A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discon...A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.展开更多
Although boundary displacement and traction are independent field variables in boundary conditions of an elasticity problem at a non-singular boundary point, there exist definite relations of singularity intensities b...Although boundary displacement and traction are independent field variables in boundary conditions of an elasticity problem at a non-singular boundary point, there exist definite relations of singularity intensities between boundary displacement derivatives and tractions at a singular boundary point. The analytical forms of the relations at a singular smooth point for 2D isotropic elastic problems have been established in this work. By using the relations, positions of the singular boundary points and the corresponding singularity intensities of the unknown boundary field variables can be determined a priori. Therefore, more appropriate shape functions of the unknown boundary field variables in singular elements can be constructed. A numerical example shows that the accuracy of the BEM analysis using the developed theory is greatly increased.展开更多
An application of the boundary element method (BEM) is presented to calculate the behaviors of a spiral grooved thrust bearing (SGTB). The basic reason is that the SGTB has very complex boundary conditions that can hi...An application of the boundary element method (BEM) is presented to calculate the behaviors of a spiral grooved thrust bearing (SGTB). The basic reason is that the SGTB has very complex boundary conditions that can hinder the effective or sufficient applications of the finite difference method (FDM) and the finite element method (FEM), despite some existing work based on the FDM and the FEM. In other to apply the BEM, the pressure control equation, i. e., Reynolds' equation, is first transformed into Laplace's and Poisson's form of the equations. Discretization of the SGTB with a set of boundary elements is thus explained in detail, which also includes the handling of boundary conditions. The Archimedean SGTB is chosen as an example of the application Of BEM, and the relationship between the behaviors and structure parameters of the bearing are found and discussed through this calculation. The obtained results lay a solid foundation for a further work of the design of the SGTB.展开更多
This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design metho...This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design method. Comparison of the design provisions of the GB 50011-2010 code and those of the American code ACI 318-14 indicates a possible deficiency in the T-shaped wall design provisions in GB 50011-2010. A case study of a typical T-shaped wall designed in accordance with GB 50011-2010 also indicates the insufficient extent of the boundary element at the non-flange end and overly conservative design of the flange end boundary element. Improved designs for special boundary elements ofT-shaped walls are developed using a displacement-based method. The proposed design formulas produce a longer boundary element at the non-flange end and a shorter boundary element at the flange end, relative to those of the GB 50011-2010 provisions. Extensive numerical analysis indicates that T-shaped walls designed using the proposed formulas develop inelastic drift of 0.01 for both cases of the flange in compression and in tension.展开更多
This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution.The geometries of the structures are represented by Catmull-Clark subdivision surfaces,which are able to build...This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution.The geometries of the structures are represented by Catmull-Clark subdivision surfaces,which are able to build gap-free Computer-Aided Design models and meanwhile tackle the extraordinary points that are commonly encountered in geometricmodelling.The acoustic fields are simulated using the isogeometric boundary elementmethod,and a density-based topology optimization is conducted to optimize distribution of sound-absorbing materials adhered to structural surfaces.The approach enables one to perform acoustic optimization from Computer-Aided Design models directly without needingmeshing and volume parameterization,thereby avoiding the geometric errors and time-consuming preprocessing steps in conventional simulation and optimization methods.The effectiveness of the present method is demonstrated by three dimensional numerical examples.展开更多
In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the...In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.展开更多
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide...We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.展开更多
To simulate ballast performance accurately and efficiently,the input in discrete element models should be carefully selected,including the contact model and applied particle shape.To study the effects of the contact m...To simulate ballast performance accurately and efficiently,the input in discrete element models should be carefully selected,including the contact model and applied particle shape.To study the effects of the contact model and applied particle shape on the ballast performance(shear strength and deformation),the direct shear test(DST)model and the large-scale process simulation test(LPST)model were developed on the basis of two types of contact models,namely the rolling resistance linear(RRL)model and the linear contact(LC)model.Particle shapes are differentiated by clumps.A clump is a sphere assembly for one ballast particle.The results show that compared with the typical LC model,the RRL method is more efficient and realistic to predict shear strength results of ballast assemblies in DSTs.In addition,the RRL contact model can also provide accurate vertical and lateral ballast deformation under the cyclic loading in LPSTs.展开更多
