The Experts below are selected from a list of 5319 Experts worldwide ranked by ideXlab platform
Hong Zheng - One of the best experts on this subject based on the ideXlab platform.
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A Three-Node Triangular Element with Continuous Nodal Stress (Trig3-CNS) for Geometry Nonlinear Solid Mechanics Problems
International Journal of Computational Methods, 2018Co-Authors: Guanhua Sun, Yongtao Yang, Hong ZhengAbstract:This paper investigates the performance of the three-node triangular element with continuous nodal stress (Trig3-CNS) for geometry nonlinear solid mechanic problems. This Trig3-CNS element was recently proposed to improve accuracy of the finite element method (FEM). By synergizing the individual strengths of Meshfree method and FEM, the Trig3-CNS element achieves higher accuracy and convergence rate. Furthermore, Trig3-CNS presents high tolerance to Mesh Distortion. Therefore, it is potentially useful for geometry nonlinear solid mechanics problems in which Mesh Distortion takes place. Compared with the traditional hybrid “FE-Meshfree” elements, Trig3-CNS naturally processes CNS without requiring any extra operation in post-processing. Numerical tests in the present work show that for geometry nonlinear analysis, the results of the Trig3-CNS element are better than the 3-node triangular element (Trig3) and 4-node isoparametric quadrilateral element (Quad4). In addition, the performance of Trig3-CNS is comparable to that of traditional hybrid “FE-Meshfree” elements.
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A Three-Node Triangular Element with Continuous Nodal Stress (Trig3-CNS) for Geometry Nonlinear Solid Mechanics Problems
International Journal of Computational Methods, 2017Co-Authors: Guanhua Sun, Yongtao Yang, Hong ZhengAbstract:This paper investigates the performance of the three-node triangular element with continuous nodal stress (Trig3-CNS) for geometry nonlinear solid mechanic problems. This Trig3-CNS element was recently proposed to improve accuracy of the finite element method (FEM). By synergizing the individual strengths of Meshfree method and FEM, the Trig3-CNS element achieves higher accuracy and convergence rate. Furthermore, Trig3-CNS presents high tolerance to Mesh Distortion. Therefore, it is potentially useful for geometry nonlinear solid mechanics problems in which Mesh Distortion takes place. Compared with the traditional hybrid “FE-Meshfree” elements, Trig3-CNS naturally processes CNS without requiring any extra operation in post-processing. Numerical tests in the present work show that for geometry nonlinear analysis, the results of the Trig3-CNS element are better than the 3-node triangular element (Trig3) and 4-node isoparametric quadrilateral element (Quad4). In addition, the performance of Trig3-CNS is com...
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A partition-of-unity based FE-Meshfree hexahedral element with continuous nodal stress
Computers & Structures, 2017Co-Authors: Yongtao Yang, Li Chen, Xuhai Tang, Hong Zheng, Quansheng LiuAbstract:An FE-Meshfree hexahedral element with continuous nodal stress (Hexa8-CNS) is presented.The derivatives of Hexa8-CNS shape function are continuous at nodes.Hexa8-CNS element is able to achieve nodal stress without any smoothing operation.Comparing to 8-node hexahedral element, the Hexa8-CNS element has high tolerance to Mesh Distortion. A hybrid FE-Meshfree eight-node hexahedral element with continuous nodal stress (Hexa8-CNS) is developed using the concept of partition of unity (PU). One feature of Hexa8-CNS is to achieve continuous nodal stress, meanwhile construct high-order global approximations without adding external node, which leads to high accuracy and convergence rate. Moreover, it is free from the linear dependence problem which cripples many of the PU-based finite elements. Numerical results show that the performance of the element is superior to that of Hexa8 element. Besides, the present element has excellent Mesh Distortion tolerant capabilities.
