The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock mater...The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock materials.In this study,we present a novel approach that introduces a 3D numerical manifold method(3D-NMM)with a geometric kernel to enhance computational efficiency.Specifically,the maximum tensile stress criterion is adopted as a crack growth criterion to achieve strong discontinuous crack growth,and a local crack tracking algorithm and an angle correction technique are incorporated to address minor limitations of the algorithm in a 3D model.The implementation of the program is carried out in Python,using object-oriented programming in two independent modules:a calculation module and a crack module.Furthermore,we propose feasible improvements to enhance the performance of the algorithm.Finally,we demonstrate the feasibility and effectiveness of the enhanced algorithm in the 3D-NMM using four numerical examples.This study establishes the potential of the 3DNMM,combined with the local tracking algorithm,for accurately modeling 3D crack propagation in brittle rock materials.展开更多
3D evaluation method of cutting surface topography for C/Ph composites was established.The cutting surface was measured by Talyscan 150,using 3D non-contact measurement.Through the results of 2D and 3D roughness evalu...3D evaluation method of cutting surface topography for C/Ph composites was established.The cutting surface was measured by Talyscan 150,using 3D non-contact measurement.Through the results of 2D and 3D roughness evaluating for C/Ph composite and Duralumin,the 2D evaluation method of the cutting surface topography of C/Ph composite loses a lot of information,the characteristics of the surface topography of C/Ph composite can be comprehensively and authentically evaluated only by 3D evaluation method.Furthermore,3D amplitude and spatial parameters were adopted to evaluate the surface.The results show that： the topography of the C/Ph composite is anisotropic,there are more valleys in the machined surface of C/Ph than that of duralumin,and there are not obvious feeding textures for C/Ph,which indicates the machining mechanism is different from the metal.In conclusion,the topography of the C/Ph composite cutting surface is anisotropic;the cutting surface of C/Ph composite needs 3D evaluation method.展开更多
This paper aims to establish a 3D evaluation method for cutting surface topography of C/C composites. The cutting surface is measured by Talyscan 150, using 3D non-contact measurement. By evaluating 2D and 3D roughnes...This paper aims to establish a 3D evaluation method for cutting surface topography of C/C composites. The cutting surface is measured by Talyscan 150, using 3D non-contact measurement. By evaluating 2D and 3D roughness of C/C composite and Duralumin, the 2D evaluation method of the cutting surface topography of C/C composite loses a lot of information, and the characteristics of the surface topography of C/C composite can be comprehensively and authentically evaluated only by the 3D evaluation method. Furthermore, 3D amplitude and spatial parameters are adopted to evaluate the surface and the results show that： the topography of the C/C composite is anisotropy and there are no obvious feeding textures but abrupt peaks and valleys on surface of the C/C composite, which indicates that the machining mecha- nism is different from that of the metal. In conclusion, The C/C composite surface is evaluated using a 3D evaluation method, the roughness error is small, and the unique topography characteristics earl be au- thentically evaluated.展开更多
A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analo...A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares （MLS） approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only dis- placement degrees of freedom （d.o.f.s）, is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.展开更多
A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is ...A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.展开更多
板结构的稳定性在船舶设计和强度校核中占据重要地位。为研究船体薄板的剪切稳定性,本文设计画框式夹具对方形薄板进行面内剪切屈曲试验,试验中采用三维数字图像相关法(3 Dimensions Digital Image Correlation,简称3D-DIC),获得了载荷...板结构的稳定性在船舶设计和强度校核中占据重要地位。为研究船体薄板的剪切稳定性,本文设计画框式夹具对方形薄板进行面内剪切屈曲试验,试验中采用三维数字图像相关法(3 Dimensions Digital Image Correlation,简称3D-DIC),获得了载荷-端部伸长率曲线、全场位移/应变等力学响应信息。载荷-端部伸长率关系揭示了薄板在面内剪切工况下的承载特性,确定了屈曲失稳临界载荷;通过分析薄板在典型时刻的位移场、应变场信息,发现薄板的法向变形会随面内剪切载荷增加而增大。薄板失稳后,沿垂直对角线存在对称分布的三个半波,内部波幅大于外部波幅,应变波形和云图在后屈曲过程中会趋于稳定。通过分析薄板关键点的法向位移和米塞斯应变随时间的响应曲线,提出并验证了一种识别面内受剪薄板屈曲失稳的新方法。本文为船用薄板面内剪切稳定性的试验研究和力学行为分析等提供了有益参考。展开更多
Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured...Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured-grid-based methods can model complex underground structures with high accuracy and overcome the defects of traditional methods, such as the high computational cost for improving model accuracy and the difficulty of inverting with topography. In this paper, we used the limited-memory quasi-Newton(L-BFGS) method with an unstructured finite-element grid to perform 3D MT inversions. This method avoids explicitly calculating Hessian matrices, which greatly reduces the memory requirements. After the first iteration, the approximate inverse Hessian matrix well approximates the true one, and the Newton step(set to 1) can meet the sufficient descent condition. Only one calculation of the objective function and its gradient are needed for each iteration, which greatly improves its computational efficiency. This approach is well-suited for large-scale 3D MT inversions. We have tested our algorithm on data with and without topography, and the results matched the real models well. We can recommend performing inversions based on an unstructured finite-element method and the L-BFGS method for situations with topography and complex underground structures.展开更多
