Rotationally invariant distortion resistant finite-elements

Cowan, T. W.; Coombs, William M.

doi:10.1016/j.cma.2014.02.016

Cited by 11 publications

(11 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Shang and Ouyang [1] proposed a simple and robust 4-node 12-DOF quadrilateral membrane element US-Q4 for the classical elastic problems based on the unsymmetric finite element method [42][43][44]. The unsymmetric FEM, which has been successfully applied to various applications in past years [45][46][47][48][49], employs different interpolations for the test and trial functions in the element formulation.…”

Section: Introductionmentioning

confidence: 99%

A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory

Shang

Qian

Cen

et al. 2019

Numerical Meth Engineering

View full text Add to dashboard Cite

SummaryIn this work, the recently proposed unsymmetric 4‐node 12‐DOF (degree‐of‐freedom) membrane element (Shang and Ouyang, Int J Numer Methods Eng 113(10): 1589‐1606, 2018), which has demonstrated excellent performance for the classical elastic problems, is further extended for the modified couple stress theory, to account for the size effect of materials. This is achieved via two formulation developments. Firstly, by using the penalty function method, the kinematic relations between the element's nodal drilling DOFs and the true physical rotations are enforced. Consequently, the continuity requirement for the modified couple stress theory is satisfied in weak sense, and the symmetric curvature test function can be easily derived from the gradients of the drilling DOFs. Secondly, the couple stress field that satisfies a priori the related equilibrium equations is adopted as the energy conjugate trial function to formulate the element for the modified couple stress theory. As demonstrated by a series of benchmark tests, the new element can efficiently capture the size‐dependent responses of materials and is robust to mesh distortions. Moreover, as the new element uses only three conventional DOFs per node, it can be readily incorporated into the standard finite element program framework and commonly available finite element programs.

show abstract

Section: Introductionmentioning

confidence: 99%

A simple unsymmetric 4‐node 12‐DOF membrane element for the modified couple stress theory

Shang

Qian

Cen

et al. 2019

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…It is very interesting that whether the unsymmetric element US‐ATFQ4, which possesses high distortion‐resistance for linear elastic problems, can be extended to nonlinear applications. However, some researchers negate this extension, they think that the approach, which employs the analytical solutions satisfying all governing equations for linear elasticity, restricts the element to linear elastic analysis . In fact, the analytical trial functions are only the functions of physical coordinates with material constants.…”

Section: Introductionmentioning

confidence: 99%

“…However, some researchers negate this extension, they think that the approach, which employs the analytical solutions satisfying all governing equations for linear elasticity, restricts the element to linear elastic analysis. 44 In fact, the analytical trial functions are only the functions of physical coordinates with material constants. These coordinates and material constants can be updated referring to the current configuration at each iterative step so that it is possible to use them as part of the incremental equations of the UL formulation.…”

Section: Introductionmentioning

confidence: 99%

High‐performance geometric nonlinear analysis with the unsymmetric 4‐node, 8‐DOF plane element US‐ATFQ4

Cen

et al. 2018

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary A recent unsymmetric 4‐node, 8‐DOF plane element US‐ATFQ4, which exhibits excellent precision and distortion‐resistance for linear elastic problems, is extended to geometric nonlinear analysis. Since the original linear element US‐ATFQ4 contains the analytical solutions for plane pure bending, how to modify such formulae into incremental forms for nonlinear applications and design an appropriate updated algorithm become the key of the whole job. First, the analytical trial functions should be updated at each iterative step in the framework of updated Lagrangian formulation that takes the configuration at the beginning of an incremental step as the reference configuration during that step. Second, an appropriate stress update algorithm in which the Cauchy stresses are updated by the Hughes‐Winget method is adopted to estimate current stress fields. Numerical examples show that the new nonlinear element US‐ATFQ4 also possesses amazing performance for geometric nonlinear analysis, no matter whether regular or distorted meshes are used. It again demonstrates the advantages of the unsymmetric finite element method with analytical trial functions.

show abstract

“…Some studies (Panasz et al, 2013;Cowan and Coombs, 2014) presented strict definitions of mesh distortion. In these studies, the overdeformation was also treated as mesh distortion, for example, the angle of the adjusted edges is <60°.…”

Section: Element Distortion Analysis and Treatmentmentioning

confidence: 99%