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Application of the three-node triangular element with continuous nodal stress for free vibration analysis
Computers & Structures, 2016Co-Authors: Yongtao Yang, Hong ZhengAbstract:Formulations of the Trig3-CNS element for free vibration analysis are presented.Comparing to Trig3, Trig3-CNS achieves better accuracy.Comparing to Trig3, Trig3-CNS has high tolerance to Mesh Distortion. A three-node triangular element with continuous nodal stress (Trig3-CNS) was recently proposed for static analysis. The Trig3-CNS element, which is the development of the partition-of-unity based FE-Meshfree quadrilateral element with continuous nodal stress (Quad4-CNS), uses hybrid shape functions that combine the Meshfree and finite element shape functions so as to synergize the individual strengths of Meshfree and finite element methods. As a result, high order global approximations in Trig3-CNS element could be easily constructed without adding extra nodes and DOFs, thereby achieving high accuracy and convergence rate. In this paper, the element is further applied to conduct free vibration analysis of two-dimensional solids. The numerical tests in the present work demonstrate that Trig3-CNS has higher tolerance to Mesh Distortion and gives more accurate solution as compared to the three-node triangular element (Trig3) and four-node quadrilateral element (Quad4).
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Free and forced vibration analyses using the four-node quadrilateral element with continuous nodal stress
Engineering Analysis with Boundary Elements, 2016Co-Authors: Yongtao Yang, Li Chen, Hong ZhengAbstract:Abstract The recently published four-node quadrilateral element with continuous nodal stress (Quad4-CNS) is extended to free and forced vibration analyses of two-dimensional solids. The Quad4-CNS element can be regarded as a partition-of-unity (PU) based ‘FE-Meshfree’ element which inherits better accuracy, higher convergence rate, and high tolerance to Mesh Distortion from the Meshfree methods, while preserving the Kronecker-delta property of the finite element method (FEM). Moreover, the Quad4-CNS element is free from the linear dependence problem which otherwise cripples many of the PU based finite elements. Several free and forced vibration problems are solved and the performance of the element is compared with that of the four-node isoparametric quadrilateral element (Quad4) and eight-node isoparametric quadrilateral element (Quad8). The results show that, for regular Meshes, the performance of the element is superior to that of Quad4 element, and comparable to that of Quad8 element. For distorted Meshes, the present element has better Mesh-Distortion tolerance than Quad4 and Quad8 elements.
Yongtao Yang - One of the best experts on this subject based on the ideXlab platform.
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A Three-Node Triangular Element with Continuous Nodal Stress (Trig3-CNS) for Geometry Nonlinear Solid Mechanics Problems
International Journal of Computational Methods, 2018Co-Authors: Guanhua Sun, Yongtao Yang, Hong ZhengAbstract:This paper investigates the performance of the three-node triangular element with continuous nodal stress (Trig3-CNS) for geometry nonlinear solid mechanic problems. This Trig3-CNS element was recently proposed to improve accuracy of the finite element method (FEM). By synergizing the individual strengths of Meshfree method and FEM, the Trig3-CNS element achieves higher accuracy and convergence rate. Furthermore, Trig3-CNS presents high tolerance to Mesh Distortion. Therefore, it is potentially useful for geometry nonlinear solid mechanics problems in which Mesh Distortion takes place. Compared with the traditional hybrid “FE-Meshfree” elements, Trig3-CNS naturally processes CNS without requiring any extra operation in post-processing. Numerical tests in the present work show that for geometry nonlinear analysis, the results of the Trig3-CNS element are better than the 3-node triangular element (Trig3) and 4-node isoparametric quadrilateral element (Quad4). In addition, the performance of Trig3-CNS is comparable to that of traditional hybrid “FE-Meshfree” elements.
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A Three-Node Triangular Element with Continuous Nodal Stress (Trig3-CNS) for Geometry Nonlinear Solid Mechanics Problems
International Journal of Computational Methods, 2017Co-Authors: Guanhua Sun, Yongtao Yang, Hong ZhengAbstract:This paper investigates the performance of the three-node triangular element with continuous nodal stress (Trig3-CNS) for geometry nonlinear solid mechanic problems. This Trig3-CNS element was recently proposed to improve accuracy of the finite element method (FEM). By synergizing the individual strengths of Meshfree method and FEM, the Trig3-CNS element achieves higher accuracy and convergence rate. Furthermore, Trig3-CNS presents high tolerance to Mesh Distortion. Therefore, it is potentially useful for geometry nonlinear solid mechanics problems in which Mesh Distortion takes place. Compared with the traditional hybrid “FE-Meshfree” elements, Trig3-CNS naturally processes CNS without requiring any extra operation in post-processing. Numerical tests in the present work show that for geometry nonlinear analysis, the results of the Trig3-CNS element are better than the 3-node triangular element (Trig3) and 4-node isoparametric quadrilateral element (Quad4). In addition, the performance of Trig3-CNS is com...
