A modified algorithm of linear matching method for limit analysis

Ri, Jun-Hyok; Hong, Hyon-Sik

doi:10.1007/s00419-017-1258-5

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…However, this yield surface is categorized as a general yield surface involving the interactions of axial load and bending moment. As the contour of constant complementary potential passing through a stress point on this yield surface does not enclose the whole yield surface, it does not meet the necessary condition for a monotonic decreasing upper bound solution in the limit analysis using the LMM [7]. Despite of this deficiency, the two solutions converge in all the cases studied in the current study.…”

Section: Single Ultimate Capacitymentioning

confidence: 82%

“…e upper and lower bound theorems provide the basis for bracketing the plastic limit load of a structural system that consists of the perfectly plastic materials subjected to small strain [1][2][3][4][5]. An alternative for implementing limit analysis is the linear matching method (LMM) [6,7]. e LMM is a class of programming methods based on elastic solutions with spatially distributed material stiffness.…”

Section: Introductionmentioning

confidence: 99%

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Kinematic and Static Solutions for Beam Column with Nonlinear Springs Using the Extended Linear Matching Method

Gao

2021

Shock and Vibration

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In this paper, the kinematic and static solutions for solving the static response of the beam column with nonlinear springs are presented by adopting the extended linear matching method (LMM). The extended LMM can be used to predict the displacement response of the beam-column system consisting of perfectly plastic and strain-softening materials. It is found that the kinematic solution generated by the extended LMM demonstrates a monotonic decrease for perfect plastic materials with certain restrictions on the yield surface. The potential energy of the system is proved to decrease with iterations for both perfect plastic and strain-softening materials if the loading multiplier remains constant. The extended LMM method is then applied to analyse the response of the pile system in a 3-leg offshore platform. An incremental procedure is recommended to determine the peak load for the soil exhibiting strain-softening. A displacement-control approach is used with the loading multiplier obtained from the variation of the potential energy. Good convergence of the method is obtained.

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Section: Single Ultimate Capacitymentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Kinematic and Static Solutions for Beam Column with Nonlinear Springs Using the Extended Linear Matching Method

Gao

2021

Shock and Vibration

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“…7, instead of using Eq. 5, which is called an Elastic Compensation Method (ECM) (Pisano & Fuschi, 2011;Pisano & Fuschi, 2013;Ri & Hong, 2017).…”

Section: Linear Matching Methods (Lmm)mentioning

confidence: 99%

A method for determination of equivalent limit load surface of fiber-reinforced nonlinear composites

Ri¹,

Hong²

2019

10.5267/j.esm

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In this paper, a method for determining the limit load surface of fiber-reinforced nonlinear composites such as elasto-plastic composite is proposed. Using the stress approach of the homogeneous theory and the linear matching method (LMM), the limit load surface of the fiberreinforced composite is numerically evaluated in the π-plane, and at the same time, two limit analyses determine the approximate Hill's anisotropic yield criterion for the limit load surface of the fiber-reinforced composite. The Hill's yield criterion determined by 2 limit analyses becomes the inscribed ellipse of the limit load surface evaluated numerically in the π-plane, and the limit load surface can be evaluated more accurately by the two tangent lines perpendicular to the minor axis of the inscribed ellipse and the circumscribed circle of the inscribed ellipse. This means that the limit load surface of fiber-reinforced nonlinear composite can be completely determined by only 2 limit analyses. In addition, it is found that the limit load surface is related to the equivalent strength surface of composite, and that it satisfies the Reuss and Voigt bounds.

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A dislocation-based finite element method for plastic collapse assessment in solid mechanics

Zona,

Minutolo

2024

Arch Appl Mech

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A displacement-based dislocation map has been used to build the eigenstress stress, which is the base of the structure’s limit analysis. The limit load has been calculated as the upper bound of any equilibrated stress that respects the compatibility inequalities by means of a linear optimization program. The eigenstress stress nodal parameters were assumed as the design variables, and the compatibility inequalities have been obtained from the Mises–Schleicher criterion, assuming that the stress belongs to the corresponding plastic domain. The numerical application has considered a linear secant representation of the domain, with a penalty factor on stresses, to correct the linearization error. Examples concerning a simply supported cantilever beam, a pipe section, and a plate with a circular hole highlighted the accuracy of the procedure with respect to the established literature. Moreover, the procedure has been applied to investigate plane structure examples. A square plate with variable elliptic holes has been analyzed, and the influence of ellipticity on the collapse load has been shown. The effects of porosity and heterogeneity of the structure with respect to the collapse load are shown considering the porous cantilever and representative volume element. The evaluation of the limit load along different element directions envisaged a point-wise calculation of the compatibility domain of the porous material to be used in the macro-scale analysis of the structures made of porous micro-cells.

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A modified algorithm of linear matching method for limit analysis

Cited by 4 publications

References 11 publications

Kinematic and Static Solutions for Beam Column with Nonlinear Springs Using the Extended Linear Matching Method

Kinematic and Static Solutions for Beam Column with Nonlinear Springs Using the Extended Linear Matching Method

A method for determination of equivalent limit load surface of fiber-reinforced nonlinear composites

A dislocation-based finite element method for plastic collapse assessment in solid mechanics

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