In this study, the petrophysical parameters such as density, sonic, neutron, and porosity were investigated and presented in the 3D models. The 3D models were built using geostatistical method that is used to estimate...In this study, the petrophysical parameters such as density, sonic, neutron, and porosity were investigated and presented in the 3D models. The 3D models were built using geostatistical method that is used to estimate studied parameters in the entire reservoir. For this purpose, the variogram of each parameter was determined to specify spatial correlation of data. Resulted variograms were non-monotonic. That shows anisotropy of structure. The lithology and porosity parameters are the main causes of this anisotropy. The 3D models also show that petrophysical data has higher variation in north part of reservoir than south part. In addition to, the west limb of reservoir shows higher porosity than east limb. The variation of sonic and neutron data are similar whereas the density data has opposed variation.展开更多
Content-based 3D model retrieval is of great help to facilitate the reuse of existing designs and to inspire designers during conceptual design. However, there is still a gap to apply it in industry due to the low tim...Content-based 3D model retrieval is of great help to facilitate the reuse of existing designs and to inspire designers during conceptual design. However, there is still a gap to apply it in industry due to the low time efficiency. This paper presents two new methods with high efficiency to build a Content-based 3D model retrieval system. First, an improvement is made on the ＂Shape Distribution （D2）＂ algorithm, and a new algorithm named ＂Quick D2＂ is proposed. Four sample 3D mechanical models are used in an experiment to compare the time cost of the two algorithms. The result indicates that the time cost of Quick D2 is much lower than that of D2, while the descriptors extracted by the two algorithms are almost the same. Second, an expandable 3D model repository index method with high performance, namely, RBK index, is presented. On the basis of RBK index, the search space is pruned effectively during the search process, leading to a speed up of the whole system. The factors that influence the values of the key parameters of RBK index are discussed and an experimental method to find the optimal values of the key parameters is given. Finally, ＂3D Searcher＂, a content-based 3D model retrieval system is developed. By using the methods proposed, the time cost for the system to respond one query online is reduced by 75% on average. The system has been implemented in a manufacturing enterprise, and practical query examples during a case of the automobile rear axle design are also shown. The research method presented shows a new research perspective and can effectively improve the content-based 3D model retrieval efficiency.展开更多
In order to explore the mineral resources buried in sea mud,it is necessary to use seabed resistivity measuring equipment,which works closer to the sediments than ordinary ship-based geophysical measuring equipment. B...In order to explore the mineral resources buried in sea mud,it is necessary to use seabed resistivity measuring equipment,which works closer to the sediments than ordinary ship-based geophysical measuring equipment. Because of the harsh environment of seafloor,high pressure and highly conductive seawater,marine magnetotelluric method developed slowly. The sea floor environment is similar to the environment of logging, According to the design of dual lateral logging equipment,a new equipment for seafloor electrical resistivity measurement is designed. Four 3D FEM models that contain resistivity abnormal targets are built to test the ability of this equipment to locate different shape of shallow buried resistivity abnormal targets in sea mud. The authors propose the method to correct the response curve while the bottom surface of this equipment is suspended or not parallel to the seafloor. The resistivity of targets can be calculated accurately.展开更多
In order to improve the accuracy and efficiency of 3D model retrieval,the method based on affinity propagation clustering algorithm is proposed. Firstly,projection ray-based method is proposed to improve the feature e...In order to improve the accuracy and efficiency of 3D model retrieval,the method based on affinity propagation clustering algorithm is proposed. Firstly,projection ray-based method is proposed to improve the feature extraction efficiency of 3D models. Based on the relationship between model and its projection,the intersection in 3D space is transformed into intersection in 2D space,which reduces the number of intersection and improves the efficiency of the extraction algorithm. In feature extraction,multi-layer spheres method is analyzed. The two-layer spheres method makes the feature vector more accurate and improves retrieval precision. Secondly,Semi-supervised Affinity Propagation ( S-AP) clustering is utilized because it can be applied to different cluster structures. The S-AP algorithm is adopted to find the center models and then the center model collection is built. During retrieval process,the collection is utilized to classify the query model into corresponding model base and then the most similar model is retrieved in the model base. Finally,75 sample models from Princeton library are selected to do the experiment and then 36 models are used for retrieval test. The results validate that the proposed method outperforms the original method and the retrieval precision and recall ratios are improved effectively.展开更多
