A mixed isostatic 16 dof quadrilateral membrane element with drilling rotations, based on Airy stresses

Summary A new four‐node quadrilateral membrane finite element with drilling rotational degree of freedom based on the enhanced assumed strain formulation is presented. A simple formulation is achieved by five incompatible modes that are added to the Allman‐type interpolation. Furthermore, modified shape functions are used to improve the behaviour of distorted elements. Numerical results show that the proposed new element exhibits good numerical accuracy and improved performance, and in many cases, superior to existing elements. In particular, Poisson's locking in nearly incompressible elasticity fades and the element performs well when it becomes considerably distorted even when it takes almost triangular shape. Copyright © 2016 John Wiley & Sons, Ltd.

Section: Numerical Testsmentioning

confidence: 99%

A new enhanced assumed strain quadrilateral membrane element with drilling degree of freedom and modified shape functions

Boutagouga

2016

“…Accordingly, a complete cubic basis of self-equilibrated stresses, consisting of 15 stress modes, is initially generated by a fifth-degree Airy's function. 39,49,50 Then, because the element exhibits 13 deformational modes (16 DOFs diminished by 3 rigid displacement modes), the Pian filter technique 51,52 is adopted to introduce two additional constraints. The resulting stress interpolation matrix P, Equation (7) 3 , results to be…”

Section: Stress Interpolationmentioning

confidence: 99%

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

Nodargi

Bisegna

2019

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.

“…However, the error is still bounded within a reasonable range. The work by Madeo et al is referred to here for more comparisons between numerical and analytical solutions.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…A similar concept was later adopted by Choi et al in the derivation of a displacement‐based element. Recent explorations can be spotted in the work by Fajman, Cen et al, Madeo et al, and Shang and Ouyang …”

Section: Introductionmentioning

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.