Refined 15‐DOF triangular discrete degenerated shell element with high performances

Wanji, Chen

doi:10.1002/nme.1024

Cited by 7 publications

(1 citation statement)

References 30 publications

(27 reference statements)

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“…The element for Mindlin plate cannot pass the conventional patch test of non-zero shear stress. The patch test for Mindlin plate in the papers [13,14] is the case of zero shear stress (similar to constant curvature patch test for thin plate). In the application of the patch test to the couple stress/strain gradient theory of microstructures, only zero curvature C 0 patch test can be performed [15] .…”

Section: Introductionmentioning

confidence: 99%

Enhanced patch test of finite element methods

Wanji

2006

SCI CHINA SER G

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Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test proposed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C 0-1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.

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Section: Introductionmentioning

confidence: 99%

Enhanced patch test of finite element methods

Wanji

2006

SCI CHINA SER G

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A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

Zhang¹,

Zhou²,

Li³

et al. 2011

Numerical Meth Engineering

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SUMMARYThe formulation, implementation and testing of simple, efficient and robust shell finite elements have challenged investigators over the past four decades. A new 3-node flat triangular shell element is developed by combination of a membrane component and a plate bending component. The ANDES-based membrane component includes rotational degrees of freedom, and the refined nonconforming element methodbased bending component involves a transverse shear correction. Numerical examples are carried out for benchmark tests. The results show that compared with some popular shell elements, the present one is simple but exhibits excellent all-around properties (for both membrane-and bending-dominated situations), such as free of aspect ratio locking, passing the patch test, free of shear locking, good convergence and high suitability for thin to moderately thick plates. The developed element has already been adopted in a warpage simulation package for injection molding.

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A surface model‐based simulation for warpage of injection‐molded parts

Zhou

Wang

et al. 2011

Polymer Engineering & Sci

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The mid-plane model for warpage simulation of injection-molded parts requires a mid-plane mesh whose transformation is considerably time consuming. To overcome this drawback, a surface model-based warpage simulation is presented, in which the part is represented as a perfect bonding of two half-thickness plates with their reference surfaces at the outer boundary of the part. The plates over the surface mesh are modeled as flat shell elements, and a new triangular flat shell element is developed which combines an Assumed Natural DEviatoric Strain (ANDES) based membrane component and a Refined Nonconforming Element Method (RNEM) based bending component. The bonding is accomplished by multipoint constraints and a Lagrange multiplier based elimination method is proposed for constraint application. The results show that compared with some popular shell elements, ANSYS, Moldflow and the experiments, the presented model exhibits a high performance in computation accuracy. POLYM. ENG. SCI., 51:785-794, 2011. ª 2011 Society of Plastics Engineers

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Refined 15‐DOF triangular discrete degenerated shell element with high performances

Cited by 7 publications

References 30 publications

Enhanced patch test of finite element methods

Enhanced patch test of finite element methods

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

A surface model‐based simulation for warpage of injection‐molded parts

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