A Review on Membrane Finite Elements with Drilling Degree of Freedom

Boutagouga, Djamel

doi:10.1007/s11831-020-09489-z

Cited by 8 publications

(6 citation statements)

References 144 publications

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“…Boutagouga and Djeghaba, 2014;Nguyen-Van et al, 2009;Zhang et al, 2011;Shin and Lee, 2014;Tang et al, 2016). A recent review includes most works on membrane finite elements with drilling rotation DOF presented in Boutagouga (2021).…”

Section: Co-rotational Framework and Kinematics Of The Shell Elementmentioning

confidence: 99%

Post-buckling analysis of shell-like structures using an implicit dynamic time integration scheme

Boutagouga

Mamouri

2022

MMMS

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PurposeThis paper aims to investigate post-buckling responses of shell-like structures using an implicit conservative-decaying time integration dynamic scheme.Design/methodology/approachIn this work, the authors have proposed the use of a four-node quadrilateral flat shell finite element with drilling rotational degree of freedom within the framework of an updated Lagrangian formulation mutually with an implicit conservative-dissipative time integration dynamic scheme.FindingsSeveral numerical simulations were considered to evaluate the accuracy, robustness, stability and the capacity of the considered time integration scheme to dissipate numerical noise in the presence of high frequencies. The obtained results illustrate a very satisfying performance of the implicit conservative-dissipative direct time integration scheme conjointly with the quadrilateral flat shell finite element with drilling rotation.Originality/valueThe authors have investigated the potential of the implicit dynamic scheme to deal with unstable branches after limit points in the non-linear post-buckling response of shell structures with no need for structural damping. The capability of the studied algorithm to study buckling and post-buckling behaviour of thin shell structures is illustrated through several numerical examples.

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Section: Co-rotational Framework and Kinematics Of The Shell Elementmentioning

confidence: 99%

Post-buckling analysis of shell-like structures using an implicit dynamic time integration scheme

Boutagouga

Mamouri

2022

MMMS

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“…The numerical results of the parametric studies reveal that k∕G = 10 4 is an appropriate value that can enforce the constraint at an acceptable level and doesn't make the stiffness matrix ill conditioned. The penalty stiffness part is integrated by using the one-point quadrature strategy for eliminating the possible locking problem [56][57][58][59] while the other items are calculated using the full quadrature scheme.…”

Section: 34mentioning

confidence: 99%

An efficient 4‐node facet shell element for the modified couple stress elasticity

Shang

Cen

et al. 2021

Numerical Meth Engineering

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This work proposes a simple but robust 4-node 24-DOF facet shell element for static analysis of small-scale thin shell structures. To accommodate the size effects, the modified couple stress theory is employed as the theoretical basis.The element is constructed via two main innovations. First, the trial functions that can a priori satisfy related governing differential equations are adopted as the basic functions for formulating the element interpolations. Second, the generalized conforming theory and the penalty function method are employed to meet the C 1 continuity requirement in weak sense for ensuring the computation convergence property. Several benchmarks of shells with different geometries are tested to assess the new facet shell element's capability. The numerical results reveal that the element can effectively simulate the size-dependent mechanical behaviors of small-scale thin shells, exhibiting satisfactory numerical accuracy and low susceptibility to mesh distortion. Moreover, as the shell element uses only six degrees of freedom per node, it can be incorporated into the commonly available finite element programs very readily.

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“…Early attempts date back to the work by Allman [29]. Recent research work on membrane elements with in-plane drilling degrees of freedom is reviewed by Boutagouga [30]. However, the drilling degree of freedom defined within the Cauchy theory shows significant mesh dependency, which limits its application in modelling problems involving, for example, both membrane and beam elements [31].…”

Section: Introductionmentioning

confidence: 99%

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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A Review on Membrane Finite Elements with Drilling Degree of Freedom

Cited by 8 publications

References 144 publications

Post-buckling analysis of shell-like structures using an implicit dynamic time integration scheme

Post-buckling analysis of shell-like structures using an implicit dynamic time integration scheme

An efficient 4‐node facet shell element for the modified couple stress elasticity

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

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