A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 2: Numerical applications

Franco, José Ricardo Queiroz; Ponter, A. R. S.

doi:10.1002/(sici)1097-0207(19971015)40:19<3515::aid-nme223>3.0.co;2-w

Cited by 18 publications

(3 citation statements)

References 10 publications

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“…In the case of axisymmetrical shells, the elements which show constant and conical deformation pattern are those whose meridian angles are constant and in this case it might be expected that equations (39), (41) and (42) satisfy the required biorthogonality condition (38). For curved elements, however, the deformation pattern + GH , varies as a function of the meridian angles along the element and it is no longer linear.…”

Section: A General Solution For the Biorthogonality Conditionmentioning

confidence: 99%

A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 1: Theory and fundamental relations

Franco¹,

Ponter

1997

Int. J. Numer. Meth. Engng.

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Engineering Department, ºniversity of¸eicester ºniversity Road,¸eicester¸E1 7RH, º.K. ABSTRACTThis paper describes the theory and the fundamental relations for the development of a displacement formulation for the finite element shakedown and limit analysis of axi-symmetrical shells. The material is assumed to be elastic-perfectly plastic. The technique is developed based upon an upper bound approach using a reformulated kinematic shakedown theorem for a shell with piecewise linear yield conditions. The solution of the problem is obtained by discretizing the shell into finite elements. A consistent relationship between the kinematically admissible velocity fields and the pure plastic strain rate fields during collapse needs to be enforced. Such requirement is satisfied by using the theory of conjugate approximations to minimize the residual of the two independent descriptions of the plastic strain increments. The discretized problem is then reduced to a minimization problem and solved by linear programming. The class of displacement fields chosen assumes plastic hinge lines forming at nodal points and only meridional and circumferential plastic strains occurring within the elements with no change in curvature. Examples of the application of the method are given in the accompanying paper.

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Section: A General Solution For the Biorthogonality Conditionmentioning

confidence: 99%

A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 1: Theory and fundamental relations

Franco¹,

Ponter

1997

Int. J. Numer. Meth. Engng.

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“…One or another of the above mentioned two variables can be defined by optimizing the distribution of internal limit forces S 0 . The relevance of formulating and solving the optimization problems of shell structures at shakedown is based on works important for this particular area [15,[28][29][30].…”

Section: Introductionmentioning

confidence: 99%

An extended shakedown theory on an elastic–plastic spherical shell

Atkočiūnas

Ulitinas

Kalanta

et al. 2015

Engineering Structures

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“…Numerical and experimental methods are employed to investigate the stress and strain distribution in a torispherical shell [2,3]. The stability of ellipsoidal heads under internal and external pressure is studied in [4,5]. Discussed in [6] is the imperfection sensitivity of internally-pressurized toripherical shells.…”

Section: Introductionmentioning

confidence: 99%

Elastoplastic Analysis of Novel Parabola-Arc-Shaped Head for Internal Pressure Vessel

Wang

Liu

2015

AMM

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In this paper, the elastoplastic stress analysis of a novel parabola-arc-shaped head subjected to internal pressure has been carried out using finite element method. Limit loads and burst pressures are obtained for various geometric parameters and compared with the conventional torispherical and ellipsoidal heads. For the same middle diameter and thickness, the novel parabola-arc-shaped head shows better mechanical performance than the torispherical head. The burst pressure is mainly determined by the size of cylinder and the burst always occurs in cylinder. The head can improve the burst load when the cylinder is relatively short. The improvement of the novel parabola-arc-shaped head is almost the same as the ellipsoidal head, while the torispherical head is slightly inferior. As the novel parabola-arc-shaped head can be more easily formed with less material consumed compared to the conventional ones, it should thus be applicable in engineering practice.

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A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 2: Numerical applications

Cited by 18 publications

References 10 publications

A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 1: Theory and fundamental relations

A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 1: Theory and fundamental relations

An extended shakedown theory on an elastic–plastic spherical shell

Elastoplastic Analysis of Novel Parabola-Arc-Shaped Head for Internal Pressure Vessel

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