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Weian Yao - One of the best experts on this subject based on the ideXlab platform.
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Precise Integration Symplectic Analytical Singular Element for Cracks Analysis Under Transient Thermal Conduction
International Journal of Applied Mechanics, 2020Co-Authors: Xing Ding, Tinh Quoc Bui, Weian YaoAbstract:Numerical modeling of mechanical behavior of cracks under transient thermal conduction involves solving an initial value problem (IVP) and two boundary value problems (BVPs). Both of the BVPs have ...
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Precise Integration Symplectic Analytical Singular Element for Cracks Analysis Under Transient Thermal Conduction
International Journal of Applied Mechanics, 2020Co-Authors: Xing Ding, Tinh Quoc Bui, Weian YaoAbstract:Numerical modeling of mechanical behavior of cracks under transient thermal conduction involves solving an initial value problem (IVP) and two boundary value problems (BVPs). Both of the BVPs have a Singularity issue. Drawbacks such as numerical error accumulation and high computational expense of existing numerical approaches should be overcome. This contribution intends to build a unified framework with highly efficiency and accuracy for the numerical modeling of cracks under thermal shock. The precise integration method (PIM) and the symplectic analytical Singular Element (SASE) have been demonstrated to be favorable alternatives for each problem, i.e., the PIM for solving the IVP and SASE for the BVP. However, it is found that these two methods cannot be combined directly. In order to incorporate the SASEs into the PIM, the existing SASEs are reformulated for the thermal shock cracks analysis. Details of the mathematical derivations are provided. The validity of the proposed method is demonstrated through numerical examples.
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A new crack-tip Singular Element for cracks in three-dimensional elastic bodies
Engineering Fracture Mechanics, 2020Co-Authors: Weihua Chen, Tinh Quoc Bui, Peng Zhang, Weian YaoAbstract:Abstract Symplectic analytical Singular Element (SASE) is a special crack-tip Element in the framework of finite Element method (FEM) for modelling cracks. A group of SASEs, which have been developed by the authors, for various crack problems almost in two-dimensional (2D), but not touched yet more complex ones, i.e., in three-dimensional (3D) domain. The underlying reason lies in the fact that analytical symplectic eigen solution for 3D elastic crack problem is not yet available, a 3D SASE thus cannot be constructed through a simple generalization from the 2D SASEs. This study aims to fill out this 3D gap, we thus use a trail displacement field to construct a 3D SASE. The derived strain and stress fields still possess Singularity in the vicinity of crack-tip. Finite Element formulation is derived based on the minimum total potential energy principle. It is found that some of key features of a 2D SASE still exist in the developed 3D one, e.g., the SIFs can be calculated accurately without any post-processing. Numerical examples are considered to show the accuracy and performance of the proposed Element.
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On a symplectic analytical Singular Element for cracks under thermal shock considering heat flux Singularity
Applied Mathematical Modelling, 2020Co-Authors: Xing Ding, Yanguang Zhao, Weian YaoAbstract:Abstract In a precise numerical modelling of cracks under thermal shock, the Singularity issue resulted from heat flux should also be considered in addition to the one resulted from stress. The assumptions of constant temperature distribution usually adopted in the existing studies may lead to significant error. The concerned problem involves the discretization in both space and time domains. Numerical error resulted from the Singularity issues in the space domain may be accumulated in the time domain. Hence, a unified framework which integrates reliable methods for both space and time domains are desired. In the present contribution, the classic thermal stress problem is restudied under the Hamiltonian system and the eigen functions are obtained analytically. A symplectic analytical Singular Element (SASE) for thermal stress analysis is reformulated based on the existing ones for thermal conduction and stress analyses. The Singularity issues of both stress and heat flux are considered. A unified framework is formed with the precise time domain expanding algorithm (PTDEA) for the time domain and the formulated SASE for the space domain. A self-adaptive technique is used for the PTDEA to improve the numerical efficiency. The time dependent fracture parameters i.e., heat flux intensity factors (HFITs) and the mixed mode thermal stress intensity factors (TSIFs) can be solved accurately without any post-processing. Numerical examples are given for verification and validation of the proposed method.
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Interfacial crack analysis between dissimilar viscoelastic media using symplectic analytical Singular Element
Engineering Fracture Mechanics, 2019Co-Authors: Weian Yao, Qilin JinAbstract:Abstract In this paper, a two-dimensional interfacial crack problem between two dissimilar linear viscoelastic media is numerically investigated. The problem can be formulated as a viscoelastic problem. Firstly, the viscoelastic problem in the time domain is transformed into a corresponding elastic one in the Laplace domain using the Laplace transformation. Then a symplectic analytical Singular Element (SASE) in the framework of finite Element method is applied to the obtained elastic problem. The SASE is constructed using bimaterial symplectic eigen solutions with higher order expanding terms. The eigen solutions are derived into explicit forms, and fracture parameters of the problem can be determined directly from expanding coefficients of the eigen solutions. Particularly we investigate how to obtain strain energy release rate, which is an important fracture parameter to viscoelastic fracture problem. Numerical examples are provided to demonstrate the accuracy and effectiveness of the present method.
