A novel high-performance mixed membrane finite element for the analysis of inelastic structures

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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.

Section: Interpolation Of Unknown Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Nodargi

Bisegna

2019

Self Cite

“…The stress modes can be derived from the Airy stress function, as a common practice that has been used in prior research (see, eg, other works 25,42,43 ), ie,…”

Section: Stressmentioning

confidence: 99%

A new drilling quadrilateral membrane element with high coarse‐mesh accuracy using a modified Hu‐Washizu principle

Chang

Lee

Carr

et al. 2019

Summary By utilizing a modified Hu‐Washizu principle, a new mixed variational framework and a corresponding high‐performing four‐node membrane element with drilling degrees of freedom, named as GCMQ element, are proposed. In this work, the generalized conforming concept, which is originally proposed within a displacement‐based formulation, is extended to a mixed formulation. The new element is able to handle higher‐order displacement, strain, and stress distributions. The interpolations are complete up to second order for stress and strain. The enhanced strain field is optimized so that a complete cubic displacement field can be represented. For numerical integration, a five‐point scheme is proposed to minimize computational cost. Compared to other four‐node elements in existing literature, numerical examples show that the proposed element has a better performance regarding predictions of both displacements and internal forces, particularly with coarse meshes. The new element is also free from shear locking and volumetric locking. Due to the nature of the mixed framework, GCMQ can be directly used in elastoplastic applications.

A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element

Liguori

Madeo

Garcea

2022

Mixed assumed stress finite elements (FEs) have shown good advantages over traditional displacement‐based formulations in various contexts. However, their use in incremental elasto‐plasticity is limited by the need for return mapping schemes which preserve the assumed stress interpolation. For elastic‐perfectly plastic materials and small deformation problems, the integration of the constitutive equation furnishes a closest point projection (CPP) involving all the element stress parameters. In this work, a dual decomposition strategy is adopted to split this problem into a series of CPPs at the integration points level and in a nonlinear system of equations over the element, in order to simplify its solution. The strategy is tested with a four nodes mixed shell FE, named MISS‐4, characterized by an equilibrated stress interpolation which improves the accuracy. Two decomposition strategies are tested to express the plastic admissibility either in terms of stress resultants or point‐wise Cauchy stresses. The recovered elasto‐plastic solution preserves all the advantages of MISS‐4, namely it is accurate for coarse meshes in recovering the equilibrium path and evaluating the limit load showing a quadratic rate of convergence, as demonstrated by the numerical results.