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3D slope stability analysis considering strength anisotropy by a microstructure tensor enhanced elasto-plastic finite element method
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作者 Wencheng Wei Hongxiang Tang +1 位作者 Xiaoyu Song Xiangji Ye 《Journal of Rock Mechanics and Geotechnical Engineering》 2025年第3期1664-1684,共21页
This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is e... This article presents a micro-structure tensor enhanced elasto-plastic finite element(FE)method to address strength anisotropy in three-dimensional(3D)soil slope stability analysis.The gravity increase method(GIM)is employed to analyze the stability of 3D anisotropic soil slopes.The accuracy of the proposed method is first verified against the data in the literature.We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions.Based on our numerical results,the end effect significantly impacts the failure mechanism and safety factor.Anisotropy degree notably affects the safety factor,with higher degrees leading to deeper landslides.For concave slopes,they can be approximated by straight slopes with suitable boundary conditions to assess their stability.Furthermore,a case study of the Saint-Alban test embankment A in Quebec,Canada,is provided to demonstrate the applicability of the proposed FE model. 展开更多
关键词 Strength anisotropy Elasto-plastic finite element method(fem) Three-dimensional(3D)soil slope Gravity increase method(GIM) Stability analysis Case study
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Coupled Hydrodynamics and FEM Simulation of Catamaran Pontoon
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作者 Ocid Mursid Karno Malau +5 位作者 Hartono Yudo Tuswan Muhammad Luqman Hakim Ahmad Firdhaus Andi Trimulyono Muhammad Iqbal 《China Ocean Engineering》 2025年第1期179-189,共11页
Shallow water infrastructure needs to support increased activity on the shores of Semarang.This study chooses several pontoons because of their good stability,rolling motion,and more expansive space.A coupled simulati... Shallow water infrastructure needs to support increased activity on the shores of Semarang.This study chooses several pontoons because of their good stability,rolling motion,and more expansive space.A coupled simulation method consisting of hydrodynamic and structural calculations has been used to evaluate a catamaran pontoon’s motion and structural integrity.Four different space sizes are set for the pontoon system:5 m,5.5 m,6 m,and 6.5 m.The frequency domain shows that the pontoon space affects the RAO in wave periods ranging from 3 s to 5 s.At wave periods of 3 s,4 s,and 5 s,the pontoon space significantly affects the maximum motion and chain tension parameter values,which are evaluated via time domain simulation.The critical stress of the pontoon is shown at a wave period of 5 s for 5 m and 5.5 m of pontoon space,which shows that the stress can reach 248 MPa. 展开更多
关键词 coupled simulation working pontoon HYDRODYNAMICS finite element method
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Solving fluid flow in discontinuous heterogeneous porous media and multi-layer strata with interpretable physics-encoded finite element network
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作者 Xi Wang Wei Wu He-Hua Zhu 《Journal of Rock Mechanics and Geotechnical Engineering》 2025年第9期5509-5525,共17页
Physics-informed neural networks(PINNs)have prevailed as differentiable simulators to investigate flow in porous media.Despite recent progress PINNs have achieved,practical geotechnical scenarios cannot be readily sim... Physics-informed neural networks(PINNs)have prevailed as differentiable simulators to investigate flow in porous media.Despite recent progress PINNs have achieved,practical geotechnical scenarios cannot be readily simulated because conventional PINNs fail in discontinuous heterogeneous porous media or multi-layer strata when labeled data are missing.This work aims to develop a universal network structure to encode the mass continuity equation and Darcy’s law without labeled data.The finite element approximation,which can decompose a complex heterogeneous domain into simpler ones,is adopted to build the differentiable network.Without conventional DNNs,physics-encoded finite element network(PEFEN)can avoid spectral bias and learn high-frequency functions with sharp/steep gradients.PEFEN rigorously encodes Dirichlet and Neumann boundary conditions without training.Benefiting from its discretized formulation,the discontinuous heterogeneous hydraulic conductivity is readily embedded into the network.Three typical cases are reproduced to corroborate PEFEN’s superior performance over conventional PINNs and the PINN with mixed formulation.PEFEN is sparse and demonstrated to be capable of dealing with heterogeneity with much fewer training iterations(less than 1/30)than the improved PINN with mixed formulation.Thus,PEFEN saves energy and contributes to low-carbon AI for science.The last two cases focus on common geotechnical settings of impermeable sheet pile in singlelayer and multi-layer strata.PEFEN solves these cases with high accuracy,circumventing costly labeled data,extra computational burden,and additional treatment.Thus,this study warrants the further development and application of PEFEN as a novel differentiable network in porous flow of practical geotechnical engineering. 展开更多
关键词 finite element method(fem) Physics-informed neural network(PINN) Carbon neutrality Sheet pile Sharp/steep gradients Porous flow