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A partition-of-unity based FE-Meshfree hexahedral element with continuous nodal stress
Computers & Structures, 2017Co-Authors: Yongtao Yang, Li Chen, Xuhai Tang, Hong Zheng, Quansheng LiuAbstract:An FE-Meshfree hexahedral element with continuous nodal stress (Hexa8-CNS) is presented.The derivatives of Hexa8-CNS shape function are continuous at nodes.Hexa8-CNS element is able to achieve nodal stress without any smoothing operation.Comparing to 8-node hexahedral element, the Hexa8-CNS element has high tolerance to Mesh Distortion. A hybrid FE-Meshfree eight-node hexahedral element with continuous nodal stress (Hexa8-CNS) is developed using the concept of partition of unity (PU). One feature of Hexa8-CNS is to achieve continuous nodal stress, meanwhile construct high-order global approximations without adding external node, which leads to high accuracy and convergence rate. Moreover, it is free from the linear dependence problem which cripples many of the PU-based finite elements. Numerical results show that the performance of the element is superior to that of Hexa8 element. Besides, the present element has excellent Mesh Distortion tolerant capabilities.
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Application of the three-node triangular element with continuous nodal stress for free vibration analysis
Computers & Structures, 2016Co-Authors: Yongtao Yang, Hong ZhengAbstract:Formulations of the Trig3-CNS element for free vibration analysis are presented.Comparing to Trig3, Trig3-CNS achieves better accuracy.Comparing to Trig3, Trig3-CNS has high tolerance to Mesh Distortion. A three-node triangular element with continuous nodal stress (Trig3-CNS) was recently proposed for static analysis. The Trig3-CNS element, which is the development of the partition-of-unity based FE-Meshfree quadrilateral element with continuous nodal stress (Quad4-CNS), uses hybrid shape functions that combine the Meshfree and finite element shape functions so as to synergize the individual strengths of Meshfree and finite element methods. As a result, high order global approximations in Trig3-CNS element could be easily constructed without adding extra nodes and DOFs, thereby achieving high accuracy and convergence rate. In this paper, the element is further applied to conduct free vibration analysis of two-dimensional solids. The numerical tests in the present work demonstrate that Trig3-CNS has higher tolerance to Mesh Distortion and gives more accurate solution as compared to the three-node triangular element (Trig3) and four-node quadrilateral element (Quad4).
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Free and forced vibration analyses using the four-node quadrilateral element with continuous nodal stress
Engineering Analysis with Boundary Elements, 2016Co-Authors: Yongtao Yang, Li Chen, Hong ZhengAbstract:Abstract The recently published four-node quadrilateral element with continuous nodal stress (Quad4-CNS) is extended to free and forced vibration analyses of two-dimensional solids. The Quad4-CNS element can be regarded as a partition-of-unity (PU) based ‘FE-Meshfree’ element which inherits better accuracy, higher convergence rate, and high tolerance to Mesh Distortion from the Meshfree methods, while preserving the Kronecker-delta property of the finite element method (FEM). Moreover, the Quad4-CNS element is free from the linear dependence problem which otherwise cripples many of the PU based finite elements. Several free and forced vibration problems are solved and the performance of the element is compared with that of the four-node isoparametric quadrilateral element (Quad4) and eight-node isoparametric quadrilateral element (Quad8). The results show that, for regular Meshes, the performance of the element is superior to that of Quad4 element, and comparable to that of Quad8 element. For distorted Meshes, the present element has better Mesh-Distortion tolerance than Quad4 and Quad8 elements.
S. Rajendran - One of the best experts on this subject based on the ideXlab platform.
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sufficient conditions for Mesh Distortion immune finite elements
PROCEEDINGS OF THE 2ND INTERNATIONAL SYMPOSIUM ON COMPUTATIONAL MECHANICS AND THE 12TH INTERNATIONAL CONFERENCE ON THE ENHANCEMENT AND PROMOTION OF CO, 2010Co-Authors: S. RajendranAbstract:Sufficient conditions are proposed for a displacement‐based finite element to be immune to Mesh‐Distortion effects. Numerical results confirm that an illustrative element satisfying these conditions is indeed capable of giving Mesh‐Distortion immune performance (i.e., nodal solution) even for extremely severe Mesh‐Distortions for which the Jacobian of isoparametric transformation goes negative! This is partially due to the fact that the stiffness integral is rendered free of Jacobian term.