Shangtong Yang - One of the best experts on this subject based on the ideXlab platform.
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A symplectic analytical Singular Element for steady-state thermal conduction with Singularities in anisotropic material
Journal of Heat Transfer, 2018Co-Authors: Weian Yao, Shangtong YangAbstract:Modelling of steady-state thermal conduction for crack and v-notch in anisotropic material remains challenging. Conventional numerical methods could bring significant error and the analytical solution should be used to improve the accuracy. In this study, crack and v-notch in anisotropic material are studied. The analytical symplectic eigen solutions are obtained for the first time and used to construct a new symplectic analytical Singular Element (SASE). The shape functions of the SASE are defined by the obtained eigen solutions (including higher order terms), hence the temperature as well as heat flux fields around the crack/notch tip can be described accurately. The formulation of the stiffness matrix of the SASE is then derived based on a variational principle with two kinds of variables. The nodal variable is transformed into temperature such that the proposed SASE can be connected with conventional finite Elements directly without transition Element. Structures of complex geometries and complicated boundary conditions can be analyzed numerically. The generalized flux intensity factors (GFIFs) can be calculated directly without any post-processing. A few numerical examples are worked out and it is proven that the proposed method is effective for the discussed problem, and the structure can be analyzed accurately and efficiently.
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a novel size independent symplectic analytical Singular Element for inclined crack terminating at bimaterial interface
Applied Mathematical Modelling, 2017Co-Authors: Xiaofei Hu, Q S Shen, J N Wang, Shangtong YangAbstract:Cracks often exist in composite structures, especially at the interface of two different materials. These cracks can significantly affect the load bearing capacity of the structure and lead to premature failure of the structure. In this paper, a novel Element for modeling the Singular stress state around the inclined interface crack which terminates at the interface is developed. This new Singular Element is derived based on the explicit form of the high order eigen solution which is, for the first time, determined by using a symplectic approach. The developed Singular Element is then applied in finite Element analysis and the stress intensity factors (SIFs) for a number of crack configurations are derived. It has been concluded that composites with complex geometric configurations of inclined interface cracks can be accurately simulated by the developed method, according to comparison of the results against benchmarks. It has been found that the stiffness matrix of the proposed Singular Element is independent of the Element size and the SIFs of the crack can be solved directly without any post-processing.
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Study on steady-state thermal conduction with Singularities in multi-material composites
International Journal of Heat and Mass Transfer, 2017Co-Authors: H. Y. Gao, Weian Yao, Shangtong YangAbstract:Increasing demand in material and mechanical properties has led to production of complex composite structures. The composite structures, made of different materials, possess a variety of properties derived from each material. This has brought challenges in both analytical and numerical studies in thermal conduction which is of significant importance for thermoelastic problems. Therefore, a unified and effective approach would be desirable. The present study makes a first attempt to determining the analytical symplectic eigen solution for steady-state thermal conduction problem of multi-material crack. Based on the obtained symplectic eigen solution (including higher order expanding eigen solution terms), a new symplectic analytical Singular Element (SASE) for numerical modeling is constructed. It is concluded that composite structures composed of multi-material with complex geometric shapes can be modeled by the developed method, and the generalized flux intensity factors (GFIFs) can be solved accurately and efficiently.
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A symplectic analytical Singular Element for steady-state thermal conduction with Singularities in composite structures
Numerical Heat Transfer Part B: Fundamentals, 2016Co-Authors: H. Y. Gao, Weian Yao, Shangtong YangAbstract:In modern design of composite structures, multiple materials with different properties are bound together. Accurate prediction of the strength of the interface between different materials, especially with the existence of cracks under thermal loading, is demanded in engineering. To this end, detailed knowledge on the distribution of temperature and heat flux is required. This study conducts a systematical investigation on the cracks terminated at material interface under steady-state thermal conduction. A new symplectic analytical Singular Element is constructed for the numerical modeling. Combining the proposed Element with conventional finite Elements, the generalized flux intensity factors can be solved accurately.
Wei Zhou - One of the best experts on this subject based on the ideXlab platform.
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A new variable‐order Singular boundary Element for two‐dimensional stress analysis
International Journal for Numerical Methods in Engineering, 2002Co-Authors: Kian Meng Lim, K.h. Lee, Andrew A. O. Tay, Wei ZhouAbstract:A new variable-order Singular boundary Element for two-dimensional stress analysis is developed. This Element is an extension of the basic three-node quadratic boundary Element with the shape functions enriched with variable-order Singular displacement and traction fields which are obtained from an asymptotic Singularity analysis. Both the variable order of the Singularity and the polar profile of the Singular fields are incorporated into the Singular Element to enhance its accuracy. The enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the Singular node thereby enabling direct calculation instead of through indirect extrapolation or contour-integral methods. Numerical examples involving crack, notch and corner problems in homogeneous materials and bimaterial systems show the Singular Element's great versatility and accuracy in solving a wide range of problems with various orders of Singularities. The stress intensity factors which are obtained agree very well with those reported in the literature. Copyright © 2002 John Wiley & Sons, Ltd.