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Semi-analytical finite element method applied for characterizing micropolar fibrous composites
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作者 J.A.OTERO Y.ESPINOSA-ALMEYDA +1 位作者 R.RODRIGUEZ-RAMOS J.MERODIO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第12期2147-2164,共18页
A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinfo... A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous matrix.This framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact conditions.The mathematical formulation of the local problems and the effective coefficients are presented by the AHM.The local problems obtained from the AHM are solved by the FEM,which is denoted as the SAFEM.The numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations. 展开更多
关键词 semi-analytical approach fiber-reinforced composite(FRC) effective property finite element method(fem) asymptotic homogenization method(AHM) micropolar elasticity
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Hermite Finite Element Method for Vibration Problem of Euler-Bernoulli Beam on Viscoelastic Pasternak Foundation
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作者 Pengfei Ji Zhe Yin 《Engineering(科研)》 2024年第10期337-352,共16页
Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Eul... Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Euler-Bernoulli beam on viscoelastic Pasternak foundation can be used to analyze the deformation and response of buildings under complex geological conditions. In this paper, we use Hermite finite element method to get the numerical approximation scheme for the vibration equation of viscoelastic Pasternak foundation beam. Convergence and error estimation are rigourously established. We prove that the fully discrete scheme has convergence order O(τ2+h4), where τis time step size and his space step size. Finally, we give four numerical examples to verify the validity of theoretical analysis. 展开更多
关键词 Viscoelastic Pasternak Foundation Beam Vibration Equation Hermite finite element method Error Estimation Numerical simulation
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Investigation of the dynamic characteristics of a dual rotor system and its start-up simulation based on finite element method 被引量:21
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作者 Zhong-xiu FEI Shui-guang TONG Chao WEI 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2013年第4期268-280,共13页
Recently,the finite element method(FEM) has been commonly applied in the engineering analysis of rotor dynamics.Gyroscopic moments,rotary inertia,transverse shear deformation and gravity can be included in computation... Recently,the finite element method(FEM) has been commonly applied in the engineering analysis of rotor dynamics.Gyroscopic moments,rotary inertia,transverse shear deformation and gravity can be included in computational models of rotor-bearing systems.In this paper,a finite element model and its solution method are presented for the calculation of the dynamics of dual rotor systems.A typical structure with two rotor shafts is discussed and the procedure for obtaining the coupling motion equations of the subsystems is illustrated.A computer program is developed to solve critical speeds and to simulate the transient motion.The influence of gyroscopic moments on co-rotation and counter-rotation is analyzed,and the effect of the speed ratio on critical speed is studied.The dynamic characteristics under different conditions of increasing speed during start-up are demonstrated by comparison with transient nodal displacements.The presented model provides a complete foundation for further investigation of the dynamics of dual rotor systems. 展开更多
关键词 Dual rotor system Critical speed Transient response finite element method(fem)
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DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION 被引量:3
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作者 MA Linwei MO Jianhua 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2008年第1期31-35,共5页
Single-point incremental forming (SPIF) is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation a... Single-point incremental forming (SPIF) is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method(FEM) model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters' impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger. 展开更多
关键词 Sheet metal incremental forming DEFORMATION finite element methodfem Numerical simulation
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Numerical simulation of single roller melt spinning for NdFeB alloy based on finite element method 被引量:2
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作者 Xu-Chao Wang Ming Yue +2 位作者 Dong-Tao Zhang Wei-Qiang Liu Ming-Gang Zhu 《Rare Metals》 SCIE EI CAS CSCD 2020年第10期1145-1150,共6页
The numerical simulation model of single roller melt spinning for rapid quenching process of NdFeB alloy was built,and the vacuum chamber,cooling roller and sample were taken into account as a system.The existing matu... The numerical simulation model of single roller melt spinning for rapid quenching process of NdFeB alloy was built,and the vacuum chamber,cooling roller and sample were taken into account as a system.The existing mature technology was in order to verify the correctness of simulation.The rapid quenching ribbons with different roll speeds were used as the simulation objects.The results of the numerical simulation and experiments show that the validity of the model has been testified and the reasons of the formation of complete quenching ribbons and by-product have been explained.The experimental thickness of the ribbons is proportional to the theoretical thickness.In the same spray condition,with the roll speed increasing,the thickness decreases linearly.At the speed range of25-30 m·s^(-1),the simulated calculation date is close to the experimental date,which can be considered as an ideal technological parameter. 展开更多