In order to study the failure patterns and strength of 3D braided composites from the microscopic view, the damage propagation under tensile loading steps in three kinds of unit cells is simulated. The homogenization ...In order to study the failure patterns and strength of 3D braided composites from the microscopic view, the damage propagation under tensile loading steps in three kinds of unit cells is simulated. The homogenization formula of micro-stress and the solving approach of finite element method are given firstly. A criterion is presented to determine the damage and its pattern of each element, and then the stiffness degradation method based on Murakami's geometric damage theory is used to simulate the status of damage under tensile loading steps for three kinds of unit cells. It can be seen that the damage percentage and damage pattern of damaged unit cell are totally different for different kind of unit cells. More damaged elements are observed for face cell and corner cell than that for body cell. It is also observed that the damage firstly occurs at the area of face cell, which agrees well with experimental results. It is verified that considering the effects of face and corner cells are important for the damage and strength analysis of 3D braided composites.展开更多
A numerical method is put forward in this paper, using the boundary element method （BEM） to model 3D terrain effects on magnetotelluric （MT） surveys, Using vector integral theory and electromagnetic field boundary...A numerical method is put forward in this paper, using the boundary element method （BEM） to model 3D terrain effects on magnetotelluric （MT） surveys, Using vector integral theory and electromagnetic field boundary conditions, the boundary problem of two electromagnetic fields in the upper half space （air） and lower half space （earth medium） was transformed into two vector integral equations just related to the topography ： one magnetic equation for computing the magnetic field and the other electrical equation for computing the electrical field. The topography integral is decomposed into a series of integrals in a triangle element. For the integral in a triangle element, we suppose that the electromagnetic field in it is the stack of the electromagnetic field in the homogeneous earth and the topography response which is a constant; so the computation becomes simple, convenient and highly accurate. By decomposition and computation, each vector integral equation can be calculated by solving three linear equations that are related to the three Cartesian directions. The matrix of these linear equations is diagonally dominant and can be solved using the Symmetric Successive Over-Relaxation （SSOR） method. The apparent resistivity curve of MT on two 3D terrains calculated by BEM is shown in this paper.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.42172312 and 52211540395)support from the Institut Universitaire de France(IUF).
文摘The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock materials.In this study,we present a novel approach that introduces a 3D numerical manifold method(3D-NMM)with a geometric kernel to enhance computational efficiency.Specifically,the maximum tensile stress criterion is adopted as a crack growth criterion to achieve strong discontinuous crack growth,and a local crack tracking algorithm and an angle correction technique are incorporated to address minor limitations of the algorithm in a 3D model.The implementation of the program is carried out in Python,using object-oriented programming in two independent modules:a calculation module and a crack module.Furthermore,we propose feasible improvements to enhance the performance of the algorithm.Finally,we demonstrate the feasibility and effectiveness of the enhanced algorithm in the 3D-NMM using four numerical examples.This study establishes the potential of the 3DNMM,combined with the local tracking algorithm,for accurately modeling 3D crack propagation in brittle rock materials.
基金Funded by the National Natural Science Foundation of China(No.50875036)
文摘3D evaluation method of cutting surface topography for C/Ph composites was established.The cutting surface was measured by Talyscan 150,using 3D non-contact measurement.Through the results of 2D and 3D roughness evaluating for C/Ph composite and Duralumin,the 2D evaluation method of the cutting surface topography of C/Ph composite loses a lot of information,the characteristics of the surface topography of C/Ph composite can be comprehensively and authentically evaluated only by 3D evaluation method.Furthermore,3D amplitude and spatial parameters were adopted to evaluate the surface.The results show that： the topography of the C/Ph composite is anisotropic,there are more valleys in the machined surface of C/Ph than that of duralumin,and there are not obvious feeding textures for C/Ph,which indicates the machining mechanism is different from the metal.In conclusion,the topography of the C/Ph composite cutting surface is anisotropic;the cutting surface of C/Ph composite needs 3D evaluation method.