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Sufficient Conditions for Mesh‐Distortion Immune Finite Elements
2010Co-Authors: S. RajendranAbstract:Sufficient conditions are proposed for a displacement‐based finite element to be immune to Mesh‐Distortion effects. Numerical results confirm that an illustrative element satisfying these conditions is indeed capable of giving Mesh‐Distortion immune performance (i.e., nodal solution) even for extremely severe Mesh‐Distortions for which the Jacobian of isoparametric transformation goes negative! This is partially due to the fact that the stiffness integral is rendered free of Jacobian term.
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A partition of unity-based 'FE-Meshfree' QUAD4 element for geometric non-linear analysis
International Journal for Numerical Methods in Engineering, 2009Co-Authors: S. Rajendran, Baili Zhang, K.m. LiewAbstract:The recently published ‘FE–Meshfree’ QUAD4 element is extended to geometrical non-linear analysis. The shape functions for this element are obtained by combining Meshfree and finite element shape functions. The concept of partition of unity (PU) is employed for the purpose. The new shape functions inherit their higher order completeness properties from the Meshfree shape functions and the Mesh-Distortion tolerant compatibility properties from the finite element (FE) shape functions. Updated Lagrangian formulation is adopted for the non-linear solution. Several numerical example problems are solved and the performance of the element is compared with that of the well-known Q4, QM6 and Q8 elements. The results show that, for regular Meshes, the performance of the element is comparable to that of QM6 and Q8 elements, and superior to that of Q4 element. For distorted Meshes, the present element has better Mesh-Distortion tolerance than Q4, QM6 and Q8 elements. Copyright © 2009 John Wiley & Sons, Ltd.
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A technique to develop Mesh-Distortion immune finite elements
Computer Methods in Applied Mechanics and Engineering, 2009Co-Authors: S. RajendranAbstract:Three sufficient conditions are proposed for an iso-parametric finite element formulation to be immune to Mesh-Distortion effects, even for extremely distorted element geometries for which the Jacobian geometric mapping goes negative! Illustrative element formulations are presented to test the sufficiency of the proposed conditions. Numerical results confirm that the illustrative elements are indeed capable of giving Mesh-Distortion immune solution for extreme Mesh Distortions. This has been possible partly because the stiffness integral is free of the Jacobian term in the new formulation.
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Mesh‐Distortion immunity assessment of QUAD8 elements by strong‐form patch tests
Communications in Numerical Methods in Engineering, 2006Co-Authors: S. Rajendran, E. T. Ooi, J. H. YeoAbstract:Strong-form patch tests are conducted to assess the Mesh-Distortion immunity of three types of 8-noded plane quadrilateral elements. Patches with various types of Mesh-Distortions are considered for the purpose. The PM-QUAD8 element passes all the patch tests, viz., constant-, linear- and quadratic strain patch tests in the strong form. The ability to pass all the patch tests translates to the fact that this element is free from completeness defect as well as compatibility defect. The classical isoparametric element (PP-QUAD8), however, suffers from completeness defect while its metric counterpart (MM-QUAD8) suffers from compatibility defect and hence these two elements fail some of the patch tests. Copyright © 2006 John Wiley & Sons, Ltd.
Song Cen - One of the best experts on this subject based on the ideXlab platform.
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Shape-free finite element method: The plane hybrid stress-function (HS-F) element method for anisotropic materials
Science China Physics Mechanics and Astronomy, 2011Co-Authors: Song Cen, Guo-hua Zhou, Mingjue ZhouAbstract:The sensitivity problem to Mesh Distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method. By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy stress function ϕ of the anisotropic materials, 8- and 12-node plane quadrilateral hybrid stress-function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy. Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and stress solutions than those obtained from other models. They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle. It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to Mesh Distortion and can produce highly accurate stress solutions.