关键词 NDFEB Melt spinning finite element method Numerical simulation
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Flow simulation considering adsorption boundary layer based on digital rock and finite element method 被引量:2
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作者 Yong-Fei Yang Ke Wang +7 位作者 Qian-Fei Lv Roohollah Askari Qing-Yan Mei Jun Yao Jie-Xin Hou Kai Zhang Ai-Fen Li Chen-Chen Wang 《Petroleum Science》 SCIE CAS CSCD 2021年第1期183-194,共12页
Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,compara... Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,comparatively fewer works have been devoted to study the effect of adsorption boundary layer(ABL)in throats based on the digital rock method.By considering an ABL,we investigate its effects on fluid flow.We build digital rock model based on computed tomography technology.Then,microscopic pore structures are extracted with watershed segmentation and pore geometries are meshed through Delaunay triangulation approach.Finally,using the meshed digital simulation model and finite element method,we investigate the effects of viscosity and thickness of ABL on microscale flow.Our results demonstrate that viscosity and thickness of ABL are major factors that significantly hinder fluid flow in throats. 展开更多
关键词 Digital rock Low-permeability rocks CT technology Adsorption boundary layer Numerical simulation finite element method
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Finite element method simulation of shotpeening wing skin panel 被引量:1
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作者 吴为 曾元松 +1 位作者 黄遐 李志强 《中国有色金属学会会刊:英文版》 CSCD 2005年第2期443-446,共4页
Finite element method(FEM) was used to simulate the forming process of shotpeening the wing skin panel. Experiment of shotpeeing the wing skin panel was carried out. The results show that equivalent deformation in sho... Finite element method(FEM) was used to simulate the forming process of shotpeening the wing skin panel. Experiment of shotpeeing the wing skin panel was carried out. The results show that equivalent deformation in shotpeening process can be obtained using the elongation and bending result caused by thermal stress that is induced by applying temperature load on the surface of the part. Deformation of the part in the shotpeeing process can be analyzed using this method. The parameters and their relationships are identified. 展开更多
关键词 喷丸硬化成型 边皮平行 有限元法 计算机仿真
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Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method 被引量:12
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作者 Qi Zhao Andrea Lisjak +2 位作者 Omid Mahabadi Qinya Liu Giovanni Grasselli 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2014年第6期574-581,共8页
Hydraulic fracturing (HF) technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid ... Hydraulic fracturing (HF) technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid injection, which creates an interconnected fracture network and increases the hydrocarbonproduction. Meanwhile, microseismic (MS) monitoring is one of the most effective approaches to evaluatesuch stimulation process. In this paper, the combined finite-discrete element method (FDEM) isadopted to numerically simulate HF and associated MS. Several post-processing tools, includingfrequency-magnitude distribution (b-value), fractal dimension (D-value), and seismic events clustering,are utilized to interpret numerical results. A non-parametric clustering algorithm designed specificallyfor FDEM is used to reduce the mesh dependency and extract more realistic seismic information.Simulation results indicated that at the local scale, the HF process tends to propagate following the rockmass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to themaximum in-situ stress. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved. 展开更多
关键词 Hydraulic fracturing(HF) Numerical simulation Microseismic(MS) finite-discrete element method(FDEM) Clustering Kernel density estimation(KDE)
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Application of Wavelet Finite Element Method to Simulation of the Temperature Field of Copier Paper 被引量:1
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作者 YANGSheng-jun MAJun-xing 《International Journal of Plant Engineering and Management》 2002年第4期191-197,共7页
Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copie... Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method, which provides a new method for improving the copier properties. 展开更多
关键词 copier paper temperature field wavelet finite element method simulation
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Large eddy simulation for wind field analysis based on stabilized finite element method
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作者 Cheng HUANG Yan BAO Dai ZHOU Jin-quan XU 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2011年第4期278-290,共13页
