SOLID ELEMENTS WITH ROTATIONAL DOFs BY EXPLICIT HYBRID STABILIZATION

Sze, K. Y.; Soh, Ai‐Kah; Sim, Y. S.

doi:10.1002/(sici)1097-0207(19960915)39:17<2987::aid-nme986>3.0.co;2-h

Cited by 12 publications

(1 citation statement)

References 31 publications

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“…In the 2D element formulation, the famous Allman's interpolation is used to determine the displacement test function. For the 3D cases, there are also some interpolations equipped with rotation DOFs, such as References . However, these interpolations seem somewhat complex.…”

Section: Introductionmentioning

confidence: 99%

8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity

Shang

Jia

2020

Numerical Meth Engineering

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A new C 0 8-node 48-DOF hexahedral element is developed for analysis of size-dependent problems in the context of the modified couple stress theory by extending the methodology proposed in our recent work (Shang et al., Int J Numer Methods Eng 119(9): 807-825, 2019) to the three-dimensional (3D) cases.There are two major innovations in the present formulation. First, the independent nodal rotation degrees of freedom (DOFs) are employed to enhance the standard 3D isoparametric interpolation for obtaining the displacement and strain test functions, as well as to approximatively design the physical rotation field for deriving the curvature test function. Second, the equilibrium stress functions instead of the analytical functions are used to formulate the stress trial function whilst the couple stress trial function is directly obtained from the curvature test function by using the constitutive relationship. Besides, the penalty function is introduced into the virtual work principle for enforcing the C 1 continuity condition in weak sense. Several benchmark examples are examined and the numerical results demonstrate that the element can simulate the size-dependent mechanical behaviors well, exhibiting satisfactory accuracy and low susceptibility to mesh distortion. K E Y W O R D Shexahedral element, modified couple stress theory, rotation degree of freedom, size-dependent, unsymmetric FEM INTRODUCTIONMany experimental observations have shown that the micro/nano structures, which have been widely used in modern engineering applications, may experience size-dependent mechanical behaviors. Various non-classical higher-order continuum theories, such as the strain gradient theory (SGT) and the couple stress theory (CST), have been developed for describing such size-dependent phenomena. 1-7 However, as these higher-order theories are more complex than the classical one, the analytical or semi-analytical solutions are available only for restricted problems with simple geometries and certain boundary conditions. Therefore, the numerical approaches with high accuracy and efficiency are clearly required for the solution procedure, in which the well-accepted finite element method (FEM) is usually recognized as a very efficient choice. In recent year, the isogeometric method 8-11 and the meshless method, 12,13 which can formulate highly continuous basis functions, have also been applied to the size-dependent problems. However, the computation expenses Int J Numer Methods Eng. 2020;121:2683-2700. wileyonlinelibrary.com/journal/nme

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Section: Introductionmentioning

confidence: 99%

8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity

Shang

Jia

2020

Numerical Meth Engineering

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Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s

Sze

Pan

2000

Int. J. Numer. Meth. Engng.

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SUMMARYThis paper presents two hybrid stress four-node tetrahedron solid elements which are equipped with the rotational d.o.f.s proposed by Allman. Inasmuch Allman's rotation is employed, the elements are plagued by zero-energy rotation modes which induce no strain. A modi"ed Hellinger}Reissner functional that treats the rotation and the skew symmetric stress as independent "elds is employed to formulate a stabilization scheme. Particular e!ort has been made to reduce the number of stress modes to minimum without sacri"cing the frame invariance and proper rank of the element. The computational cost of the element is reduced by adopting orthogonal constant and non-constant symmetric stress modes. Numerical benchmark tests indicate that accuracy of the element with the minimum number of stress modes is close to another multi-"eld element which, however, is not frame invariant and exhibits unsuppressed zero-energy deformation modes.

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Generalized nodes and high-performance elements

Tian

Yagawa

2005

Int. J. Numer. Meth. Engng

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SUMMARYThe paper concerns the development of robust and high accuracy finite elements with only corner nodes using a partition-of-unity-based finite-element approximation. Construction of the partition-ofunity-based approximation is accomplished by a physically defined local function of displacements. A 4-node quadratic tetrahedral element and a 3-node quadratic triangular element are developed. Eigenvalue analysis shows that linear dependencies in the partition-of-unity-based finite-element approximation constructed for the new elements are eliminable. Numerical calculations demonstrate that the new elements are robust, insensitive to mesh distortion, and offer quadratic accuracy, while also keeping mesh generation extremely simple.

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SOLID ELEMENTS WITH ROTATIONAL DOFs BY EXPLICIT HYBRID STABILIZATION

Cited by 12 publications

References 31 publications

8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity

8‐node hexahedral unsymmetric element with rotation degrees of freedom for modified couple stress elasticity

Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s

Generalized nodes and high-performance elements

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