基金Supported by the National Natural Science Foundation of China (No. 50875036)
文摘This paper aims to establish a 3D evaluation method for cutting surface topography of C/C composites. The cutting surface is measured by Talyscan 150, using 3D non-contact measurement. By evaluating 2D and 3D roughness of C/C composite and Duralumin, the 2D evaluation method of the cutting surface topography of C/C composite loses a lot of information, and the characteristics of the surface topography of C/C composite can be comprehensively and authentically evaluated only by the 3D evaluation method. Furthermore, 3D amplitude and spatial parameters are adopted to evaluate the surface and the results show that： the topography of the C/C composite is anisotropy and there are no obvious feeding textures but abrupt peaks and valleys on surface of the C/C composite, which indicates that the machining mecha- nism is different from that of the metal. In conclusion, The C/C composite surface is evaluated using a 3D evaluation method, the roughness error is small, and the unique topography characteristics earl be au- thentically evaluated.
基金supported by the National Natural Science Foundation of China (11172192)the College Postgraduate Research and Innovation Project of Jiangsu province (CXZZ12 0803)
文摘A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares （MLS） approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only dis- placement degrees of freedom （d.o.f.s）, is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.
基金supported by the Yunnan Provincial Applied Basic Research Program of China(No. KKSY201207019)
文摘A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.
文摘板结构的稳定性在船舶设计和强度校核中占据重要地位。为研究船体薄板的剪切稳定性,本文设计画框式夹具对方形薄板进行面内剪切屈曲试验,试验中采用三维数字图像相关法(3 Dimensions Digital Image Correlation,简称3D-DIC),获得了载荷-端部伸长率曲线、全场位移/应变等力学响应信息。载荷-端部伸长率关系揭示了薄板在面内剪切工况下的承载特性,确定了屈曲失稳临界载荷;通过分析薄板在典型时刻的位移场、应变场信息,发现薄板的法向变形会随面内剪切载荷增加而增大。薄板失稳后,沿垂直对角线存在对称分布的三个半波,内部波幅大于外部波幅,应变波形和云图在后屈曲过程中会趋于稳定。通过分析薄板关键点的法向位移和米塞斯应变随时间的响应曲线,提出并验证了一种识别面内受剪薄板屈曲失稳的新方法。本文为船用薄板面内剪切稳定性的试验研究和力学行为分析等提供了有益参考。
基金financially supported by the National Natural Science Foundation of China(No.41774125)Key Program of National Natural Science Foundation of China(No.41530320)+1 种基金the Key National Research Project of China(Nos.2016YFC0303100 and 2017YFC0601900)the Strategic Priority Research Program of Chinese Academy of Sciences Pilot Special(No.XDA 14020102)
文摘Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured-grid-based methods can model complex underground structures with high accuracy and overcome the defects of traditional methods, such as the high computational cost for improving model accuracy and the difficulty of inverting with topography. In this paper, we used the limited-memory quasi-Newton(L-BFGS) method with an unstructured finite-element grid to perform 3D MT inversions. This method avoids explicitly calculating Hessian matrices, which greatly reduces the memory requirements. After the first iteration, the approximate inverse Hessian matrix well approximates the true one, and the Newton step(set to 1) can meet the sufficient descent condition. Only one calculation of the objective function and its gradient are needed for each iteration, which greatly improves its computational efficiency. This approach is well-suited for large-scale 3D MT inversions. We have tested our algorithm on data with and without topography, and the results matched the real models well. We can recommend performing inversions based on an unstructured finite-element method and the L-BFGS method for situations with topography and complex underground structures.
文摘In this study, the petrophysical parameters such as density, sonic, neutron, and porosity were investigated and presented in the 3D models. The 3D models were built using geostatistical method that is used to estimate studied parameters in the entire reservoir. For this purpose, the variogram of each parameter was determined to specify spatial correlation of data. Resulted variograms were non-monotonic. That shows anisotropy of structure. The lithology and porosity parameters are the main causes of this anisotropy. The 3D models also show that petrophysical data has higher variation in north part of reservoir than south part. In addition to, the west limb of reservoir shows higher porosity than east limb. The variation of sonic and neutron data are similar whereas the density data has opposed variation.