In this paper,a stabilized finite element technique,actualized by streamline upwind Petrov-Galerkin(SUPG) stabilized method and three-step finite element method(FEM),for large eddy simulation(LES) is developed to pred... In this paper,a stabilized finite element technique,actualized by streamline upwind Petrov-Galerkin(SUPG) stabilized method and three-step finite element method(FEM),for large eddy simulation(LES) is developed to predict the wind flow with high Reynolds numbers.Weak form of LES motion equation is combined with the SUPG stabilized term for the spatial finite element discretization.An explicit three-step scheme is implemented for the temporal discretization.For the numerical example of 2D wind flow over a square rib at Re=4.2×105,the Smagorinsky's subgrid-scale(SSGS) model,the DSGS model,and the DSGS model with Cabot near-wall model are applied,and their results are analyzed and compared with experimental results.Furthermore,numerical examples of 3D wind flow around a surface-mounted cube with different Reynolds numbers are performed using DSGS model with Cabot near-wall model based on the present stabilized method to study the wind field and compared with experimental and numerical results.Finally,vortex structures for wind flow around a surface-mounted cube are studied by present numerical method.Stable and satisfactory results are obtained,which are consistent with most of the measurements even under coarse mesh. 展开更多
关键词 Large eddy simulation(LES) Subgrid-scale model Stabilized finite element method(fem) Unstructured grid Wind flow
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Nonlinear simulation of arch dam cracking with mixed finite element method
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作者 Ren Hao Li Tongchun Chen Huifang Zhao Lanhao 《Water Science and Engineering》 EI CAS 2008年第2期88-101,共14页
This paper proposes a new, simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period, which takes into account the arch dam construction process and... This paper proposes a new, simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period, which takes into account the arch dam construction process and temperature loads. In the calculation mesh, the contact surface of pair nodes is located at places on the arch dam where cracking is possible. A new effective iterative method, the mixed finite element method for friction-contact problems, is improved and used for nonlinear simulation of the cracking process. The forces acting on the structure are divided into two parts: external forces and contact forces. The displacement of the structure is chosen as the basic variable and the nodal contact force in the possible contact region of the local coordinate system is chosen as the iterative variable, so that the nonlinear iterative process is only limited within the possible contact surface and is much more economical. This method was used to simulate the cracking process of the Shuanghe Arch Dam in Southwest China. In order to prove the validity and accuracy of this method and to study the effect of thermal stress on arch dam cracking, three schemes were designed for calculation. Numerical results agree with actual measured data, proving that it is feasible to use this method to simulate the entire process of nonlinear arch dam cracking. 展开更多
关键词 mixed finite element method contact pair nodes crack of arch dam simulation thermal stress
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Modeling and Simulation of Valve Cycle in Vein Using an Immersed Finite Element Method
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作者 Xiang Liu Liangbo Sun +2 位作者 Mingzhen Wang Bin Li Lisheng Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第4期153-183,共31页
A vein model was established to simulate the periodic characteristics of blood flow and valve deformation in blood-induced valve cycles.Using an immersed finite element method which was modified by a ghost fluid techn... A vein model was established to simulate the periodic characteristics of blood flow and valve deformation in blood-induced valve cycles.Using an immersed finite element method which was modified by a ghost fluid technique,the interaction between the vein and blood was simulated.With an independent solid solver,the contact force between vein tissues was calculated using an adhesive contact method.A benchmark simulation of the normal valve cycle validated the proposed model for a healthy vein.Both the opening orifice and blood flow rate agreed with those in the physiology.Low blood shear stress and maximum leaflet stress were also seen in the base region of the valve.On the basis of the healthy model,a diseased vein model was subsequently built to explore the sinus lesions,namely,fibrosis and atrophy which are assumed stiffening and softening of the sinus.Our results showed the opening orifice of the diseased vein was inversely proportional to the corresponding modulus of the sinus.A drop in the transvalvular pressure gradient resulted from the sinus lesion.Compared to the fibrosis,the atrophy of the sinus apparently improved the vein deformability but simultaneously accelerated the deterioration of venous disease and increased the risk of potential fracture.These results provide understandings of the normal/abnormal valve cycle in vein,and can be also helpful for the prosthesis design. 展开更多
关键词 Numerical simulation fluid-structure interaction immersed finite element method adhesive contact method bio-mechanics venous valve.