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a new variable order Singular boundary Element for two dimensional stress analysis
International Journal for Numerical Methods in Engineering, 2002Co-Authors: Kian Meng Lim, K.h. Lee, Andrew A. O. Tay, Wei ZhouAbstract:A new variable-order Singular boundary Element for two-dimensional stress analysis is developed. This Element is an extension of the basic three-node quadratic boundary Element with the shape functions enriched with variable-order Singular displacement and traction fields which are obtained from an asymptotic Singularity analysis. Both the variable order of the Singularity and the polar profile of the Singular fields are incorporated into the Singular Element to enhance its accuracy. The enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the Singular node thereby enabling direct calculation instead of through indirect extrapolation or contour-integral methods. Numerical examples involving crack, notch and corner problems in homogeneous materials and bimaterial systems show the Singular Element's great versatility and accuracy in solving a wide range of problems with various orders of Singularities. The stress intensity factors which are obtained agree very well with those reported in the literature. Copyright © 2002 John Wiley & Sons, Ltd.
Lei Chen - One of the best experts on this subject based on the ideXlab platform.
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a novel variable power Singular Element in g space with strain smoothing for bi material fracture analyses
Engineering Analysis With Boundary Elements, 2011Co-Authors: Lei Chen, G R Liu, Kaiyang Zeng, Jian ZhangAbstract:This paper aims to formulate a triangular five-node (T5) Singular crack-tip Element in G space with strain smoothing to simulate an rλ−1 (0<λ<1) stress Singularity for bi-material fracture analyses. In the present formulation, a direct point interpolation with a proper fractional order of extra basis functions is specially employed to construct variable power type Singular shape functions that are in a G1 space. Within strain smoothing, the Singular terms of functions as well as mapping procedures are no longer necessary to compute the stiffness matrix. Furthermore, thanks to the point interpolation, the proposed Singular Element eliminates the need to shift the position of the side nodes adjacent to the crack-tip, and is thus quite straightforward and easily implemented in existing codes. The effectiveness of the present Singular Element is demonstrated via numerical examples of a wide range of material combinations and boundary conditions.
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A Singular ES-FEM for plastic fracture mechanics
Computer Methods in Applied Mechanics and Engineering, 2011Co-Authors: Yuming Jiang, Lei Chen, Gui-rong Liu, Yong-wei Zhang, Tong Earn TayAbstract:Abstract The stress and strain fields around the crack tip for power hardening material, which are Singular as r approaches zero, are crucial to fracture and fatigue of structures. To simulate effectively the strain and stress around the crack tip, we develop a seven-node Singular Element which has a displacement field containing the HRR term and the second order term. The novel Singular Element is formulated based on the edge-based smoothed finite Element method (ES-FEM). With one layer of these Singular Elements around the crack tip, the ES-FEM works very well for simulating plasticity around the crack tip based on the small strain formulation. Two examples are presented with detailed comparison with other methods. It is found that the results of the presented Singular ES-FEM are closer to reference solution, which demonstrates the applicability and the effectiveness of our method for the plastic field around the crack tip.
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A novel variable power Singular Element in G space with strain smoothing for bi-material fracture analyses
Engineering Analysis with Boundary Elements, 2011Co-Authors: Lei Chen, Kaiyang Zeng, Gui-rong Liu, Jian ZhangAbstract:This paper aims to formulate a triangular five-node (T5) Singular crack-tip Element in G space with strain smoothing to simulate an rλ−1 (0
Jian Zhang - One of the best experts on this subject based on the ideXlab platform.
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a novel variable power Singular Element in g space with strain smoothing for bi material fracture analyses
Engineering Analysis With Boundary Elements, 2011Co-Authors: Lei Chen, G R Liu, Kaiyang Zeng, Jian ZhangAbstract:This paper aims to formulate a triangular five-node (T5) Singular crack-tip Element in G space with strain smoothing to simulate an rλ−1 (0<λ<1) stress Singularity for bi-material fracture analyses. In the present formulation, a direct point interpolation with a proper fractional order of extra basis functions is specially employed to construct variable power type Singular shape functions that are in a G1 space. Within strain smoothing, the Singular terms of functions as well as mapping procedures are no longer necessary to compute the stiffness matrix. Furthermore, thanks to the point interpolation, the proposed Singular Element eliminates the need to shift the position of the side nodes adjacent to the crack-tip, and is thus quite straightforward and easily implemented in existing codes. The effectiveness of the present Singular Element is demonstrated via numerical examples of a wide range of material combinations and boundary conditions.
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A novel variable power Singular Element in G space with strain smoothing for bi-material fracture analyses
Engineering Analysis with Boundary Elements, 2011Co-Authors: Lei Chen, Kaiyang Zeng, Gui-rong Liu, Jian ZhangAbstract:This paper aims to formulate a triangular five-node (T5) Singular crack-tip Element in G space with strain smoothing to simulate an rλ−1 (0