This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and S...This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and Startled and the crack tip displacement discontinuity elements proposed by the author. In the numerical method implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical method is called a hybrid displacement discontinuity method. The following test examples of crack problems in an infinite plate under tension are included： “ center-inclined cracked plate”, “interaction of two collinear cracks with equal length”, “interaction of three collinear cracks with equal length”, “interaction of two parallel cracks with equal length”, and “interaction of one horizontal crack and one inclined crack”. The present numerical results show that the numerical method is simple yet very accurate for analyzing the interaction of multiple cracks in an infinite plate.展开更多
Because of the high importance of transportation tunnels,most precise analyses of stress concentration and displacement around them are essential to provide safety of them as much as possible.Recently,various numerica...Because of the high importance of transportation tunnels,most precise analyses of stress concentration and displacement around them are essential to provide safety of them as much as possible.Recently,various numerical methods such as finite element method(FEM),discrete element method(DEM),finite difference method(FDM)and boundary element method(BEM)have been used extremely in geosciences problems,but among these numerical methods,BEM has been used less than others because the computational algorithm is not so straightforward.This paper suggests the implementation of the indirect boundary element method(IBEM)as a formulation of BEM to analyze displacement around Shiraz-Esfahan railway tunnel in Zagros Mountains southwest of Iran.For this purpose,this tunnel has been modeled numerically using two-dimensional fictitious stress method(TWOFS)algorithm.To validate the results,they were compared with FEM results as a commonly used numerical method.Results of current theoretical study have shown that the presented approach using IBEM is reasonably accurate and can be used for analysis of displacement in geosciences problems.In rock mechanics,for problems with a low ratio of boundary surface to volume,FEM is not very well suited and may be cumbersome,but use of such a proposed IBEM approach can be particularly attractive.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10272037)
文摘A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.
文摘Although boundary displacement and traction are independent field variables in boundary conditions of an elasticity problem at a non-singular boundary point, there exist definite relations of singularity intensities between boundary displacement derivatives and tractions at a singular boundary point. The analytical forms of the relations at a singular smooth point for 2D isotropic elastic problems have been established in this work. By using the relations, positions of the singular boundary points and the corresponding singularity intensities of the unknown boundary field variables can be determined a priori. Therefore, more appropriate shape functions of the unknown boundary field variables in singular elements can be constructed. A numerical example shows that the accuracy of the BEM analysis using the developed theory is greatly increased.
基金This project is supported by National Natural Science Foundation of China.
文摘An application of the boundary element method (BEM) is presented to calculate the behaviors of a spiral grooved thrust bearing (SGTB). The basic reason is that the SGTB has very complex boundary conditions that can hinder the effective or sufficient applications of the finite difference method (FDM) and the finite element method (FEM), despite some existing work based on the FDM and the FEM. In other to apply the BEM, the pressure control equation, i. e., Reynolds' equation, is first transformed into Laplace's and Poisson's form of the equations. Discretization of the SGTB with a set of boundary elements is thus explained in detail, which also includes the handling of boundary conditions. The Archimedean SGTB is chosen as an example of the application Of BEM, and the relationship between the behaviors and structure parameters of the bearing are found and discussed through this calculation. The obtained results lay a solid foundation for a further work of the design of the SGTB.
基金International Science&Technology Cooperation Program of China under Grant No.2014DFA70950Tsinghua University Initiative Scientific Research Program under Grant No.2012THZ02-1National Natural Science Foundation of China under Grant No.91315301
文摘This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design method. Comparison of the design provisions of the GB 50011-2010 code and those of the American code ACI 318-14 indicates a possible deficiency in the T-shaped wall design provisions in GB 50011-2010. A case study of a typical T-shaped wall designed in accordance with GB 50011-2010 also indicates the insufficient extent of the boundary element at the non-flange end and overly conservative design of the flange end boundary element. Improved designs for special boundary elements ofT-shaped walls are developed using a displacement-based method. The proposed design formulas produce a longer boundary element at the non-flange end and a shorter boundary element at the flange end, relative to those of the GB 50011-2010 provisions. Extensive numerical analysis indicates that T-shaped walls designed using the proposed formulas develop inelastic drift of 0.01 for both cases of the flange in compression and in tension.