基金supported by National Natural Science Foundation of China(Grant No. 51175287)National Science and Technology Major Project(Grant No. 2011ZX02403)
文摘Content-based 3D model retrieval is of great help to facilitate the reuse of existing designs and to inspire designers during conceptual design. However, there is still a gap to apply it in industry due to the low time efficiency. This paper presents two new methods with high efficiency to build a Content-based 3D model retrieval system. First, an improvement is made on the ＂Shape Distribution （D2）＂ algorithm, and a new algorithm named ＂Quick D2＂ is proposed. Four sample 3D mechanical models are used in an experiment to compare the time cost of the two algorithms. The result indicates that the time cost of Quick D2 is much lower than that of D2, while the descriptors extracted by the two algorithms are almost the same. Second, an expandable 3D model repository index method with high performance, namely, RBK index, is presented. On the basis of RBK index, the search space is pruned effectively during the search process, leading to a speed up of the whole system. The factors that influence the values of the key parameters of RBK index are discussed and an experimental method to find the optimal values of the key parameters is given. Finally, ＂3D Searcher＂, a content-based 3D model retrieval system is developed. By using the methods proposed, the time cost for the system to respond one query online is reduced by 75% on average. The system has been implemented in a manufacturing enterprise, and practical query examples during a case of the automobile rear axle design are also shown. The research method presented shows a new research perspective and can effectively improve the content-based 3D model retrieval efficiency.
文摘In order to explore the mineral resources buried in sea mud,it is necessary to use seabed resistivity measuring equipment,which works closer to the sediments than ordinary ship-based geophysical measuring equipment. Because of the harsh environment of seafloor,high pressure and highly conductive seawater,marine magnetotelluric method developed slowly. The sea floor environment is similar to the environment of logging, According to the design of dual lateral logging equipment,a new equipment for seafloor electrical resistivity measurement is designed. Four 3D FEM models that contain resistivity abnormal targets are built to test the ability of this equipment to locate different shape of shallow buried resistivity abnormal targets in sea mud. The authors propose the method to correct the response curve while the bottom surface of this equipment is suspended or not parallel to the seafloor. The resistivity of targets can be calculated accurately.
基金Sponsored by the National Natural Science Foundation of China (Grant No. 51075083)
文摘In order to improve the accuracy and efficiency of 3D model retrieval,the method based on affinity propagation clustering algorithm is proposed. Firstly,projection ray-based method is proposed to improve the feature extraction efficiency of 3D models. Based on the relationship between model and its projection,the intersection in 3D space is transformed into intersection in 2D space,which reduces the number of intersection and improves the efficiency of the extraction algorithm. In feature extraction,multi-layer spheres method is analyzed. The two-layer spheres method makes the feature vector more accurate and improves retrieval precision. Secondly,Semi-supervised Affinity Propagation ( S-AP) clustering is utilized because it can be applied to different cluster structures. The S-AP algorithm is adopted to find the center models and then the center model collection is built. During retrieval process,the collection is utilized to classify the query model into corresponding model base and then the most similar model is retrieved in the model base. Finally,75 sample models from Princeton library are selected to do the experiment and then 36 models are used for retrieval test. The results validate that the proposed method outperforms the original method and the retrieval precision and recall ratios are improved effectively.
基金National Natural Science Foundation of China (10772115)
文摘In order to study the failure patterns and strength of 3D braided composites from the microscopic view, the damage propagation under tensile loading steps in three kinds of unit cells is simulated. The homogenization formula of micro-stress and the solving approach of finite element method are given firstly. A criterion is presented to determine the damage and its pattern of each element, and then the stiffness degradation method based on Murakami's geometric damage theory is used to simulate the status of damage under tensile loading steps for three kinds of unit cells. It can be seen that the damage percentage and damage pattern of damaged unit cell are totally different for different kind of unit cells. More damaged elements are observed for face cell and corner cell than that for body cell. It is also observed that the damage firstly occurs at the area of face cell, which agrees well with experimental results. It is verified that considering the effects of face and corner cells are important for the damage and strength analysis of 3D braided composites.
基金This paper is supported by the National Natural Science Foundation ofChina (No .40344002) .
文摘A numerical method is put forward in this paper, using the boundary element method （BEM） to model 3D terrain effects on magnetotelluric （MT） surveys, Using vector integral theory and electromagnetic field boundary conditions, the boundary problem of two electromagnetic fields in the upper half space （air） and lower half space （earth medium） was transformed into two vector integral equations just related to the topography ： one magnetic equation for computing the magnetic field and the other electrical equation for computing the electrical field. The topography integral is decomposed into a series of integrals in a triangle element. For the integral in a triangle element, we suppose that the electromagnetic field in it is the stack of the electromagnetic field in the homogeneous earth and the topography response which is a constant; so the computation becomes simple, convenient and highly accurate. By decomposition and computation, each vector integral equation can be calculated by solving three linear equations that are related to the three Cartesian directions. The matrix of these linear equations is diagonally dominant and can be solved using the Symmetric Successive Over-Relaxation （SSOR） method. The apparent resistivity curve of MT on two 3D terrains calculated by BEM is shown in this paper.
