A locking‐free nine‐DOF triangular plate element with incompatible approximation

Cai, Yongchang; Zhu, Hehua

doi:10.1002/nme.5307

Cited by 7 publications

(3 citation statements)

References 25 publications

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“…From the point of view of the 2D analysis, the total computational cost of the present elements is bearable and worthy in terms of its advantages in formulation and implementation. HSDTs which have almost the same computational efficiency of DST-BL/RDKTM could also be constructed using the reduced integral method similar to our previous work [55], but the present HSDTs avoiding the reduced integration by paying a certain computational cost are more practicable in engineering analysis.…”

Section: Clamped Square Plate Subjected To Uniform Loadmentioning

confidence: 99%

“…Please refer to Cai and Zhu [55] for the detailed derivation of the displacement boundary condition fixed at a point or the given displacement boundary condition. …”

Section: Imposing Displacement Boundary Conditionmentioning

confidence: 99%

“…In Cai and Zhu [55], a locking-free MTP9 (Mindlin type Triangular Plate element with nine degrees of freedom) using incompatible polynomial approximation is proposed. It also provides a new way and methodology to develop simple and efficient plate/shell elements based on HSDTs.…”

Section: Introductionmentioning

confidence: 99%

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A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

Gou¹,

Cai²,

Zhu³

2018

Applied Sciences

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Featured Application: Due to the mathematical complexity raised by a high continuity requirement, developing simple/efficient standard finite elements with general polynomial approximations applicable for arbitrary HSDTs seems to be a difficult task at the present theoretical level. In this article, a series of High-order Shear Deformation Triangular Plate Elements (HSDTPEs) are developed using polynomial approximation for the analysis of isotropic thick-thin plates, through-thickness functionally graded plates, and cracked plates. The HSDTPEs have the advantage of simplicity in formulation, are free from shear locking, avoid using a shear correction factor and reduced integration, and provide stable solutions for thick and thin plates. The work can be further applied to plates and shells analysis with arbitrary shapes of elements, as well as more general problems related to the shear deformable effect, such as fracture and functionally graded plates. Abstract:The High-order Shear Deformation Theories (HSDTs) which can avoid the use of a shear correction factor and better predict the shear behavior of plates have gained extensive recognition and made quite great progress in recent years, but the general requirement of C 1 continuity in approximation fields in HSDTs brings difficulties for the numerical implementation of the standard finite element method which is similar to that of the classic Kirchhoff-Love plate theory. As a strong complement to HSDTs, in this work, a series of simple High-order Shear Deformation Triangular Plate Elements (HSDTPEs) using incompatible polynomial approximation are developed for the analysis of isotropic thick-thin plates, cracked plates, and through-thickness functionally graded plates. The elements employ incompatible polynomials to define the element approximation functions u/v/w, and a fictitious thin layer to enforce the displacement continuity among the adjacent plate elements. The HSDTPEs are free from shear-locking, avoid the use of a shear correction factor, and provide stable solutions for thick and thin plates. A variety of numerical examples are solved to demonstrate the convergence, accuracy, and robustness of the present HSDTPEs.

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Section: Clamped Square Plate Subjected To Uniform Loadmentioning

confidence: 99%

“…Please refer to Cai and Zhu [55] for the detailed derivation of the displacement boundary condition fixed at a point or the given displacement boundary condition. …”

Section: Imposing Displacement Boundary Conditionmentioning

confidence: 99%

See 1 more Smart Citation

A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

Gou¹,

Cai²,

Zhu³

2018

Applied Sciences

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Independent cover isogeometric Reissner‐Mindlin shell model for the simulation of the fabricated lining

Cai

Chen

2021

Num Anal Meth Geomechanics

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The fabricated lining is widely used in the underground rail transit, water conveyance system and river‐crossing tunnel. It is generally composed of the precast concrete segments, joints, bolts and reinforcements. Compression and separation often coexist in a single joint, which brings great challenges to the modeling and calculation of the fabricated lining. In this paper, an independent cover isogeometric Reissner‐Mindlin shell model (denoted as the ICI‐R shell model) is proposed for the simulation of the fabricated lining. In the ICI‐R shell model, each segment is regarded as an independent cover, whose geometry is described with the nonuniform rational B‐splines (NURBS) surface, and an isogeometric displacement function is defined based on the Reissner‐Mindlin shell deformation theory. The adjacent segments are connected with the fictitious thin layers, of which the normal and tangential deformations and stresses can be correctly calculated. Within this framework, the difficulties in the continuity‐discontinuity coupling analysis occurring when using the existing shell models are well solved, and the fabricated lining can be simulated expediently. The ICI‐R shell model has the advantages of clear physical meaning, concise formulas and convenient implementation. Benefiting from the strong capability of representing geometries of NURBS and the simplicity of the formulation of the ICI‐R shell model, the parameterized modeling and automatic calculation of the fabricated lining can be easily achieved for simplifying the analysis process and reducing user cost for geotechnical engineers. The successful application in the benchmark tests and engineering example shows the versatility, efficiency and robustness of the ICI‐R shell model.

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A New Locking-Free Thick/Thin Shell Element with Incompatible Approximation in a General Orthogonal Curvilinear Coordinate System

Chen

Cai

Yan

2020

Computational and Experimental Simulations in Engineering

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A locking‐free nine‐DOF triangular plate element with incompatible approximation

Cited by 7 publications

References 25 publications

A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

Independent cover isogeometric Reissner‐Mindlin shell model for the simulation of the fabricated lining

A New Locking-Free Thick/Thin Shell Element with Incompatible Approximation in a General Orthogonal Curvilinear Coordinate System

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