基金We acknowledge the support of the National Natural Science Foundation of China(NSFC)under Grant Nos.51904202 and 11702238Stephane Bordas thanks the financial support of Intuitive modeling and SIMulation platform(IntuiSIM)(PoC17/12253887)grant by Luxembourg National Research Fund.
文摘This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution.The geometries of the structures are represented by Catmull-Clark subdivision surfaces,which are able to build gap-free Computer-Aided Design models and meanwhile tackle the extraordinary points that are commonly encountered in geometricmodelling.The acoustic fields are simulated using the isogeometric boundary elementmethod,and a density-based topology optimization is conducted to optimize distribution of sound-absorbing materials adhered to structural surfaces.The approach enables one to perform acoustic optimization from Computer-Aided Design models directly without needingmeshing and volume parameterization,thereby avoiding the geometric errors and time-consuming preprocessing steps in conventional simulation and optimization methods.The effectiveness of the present method is demonstrated by three dimensional numerical examples.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374096 and 61104048)the Natural Science Foundation of Zhejiang Province of China(Grant No.Y6110751)
文摘In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.
文摘We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.
基金by the China Scholarship Council and the Natural Science Foundation of China(Grant No.51578469)We also would like to acknowledge the support of the Chinese Program of Introducing Talents of Discipline to Universities(111 Project,Grant No.B16041)。
文摘To simulate ballast performance accurately and efficiently,the input in discrete element models should be carefully selected,including the contact model and applied particle shape.To study the effects of the contact model and applied particle shape on the ballast performance(shear strength and deformation),the direct shear test(DST)model and the large-scale process simulation test(LPST)model were developed on the basis of two types of contact models,namely the rolling resistance linear(RRL)model and the linear contact(LC)model.Particle shapes are differentiated by clumps.A clump is a sphere assembly for one ballast particle.The results show that compared with the typical LC model,the RRL method is more efficient and realistic to predict shear strength results of ballast assemblies in DSTs.In addition,the RRL contact model can also provide accurate vertical and lateral ballast deformation under the cyclic loading in LPSTs.
文摘This article examines the interaction of multiple cracks in an infinite plate by using a numerical method. The numerical method consists of the non-singular displacement discontinuity element presented by Crouch and Startled and the crack tip displacement discontinuity elements proposed by the author. In the numerical method implementation, the left or the right crack tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. The numerical method is called a hybrid displacement discontinuity method. The following test examples of crack problems in an infinite plate under tension are included： “ center-inclined cracked plate”, “interaction of two collinear cracks with equal length”, “interaction of three collinear cracks with equal length”, “interaction of two parallel cracks with equal length”, and “interaction of one horizontal crack and one inclined crack”. The present numerical results show that the numerical method is simple yet very accurate for analyzing the interaction of multiple cracks in an infinite plate.
文摘Because of the high importance of transportation tunnels,most precise analyses of stress concentration and displacement around them are essential to provide safety of them as much as possible.Recently,various numerical methods such as finite element method(FEM),discrete element method(DEM),finite difference method(FDM)and boundary element method(BEM)have been used extremely in geosciences problems,but among these numerical methods,BEM has been used less than others because the computational algorithm is not so straightforward.This paper suggests the implementation of the indirect boundary element method(IBEM)as a formulation of BEM to analyze displacement around Shiraz-Esfahan railway tunnel in Zagros Mountains southwest of Iran.For this purpose,this tunnel has been modeled numerically using two-dimensional fictitious stress method(TWOFS)algorithm.To validate the results,they were compared with FEM results as a commonly used numerical method.Results of current theoretical study have shown that the presented approach using IBEM is reasonably accurate and can be used for analysis of displacement in geosciences problems.In rock mechanics,for problems with a low ratio of boundary surface to volume,FEM is not very well suited and may be cumbersome,but use of such a proposed IBEM approach can be particularly attractive.