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A novel hybrid stress-function finite element method immune to severe Mesh Distortion
IOP Conference Series: Materials Science and Engineering, 2010Co-Authors: Song Cen, Mingjue ZhouAbstract:This paper introduces a hybrid stress-function finite element method proposed recently for developing 2D finite element models immune to element shapes. Deferent from the first version of the hybrid-stress element constructed by Pian, the stress function of 2D elastic or fracture problem is regarded as the functional variable of the complementary energy functional. Then, the basic analytical solutions of are taken as the trial functions for finite element models, and meanwhile, the corresponding unknown stress-function constants are introduced. By using the principle of minimum complementary energy, these unknown stress-function constants can be expressed in terms of the displacements along element edges. Finally, the complementary energy functional can be rewritten in terms of element nodal displacement vector, and thus, the element stiffness matrix of such hybrid-function element can be obtained. As examples, two (8- and 12-node) quadrilateral plane elements and an arbitrary polygonal crack element are constructed by employing different basic analytical solutions of different stress functions. Numerical results show that, the 8- and 12-node plane models can produce the exact solutions for pure bending and linear bending problems, respectively, even the element shape degenerates into triangle and concave quadrangle; and the crack element can also predict accurate results with very low computational cost in analysis of stress-singularity problems.
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Some Recent Advances on the Quadrilateral Area Coordinate Method
Computational Mechanics, 2007Co-Authors: Song Cen, Xiao-ming Chen, Yuqiu LongAbstract:Since the Quadrilateral Area Coordinate Method (QACM) was systematically established at the end of last century [1], some successful applications of this new tool have been achieved by various researchers [2, 3]. Compared with the usual isoparametric coordinate method, the QACM can make a quadrilateral finite element model less sensitive to Mesh Distortion, and simplifies the copmputational procedures (such as no Jacobi inverse is needed).
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Computational Strategies for Curved-side Elements Formulated by Quadrilateral Area Coordinates (QAC)
Computational Methods in Engineering & Science, 2006Co-Authors: Song Cen, Depo Song, Xiao-ming Chen, Yuqiu LongAbstract:The sensitivity problem to Mesh Distortion often occurs for a quadrilateral finite element model. In order to avoiding this trouble, a new Quadrilateral Area Coordinate (QAC) method has been systematically established by generalizing the area coordinate system from triangle to quadrangle [1]. Based on the QAC method, some membrane, plate/shell elements have already been successfully developed. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to Mesh Distortion [2].
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Studies of 4-node Membrane Element with Analytical Stiffness-Matrix Based on the Quadrilateral Area Coordinates
Computational Methods in Engineering & Science, 2006Co-Authors: Song CenAbstract:The new Quadrilateral Area Coordinate (QAC) method is a powerful tool to construct 2D finite element models [1]. Compared with the traditional models using isoparametric coordinates, these new models are less sensitive to Mesh Distortion. Various elements based on QAC method have been successfully developed, among which the 4-node quadrilateral membrane element AGQ6-I is a typical one [2].
Yuqiu Long - One of the best experts on this subject based on the ideXlab platform.
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advanced finite element method in structural engineering
2009Co-Authors: Yuqiu Long, Zhifei LongAbstract:Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements - for instance, the Generalized Conforming Element method, to name one - and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to Mesh Distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements.
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Some Recent Advances on the Quadrilateral Area Coordinate Method
Computational Mechanics, 2007Co-Authors: Song Cen, Xiao-ming Chen, Yuqiu LongAbstract:Since the Quadrilateral Area Coordinate Method (QACM) was systematically established at the end of last century [1], some successful applications of this new tool have been achieved by various researchers [2, 3]. Compared with the usual isoparametric coordinate method, the QACM can make a quadrilateral finite element model less sensitive to Mesh Distortion, and simplifies the copmputational procedures (such as no Jacobi inverse is needed).
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Computational Strategies for Curved-side Elements Formulated by Quadrilateral Area Coordinates (QAC)
Computational Methods in Engineering & Science, 2006Co-Authors: Song Cen, Depo Song, Xiao-ming Chen, Yuqiu LongAbstract:The sensitivity problem to Mesh Distortion often occurs for a quadrilateral finite element model. In order to avoiding this trouble, a new Quadrilateral Area Coordinate (QAC) method has been systematically established by generalizing the area coordinate system from triangle to quadrangle [1]. Based on the QAC method, some membrane, plate/shell elements have already been successfully developed. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to Mesh Distortion [2].
