Elastoplastic analysis of plane stress/strain structures via restricted basis linear programming

Moharrami, Hamid; Mahini, M. R.; Cocchetti, Giuseppe

doi:10.1016/j.compstruc.2014.08.007

Cited by 7 publications

(5 citation statements)

References 28 publications

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“…That leads to the HW principle (Section 3.1), which can be derived by minimization of the generalized HW functional with respect to the fluxes of internal variables, and hence takes displacement, stress and strain fields as primary variables. Examples of its application in elastoplasticity can be found in [100,27,18,47,61,67]. In the same line of having a rich and flexible strain approximation, a modification of the HW principle, in which the strain field is represented as the sum of a compatible part and of an enhanced part, yields the enhanced strain (ES) formulations (Section 3.2), explored in elastoplasticity in [88,90,76,77,75].…”

Section: Mixed Variational Formulationsmentioning

confidence: 99%

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An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

Nodargi

2018

Arch Computat Methods Eng

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As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard displacement-based finite element formulations, attention is here focused on the use of mixed methods as approximation technique, within the small strain framework, for the mechanical problem of inelastic bidimensional structures. Despite a great flexibility characterizes mixed element formulations, several theoretical and numerical aspects have to be carefully taken into account in the design of a high-performance element. The present work aims at providing the basis for methodological analysis and comparison in such aspects, within the unified mathematical setting supplied by generalized standard material model and with special interest towards elastoplastic media. A critical review of the state-of-the-art computational methods is delivered in regard to variational formulations, selection of interpolation spaces, numerical solution strategies and numerical stability. Though those arguments are interrelated, a topic-oriented presentation is resorted to, for the very rich available literature to be properly examined. Finally, the performances of several significant mixed finite element formulations are investigated in numerical simulations.

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Section: Mixed Variational Formulationsmentioning

confidence: 99%

“…where (H e ) h and Q h have been introduced in equations (61) and (31) 1 , respectively, and the discrete element problem results in:…”

Section: Hallinger-reissner Functionalmentioning

confidence: 99%

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

Nodargi

2018

Arch Computat Methods Eng

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“…Nevertheless, a main choice concerns the possibility of assuming the strain as independent variable as well. In such a case, a Hu‐Washizu principle can be invoked, taking displacement, stress, and strain fields as primary variables . Alternatively, with the clue that a highly nonlinear spatial distribution of the strain field stems from a similar pattern of the plastic strain, a deeply explored strategy amounts at replacing the strain with the plastic multiplier, thus obtaining a complementary mixed formulation …”

Section: Introductionmentioning

confidence: 99%

“…In such a case, a Hu-Washizu principle can be invoked, taking displacement, stress, and strain fields as primary variables. [24][25][26][27][28] Alternatively, with the clue that a highly nonlinear spatial distribution of the strain field stems from a similar pattern of the plastic strain, a deeply explored strategy amounts at replacing the strain with the plastic multiplier, thus obtaining a complementary mixed formulation. [29][30][31][32][33][34][35] Surprisingly, much less attention has been devoted to mixed finite element formulations in problems involving damaging materials.…”

Section: Introductionmentioning

confidence: 99%

A mixed finite element for the nonlinear analysis of in‐plane loaded masonry walls

Nodargi

Bisegna

2019

Numerical Meth Engineering

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Summary A mixed membrane eight‐node quadrilateral finite element for the analysis of masonry walls is presented. Assuming that a nonlinear and history‐dependent 2D stress‐strain constitutive law is used to model masonry material, the element derivation is based on a Hu‐Washizu variational statement, involving displacement, strain, and stress fields as primary variables. As the behavior of masonry structures is often characterized by strain localization phenomena, due to strain softening at material level, a discontinuous, piecewise constant interpolation of the strain field is considered at element level, to capture highly nonlinear strain spatial distributions also within finite elements. Newton's method of solution is adopted for the element state determination problem. For avoiding pathological sensitivity to the finite element mesh, a novel algorithm is proposed to perform an integral‐type nonlocal regularization of the constitutive equations in the present mixed formulation. By the comparison with competing serendipity displacement‐based formulation, numerical simulations prove high performances of the proposed finite element, especially when coarse meshes are adopted.

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“…Cook's membrane: geometry and material propertiesThis example is also a well-known benchmark to evaluate the effectiveness of the finite element formulation in elastoplastic behavior[40,48,49]. Material properties adopted are: Poisson's ration 0…”

mentioning

confidence: 99%

Elastoplastic analysis of plane structures using improved membrane finite element with rotational DOFs: Elastoplastic analysis of plane structures

Ayadi

Meftah

Sedira

2020

Frattura Ed Integrità Strutturale

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In this work, the small-strain elastoplastic behavior of structures is analyzed using an improved nonlinear finite element formulation. In this framework, an eight-node quadrilateral finite element denoted PFR8 (Plane Fiber Rotation) that belongs to the set of elements with rotational degrees of freedom is developed. Its formulation stems from the plane adaptation of the Space Fiber Rotation (SFR) concept that considers virtual rotations of nodal fiber within the element. This approach results in an enhancement of the displacement vector approximation. Von-Mises yield criteria have been applied for yielding of the materials along with the associated flow rule. Newton-Raphson method has been used to solve the nonlinear equations. To assess the performance of the proposed element, benchmark problems are addressed and the results are compared with some analytical and numerical solutions from the literature.

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Elastoplastic analysis of plane stress/strain structures via restricted basis linear programming

Cited by 7 publications

References 28 publications

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

An Overview of Mixed Finite Elements for the Analysis of Inelastic Bidimensional Structures

A mixed finite element for the nonlinear analysis of in‐plane loaded masonry walls

Elastoplastic analysis of plane structures using improved membrane finite element with rotational DOFs: Elastoplastic analysis of plane structures

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