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Finite element method simulation for tensile process of sintered iron-base material
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作者 赵伟斌 李元元 +3 位作者 周照耀 邵明 陈维平 张文 《中国有色金属学会会刊:英文版》 CSCD 2002年第6期1099-1102,共4页
Different material properties leads to different metal fracture behaviors. Even if the powder material is composed of plastic metal, the fracture still does not show macroscopic plastic deformation characteristics if ... Different material properties leads to different metal fracture behaviors. Even if the powder material is composed of plastic metal, the fracture still does not show macroscopic plastic deformation characteristics if the material contains a large number of voids. Eight node isoparametric elastic plastic finite element method was used to simulate the tensile process of sintered powder material. By setting a number of voids in the analyzed metal cuboid, the initial density was taken into consideration. The material properties of the three dimensional solid for the tensile simulation were defined with reference to the known pure iron material parameters. The load displacement curves during elongation were obtained with a universal testing machine, and then the simulated curves were compared with the experimental results. The factors that cause the stress concentration and strength decrease were analyzed according to the simulated equivalent von Mises stress distribution. 展开更多
关键词 有限元方法模拟 张力 粉末烧结 离子基材料
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Simulation of an Ultrasonic Transducer for Medical Applications Using the Finite Element Method
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作者 Pedro Acevedo Israel Sanchez Domingue 《材料科学与工程(中英文B版)》 2015年第7期293-297,共5页
关键词 有限元模拟 超声换能器 医用 压电陶瓷 有限元法 人力资源 频率响应 应变响应
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A Study on the Computer Numerical Simulation of Radial Keratotomy by Finite Element Method
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《Chinese Journal of Biomedical Engineering(English Edition)》 1999年第4期120-121,共2页
关键词 simulation A Study on the Computer Numerical simulation of Radial Keratotomy by finite element method
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耦合SBFEM-FEM的高拱坝系统地震响应分析
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作者 陈灯红 梁羽翔 +2 位作者 刘云辉 张心瀚 胡昊文 《水力发电学报》 北大核心 2025年第4期72-84,共13页
高拱坝的巨大尺寸跨度以及需考虑的不同分区材料属性和坝基地形的复杂性,采用传统有限元法进行精细化建模时存在一定局限性。本文建立了一种耦合SBFEM-FEM高拱坝-地基-库水系统的地震分析数值分析模型。该模型以SBFEM理论为基础,通过蒙... 高拱坝的巨大尺寸跨度以及需考虑的不同分区材料属性和坝基地形的复杂性,采用传统有限元法进行精细化建模时存在一定局限性。本文建立了一种耦合SBFEM-FEM高拱坝-地基-库水系统的地震分析数值分析模型。该模型以SBFEM理论为基础,通过蒙皮单元技术耦合八叉树SBFEM自定义单元与ABAQUS内置单元,将SBFEM半解析和网格灵活的优势与ABAQUS成熟的线性与非线性求解器和前/后处理模块相结合。以XL高拱坝为例,对其进行了地震作用下线弹性、接触非线性与材料非线性动力响应分析。结果表明:本文方法相较于传统有限元法能够有效减少计算所需资源,并且能够准确模拟高拱坝在地震作用下的非线性响应及损伤情况,对大坝以及其他建筑的抗震研究具有一定的借鉴意义。 展开更多
关键词 比例边界有限元 耦合SBfem-fem 接触非线性 非线性动力响应 八叉树网格
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Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method 被引量:17
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作者 袁驷 杜炎 +1 位作者 邢沁妍 叶康生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第10期1223-1232,共10页
The element energy projection (EEP) method for computation of super- convergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear probl... The element energy projection (EEP) method for computation of super- convergent resulting in a one-dimensional finite element method (FEM) is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton's method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation (ODE) of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach. 展开更多
关键词 NONLINEARITY finite element method fem self-adaptive analysis super-convergence element energy projection (EEP)~ ordinary differential equation(ODE)
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