Axial force effect on the overall buckling of a compound reinforced shell structure with the positive Gaussian curvature at an external pressure

Equations describing the stress field and velocity field occurring in a circular cylindrical shell at plastic collapse are derived corresponding to stress states lying on each face of a yield surface for a uniform shell of material obeying the Tresca yield condition. They are then applied to the case of a shell under combined axisymmetric loadings (moment, shear force, and axial force) at one end and uniform internal or external pressure on the lateral surface. For a sufficiently long shell, complete solutions are obtained for a fixed far end, and for a certain range of values of axial force and pressure, they are obtained for a free far end. All the solutions are represented by either closed form or by quadratures. It is shown that in many cases the radial velocity field is proportional to the shear force.

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Umbilical points on surfaces in RN

Nagoya Mathematical Journal ◽

10.1017/s002776300000026x ◽

1985 ◽

Vol 100 ◽

pp. 135-143 ◽

Cited By ~ 2

Author(s):

Kazuyuki Enomoto

Keyword(s):

Gaussian Curvature ◽

Mean Curvature ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Normal Connection ◽

Round Sphere ◽

Positive Gaussian Curvature ◽

Connected Surface ◽

Umbilical Points ◽

The Mean

Let ϕ: M → RN be an isometric imbedding of a compact, connected surface M into a Euclidean space RN. ψ is said to be umbilical at a point p of M if all principal curvatures are equal for any normal direction. It is known that if the Euler characteristic of M is not zero and N = 3, then ψ is umbilical at some point on M. In this paper we study umbilical points of surfaces of higher codimension. In Theorem 1, we show that if M is homeomorphic to either a 2-sphere or a 2-dimensional projective space and if the normal connection of ψ is flat, then ψ is umbilical at some point on M. In Section 2, we consider a surface M whose Gaussian curvature is positive constant. If the surface is compact and N = 3, Liebmann’s theorem says that it must be a round sphere. However, if N ≥ 4, the surface is not rigid: For any isometric imbedding Φ of R3 into R4 Φ(S2(r)) is a compact surface of constant positive Gaussian curvature 1/r2. We use Theorem 1 to show that if the normal connection of ψ is flat and the length of the mean curvature vector of ψ is constant, then ψ(M) is a round sphere in some R3 ⊂ RN. When N = 4, our conditions on ψ is satisfied if the mean curvature vector is parallel with respect to the normal connection. Our theorem fails if the surface is not compact, while the corresponding theorem holds locally for a surface with parallel mean curvature vector (See Remark (i) in Section 3).

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Strength and stability of double cylindrical shell structure subjected to hydrostatic external pressure—Part I: strength

Marine Structures ◽

10.1016/s0951-8339(03)00034-0 ◽

2003 ◽

Vol 16 (5) ◽

pp. 373-395 ◽

Cited By ~ 2

Author(s):

Ding Haixu

Keyword(s):

Cylindrical Shell ◽

Shell Structure ◽

External Pressure ◽

Pressure Part

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Tensor force effect on proton shell structure in neutron-rich Ca isotopes

Science China Physics Mechanics and Astronomy ◽

10.1007/s11433-013-5143-0 ◽

2013 ◽

Vol 56 (9) ◽

pp. 1719-1729 ◽

Cited By ~ 8

Author(s):

ZhenYu Li ◽

YanZhao Wang ◽

GuoLiang Yu ◽

JianZhong Gu

Keyword(s):

Shell Structure ◽

Tensor Force ◽

Force Effect ◽

Proton Shell

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Optimization of a composite conical ring-reinforced shell under external pressure

Soviet Applied Mechanics ◽

10.1007/bf00883857 ◽

1983 ◽

Vol 19 (12) ◽

pp. 1082-1089 ◽

Cited By ~ 1

Author(s):

R. B. Rikards ◽

V. O. �glais ◽

M. V. Goldmanis

Keyword(s):

External Pressure ◽

Reinforced Shell

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Influence of Pressure in Pipeline Design: Effective Axial Force

24th International Conference on Offshore Mechanics and Arctic Engineering: Volume 3 ◽

10.1115/omae2005-67502 ◽

2005 ◽

Cited By ~ 14

Author(s):

Olav Fyrileiv ◽

Leif Collberg

Keyword(s):

Axial Force ◽

Local Buckling ◽

External Pressure ◽

Pressure Effects ◽

Offshore Pipeline ◽

Local Stresses ◽

Global Buckling ◽

The One ◽

Pipeline Design ◽

Force Concept

This paper discusses use of the effective axial force concept in offshore pipeline design in general and in DNV codes in particular. The concept of effective axial force or effective tension has been known and used in the pipeline and riser industry for some decades. However, recently a discussion about this was initiated and doubt on how to treat the internal pressure raised. Hopefully this paper will contribute to explain the use of this concept and remove the doubts in the industry, if it exists at all. The concept of effective axial force allows calculation of the global behaviour without considering the effects of internal and/or external pressure in detail. In particular, global buckling, so-called Euler buckling, can be calculated as in air by applying the concept of effective axial force. The effective axial force is also used in the DNV-RP-F105 “Free spanning pipelines” to adjust the natural frequencies of free spans due to the change in geometrical stiffness caused by the axial force and pressure effects. A recent paper claimed, however, that the effect was the opposite of the one given in the DNV-RP-F105 and may cause confusion about what is the appropriate way of handling the pressure effects. It is generally accepted that global buckling of pipelines is governed by the effective axial force. However, in the DNV Pipeline Standard DNV-OS-F101, also the local buckling criterion is expressed by use of the effective axial force concept which easily could be misunderstood. Local buckling is, of course, governed by the local stresses, the true stresses, in the pipe steel wall. Thus, it seems unreasonable to include the effective axial force and not the true axial force as used in the former DNV Pipeline Standard DNV’96. The reason for this is explained in detail in this paper. This paper gives an introduction to the concept of effective axial force. Further it explains how this concept is applied in modern offshore pipeline design. Finally the background for using the effective axial force in some of the DNV pipeline codes is given.

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