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

Chang, Theodore L.; Lee, Chin-Long; Carr, Athol J.; Dhakal, Rajesh; Pampanin, Stefano

doi:10.1002/nme.6066

Cited by 8 publications

(7 citation statements)

References 50 publications

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“…By proper construction, for example, providing sufficient number of integration points and choosing the same shape functions for κ (ε) and µ (σ), H 4 and H 5 can be square and invertible. Similar to the work by the authors [36], by static condensation, Eq. ( 38) can be transformed to the one,…”

Section: Option Two -Invertible H 4 and Hmentioning

confidence: 54%

New mixed formulation and mesh dependency of finite elements based on the consistent couple stress theory

Chang¹,

Lee²

2022

Preprint

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This work presents a general finite element formulation based on a six-field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both elastic and inelastic materials is derived to minimise computation cost. With proper interpolations, membrane elements of various nodes are proposed as the examples. The implemented finite elements are used to conduct numerical experiments to investigate the performance of the in-plane drilling degrees of freedom introduced by the consistent couple stress theory. The mesh dependency issue is also studied with both elastic and inelastic materials.It is shown that the consistent couple stress theory provides an objective definition of rotation compared with the Cauchy theory but additional regularisation (or other techniques) is required to overcome mesh/size dependency in softening or fracture related problems. In the case of hardening continuum problems and/or large characteristic lengths, the proposed formulation and elements offer a more reliable approach to model structures with both translational and rotational degrees of freedom.

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Section: Option Two -Invertible H 4 and Hmentioning

confidence: 54%

New mixed formulation and mesh dependency of finite elements based on the consistent couple stress theory

Chang¹,

Lee²

2022

Preprint

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“…By recalling Equations (9), (16), and (17), the element compliance matrix, H e , and the compatibility matrix, Q e , (see Equation (18)) are rewritten as…”

Section: Compliance and Compatibility Fe Matricesmentioning

confidence: 99%

“…Mixed elements are also developed in the framework of the virtual element method by Artioli et al [9][10][11] Furthermore, mixed FE are largely used for the geometrically nonlinear analysis of thin-walled structures. [12][13][14][15][16] Recent formulations of mixed FE can be found in References 17,18. Moreover, mixed FE are diffusely employed for the analysis of structures undergoing physical nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

An efficient isostatic mixed shell element for coarse mesh solution

Madeo

Liguori

Zucco

et al. 2020

Numerical Meth Engineering

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A novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger-Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of kinematical parameters minus the number of rigid body motions. We name this new FE MISS-8. MISS-8 has generalized displacements and rotations interpolated along its contour and drilling rotation is also considered as degree of freedom. The element is integrated exactly on its contour, it does not suffer from rank defectiveness and it is locking-free. Furthermore, it is efficient for recovering both stress and displacement fields when coarse meshes are used. The numerical investigation on its performance confirms the suitability, accuracy, and efficiency to recover elastic solutions of thick-and thin-walled beam-like structures. Numerical results obtained with the proposed FE are also compared with those obtained with isogeometric high-performance solutions. Finally, numerical results show a rate of convergence between h 2 and h 4 .

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“…To ease the problem, as well as to achieve a better balance between analysis efficiency and accuracy, a mixed membrane element called GCMQ (generalized conforming mixed quadrilateral) is proposed recently [3]. This paper evaluates the performance of GCMQ in the context of nonlinear time history analysis.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Reinforced Concrete Shear Wall Building Using a Novel Finite Element

Chang¹,

Lee²,

Carr³

et al. 2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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To simulate reinforced concrete shear walls under seismic loads, a new finite element called GCMQ (generalized conforming mixed quadrilateral) developed based on the threefield Hu-Washizu variational principle is adopted in this paper for the nonlinear time history analysis of a reinforced concrete shear wall multistory building. Unlike other well-known 1D wall elements, GCMQ is a 2D membrane element that exhibits very good performance in terms of coarse mesh accuracy. It takes into consideration the nonlinear distribution of both strain and stress across the wall width, which is difficult to achieve with 1D elements that often adopt 'plane sections remain plane' assumption. Two shear wall examples are analysed in this paper. With a smeared approach adopted for reinforcement and a proper material model for concrete, GCMQ can simulate accurate global response with a coarse mesh grid. For time efficient analysis, one element per storey could also be adopted. GCMQ provides a more versatile solution to wall simulation and could be a useful tool in future analysis and design of wall structures. 4565 COMPDYN 2019 7 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.

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

Cited by 8 publications

References 50 publications

New mixed formulation and mesh dependency of finite elements based on the consistent couple stress theory

New mixed formulation and mesh dependency of finite elements based on the consistent couple stress theory

An efficient isostatic mixed shell element for coarse mesh solution

Dynamic Analysis of a Reinforced Concrete Shear Wall Building Using a Novel Finite Element

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