Exact solutions of sequential limit analysis of pressurized cylinders with combined hardening based on a generalized Hölder inequality: Formulation and validation

Leu, S.-Y.; Li, R.-S.

doi:10.1016/j.ijmecsci.2012.08.004

Cited by 12 publications

(8 citation statements)

References 24 publications

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“…Namely maximize =minimize (16) As shown above, we have validated the strong duality between the primal problem (6) and the dual problem (15). Based on the primal formulation (6) or the dual formulation (15), we can acquire the exact solution by equating the greatest lower bound to the least upper bound as done in limit analysis [33][34][35].…”

Section: Analytical Backgroundmentioning

confidence: 89%

“…In the previous work on limit analysis [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], a generalized Hölder inequality [36] was employed to play a key role in establishing the kinematic (dual) formulation from the corresponding static (primal) formulation [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. By using a generalized Hölder inequality [36], we also equate the greatest lower bound to the least upper bound [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Based on the strong duality, exact solutions for certain sequential limit analysis problems have been acquired [33]…”

Section: Introductionmentioning

confidence: 99%

“…By using a generalized Hölder inequality [36], we also equate the greatest lower bound to the least upper bound [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Based on the strong duality, exact solutions for certain sequential limit analysis problems have been acquired [33][34][35]. On the other hand, Yang [22] stated the primal (lower bound) formulation in the form of l -norm [22,[36][37] on axial forces of truss members while dealing with large deformation of truss structures by limit analysis sequentially.…”

Section: Introductionmentioning

confidence: 99%

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Shakedown Analysis of Framed Structures: Strong Duality and Primal-dual Analysis

Leu

2014

Procedia Engineering

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The paper is aimed to illustrate the strong duality between the lower and upper bound formulations of shakedown analysis in a novel way. By the lower or upper bound theorem, shakedown analysis is a well-known direct method to evaluate the load carrying capacity of a structure subjected to cyclic loads. In the paper, the Hölder inequality is uniquely utilized to establish the upper bound formulation from the lower bound formulation. Accordingly, the strong duality between them is revealed by duality theorems. Following that, shakedown analysis is performed by the primal-dual algorithm provided by the computing tool MATLAB. Moreover, elastic-plastic analysis is also conducted for comparisons and validations using the commercial finiteelement code ABAQUS. Finally, comparisons with good agreement validate the numerical results presented in the paper.

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Section: Analytical Backgroundmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shakedown Analysis of Framed Structures: Strong Duality and Primal-dual Analysis

Leu

2014

Procedia Engineering

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“…Isotropic hardening model for matrix phase used in this study is isotropic hardening as in Equation 1 and, for non-linear hardening, the most common equations used for isotropic hardening are power law (Ludwik law), Equation 2, and the exponential law (Voce law), Equation 3, which were equations used recently by several authors, for example, Chaboche, 1986, Simo and Hughes, 2006, Steglich et al, 2005, Allain and Bouaziz, 2008, Seifert and Schmidt, 2008, Seifert and Schmidt, 2009, Cardoso and Yoon, 2009, Taherizadeh et al, 2009, Cao et al, 2009, Leu and Li, 2012, Chaaba, 2013. Linear and non-linear evolutions of isotropic hardening, for the matrix phase only, can be calculated according to the equations below, power law or exponential law, respectively:…”

Section: Introductionmentioning

confidence: 99%

Analytical and Numerical Investigation of Hardening Behavior of Porous Media

Khdir

2019

Polytechnic j.

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In this study, a comparative analysis is presented between a new proposed analytical model and numerical results for macroscopic behavior of porous media with isotropic hardening in its matrix. The macroscopic behavior of a sufficiently large representative volume element (RVE), with 200 identical spherical voids, was simulated numerically using finite element method and compared with elementary volume element that contains one void. The matrix of the porous material is considered as elasto-plastic with isotropic hardening obeys exponential law for isotropic hardening. A new parameter was added with exponential law for isotropic hardening to represent the new proposed analytical model for macroscopic isotropic porous hardening. The new added parameter B depended only on the porosity. The results of the new proposed analytical model were compared with numerical results for different types of cyclic loading. Very good agreements were found between the numerical results and the proposed analytical model.

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“…The first strict elastic/plastic solution for the expansion of a hollow cylinder of elastic/plastic material at large strains has been provided by Hill et al ( 1947 ). Subsequent limit analysis has been used by Leu ( 2007 , 2009 ), Leu and Li ( 2012 ) to find solutions for several rigid plastic models. A constitutive equation for nonlinear viscoelasticity has been adopted by Wineman and Min ( 1996 ).…”

Section: Introductionmentioning

confidence: 99%

Evolution of internal variables in an expanding hollow cylinder at large plastic strains

et al. 2016

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An efficient method for calculating the evolution of internal variables in an expanding hollow cylinder of rigid/plastic material is proposed. The conventional constitutive equations for rigid plastic, hardening material are supplemented with quite an arbitrary set of evolution laws for internal variables assuming that the material is incompressible. No restriction is imposed on the hardening law. The problem is solved in Lagrangian coordinates. This significantly facilitates a numerical treatment of the problem. In particular, the initial/boundary value problem is reduced to a system of equations in characteristic coordinates. A finite difference scheme is used for solving these equations. An illustrative example is presented assuming that the internal variables are the equivalent plastic strain and a damage parameter.

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Exact solutions of sequential limit analysis of pressurized cylinders with combined hardening based on a generalized Hölder inequality: Formulation and validation

Cited by 12 publications

References 24 publications

Shakedown Analysis of Framed Structures: Strong Duality and Primal-dual Analysis

Shakedown Analysis of Framed Structures: Strong Duality and Primal-dual Analysis

Analytical and Numerical Investigation of Hardening Behavior of Porous Media

Evolution of internal variables in an expanding hollow cylinder at large plastic strains

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