lement pn:s d e I'extremite d ' un g lacier en etat sta tionna ire est etudie it I'aide d ' un modele theoriqu e : un materi au pl astique-rig ide avec un e con trainte d' ecou lement consta nt sur un li t rugueux hori zonta l. Pa rtant d ' un e ligne de g lissement choisie d'une ma ni ere a ppropriee lo in de I'extremite, le champ d e lignes d e g lissem ent est construit num eriquem ent et continue jusqu 'a I'extre mite du g lacier. Ce cha mp prend rapidement un e for me independante d es conditi ons precises d e depa r t. Dans la region d ' une fa ibl e p ente superfi c ielle, il y a accord avec la solution a na lytique approchee publiee a nteri eu rement (Nye, 195 1) . Pour eviter la non a pplication d e la m e thod e, il s'est avere necessaire de m odifier le lit d ' un e grossiere va leur d ans les 3 derniers metres. En prati que, la glace peut perdre le contact avec le lit tres pres de I'ex tremite et son effet sur la solu tion est discute.L e champ des vitesses est calcul e pou r un e vitesse uniforme d e I'ablation. D'autres distributions de la vitesse d'ablation p euvent ctre u ti lisees, ma is il y a un grad ient cri tiqu e de la vitesse d 'a blation en-d essous duquel le champ d e lignes de g lissement est faux.ZUSAMMENFASSUNG . P lastizitiitsl6sung fiir eine Cletscherzullge. Die E isbewegung na he am Ende ein es stationaren G letschers wird mit Hilfe e in es theoretischen Modell es untersu cht: plastisch-starres Materi a l unter konstanter Fliess-Spannung, das a uf rau hem, hori zonta lem U ntergrund a ufliegt. Ausgehend von ein er passend gewahlten G leit lin ie mit g rossem Zungenabstand wi rd d as G leitl ini enfeld numerisch konstrui ert und bis zur G letscherzu nge fortgesetzt. D as F eld nimmt rasch ein e Gesta lt a n, d ie von d en genauen Ausgangsbedingungen una bhangig ist. Im Gebiet m it geringer Oberflachenneigung stimmt es m it der fruher m...

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“…It is recalled that, for r, ==y" the loads F;= (H=O,v=(1r+2)BC,) and F; = (H=BCs,v=O) respectively derived by Prandtl (1923) and Salençon and Pecker (1995) for foundation Iying on homogeneous cohesive soi!, are lower bound solutions for the bearing capacity in the column reinforced situation soil for the case of a purely cohesive reinforcement material.…”

Section: Yield Design Solutions To Bearing Capacity Ora Column-rein[omentioning

confidence: 99%