A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation ...A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O（h^2） for both the original variable u in H1 （Ω） norm and the flux p = u in H（div, Ω） norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O（h^3） are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.展开更多
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
高位滑坡对建筑集群的冲击破坏时常导致严重的人员伤亡,基于光滑粒子流体动力学-离散元法-有限元法(smoothed particle hydrodynamics-discrete element method-finite element method,SPH-DEM-FEM)耦合的数值模型,开展了高位滑坡对框...高位滑坡对建筑集群的冲击破坏时常导致严重的人员伤亡,基于光滑粒子流体动力学-离散元法-有限元法(smoothed particle hydrodynamics-discrete element method-finite element method,SPH-DEM-FEM)耦合的数值模型,开展了高位滑坡对框架结构建筑群的冲击过程、建筑结构破坏机理、冲击力时程与框架柱关键点应力和弯矩等动力机制研究。研究结果表明:SPH-DEM-FEM耦合数值方法能够有效地模拟碎石土滑坡中土(SPH)石(DEM)混合物的抛射弹跳、爬高绕流冲击运动过程。考虑了常规建筑垂直、平行于滑坡流向的三排建筑组合布局,位于滑坡近端的纵向排列建筑表现为连续性倾倒破坏,横向排列的建筑则呈现整体倾倒破坏;因前排建筑群对滑坡冲击能量的耗散及滑坡自身摩擦耗能,位于滑坡后端建筑表现为引流面墙体和前排柱发生局部破坏,结构保持稳定,损毁程度依次为上游无建筑缓冲耗能的建筑>有横向排列的建筑>有纵向排列的建筑;纵向、横向排列的建筑冲击力衰减幅度分别31%、21%。横向框架建筑整体倾倒的损毁机制表现为框架柱的直接剪断或节点塑形铰链失效;纵向框架建筑连续性倾倒的损毁机制表现为前排框架柱的失效引起后排框架柱轴向压力和极限弯矩增加,持续冲击荷载超过其极限弯矩致使后排框架柱发生弯曲破坏,最终结构倾倒。系统能量在动能、内能和摩擦耗能间转化,其中摩擦耗能占65.5%,结构耗能占23.6%,动能快速下降与内能急剧增加是建筑破坏的关键特征。展开更多
Curved beams with complex geometries are vital in numerous engineering applications,where precise vibration analysis is crucial for ensuring safe and effective designs.Traditional finite element methods(FEMs) often st...Curved beams with complex geometries are vital in numerous engineering applications,where precise vibration analysis is crucial for ensuring safe and effective designs.Traditional finite element methods(FEMs) often struggle to accurately represent the dynamic characteristics of these structures due to the limitations in their shape function approximations.To overcome this challenge,the current study introduces an innovative finite element(FE)-based technique for the undamped vibrational analysis of curved beams with arbitrary curvature,employing explicitly derived interpolation functions.Initially,the exact interpolation functions are developed for circular are elements with the force method.These functions facilitate the creation of a highly accurate stiffness matrix,which is validated against the benchmark examples.To accommodate arbitrary curvature,a systematic transformation technique is established to approximate the intricate curves with a series of circular arcs.The numerical findings indicate that increasing the number of arc segments enhances accuracy,approaching the exact solutions.The analysis of free vibrations is conducted for both circular and non-circular beams.Mass matrices are derived using two methods:lumped mass and consistent mass,where the latter is based on the interpolation functions.The effectiveness of the proposed method is confirmed through the comparisons with the existing literature,demonstrating strong agreement.Finally,several practical cases involving beams with diverse curvature profiles are analyzed.Both natural frequencies and mode shapes are determined,providing significant insights into the dynamic behavior of these structures.This research offers a dependable and efficient analytical framework for the vibrational analysis of complex curved beams,with promising implications for structural and mechanical engineering.展开更多
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
In the incremental sheet forming （ISF） process, springback is a very important factor that affects the quality of parts. Predicting and controlling springback accurately is essential for the design of the toolpath f...In the incremental sheet forming （ISF） process, springback is a very important factor that affects the quality of parts. Predicting and controlling springback accurately is essential for the design of the toolpath for ISF. A three-dimensional elasto-plastic finite element model （FEM） was developed to simulate the process and the simulated results were compared with those from the experiment. The springback angle was found to be in accordance with the experimental result, proving the FEM to be effective. A coupled artificial neural networks （ANN） and finite element method technique was developed to simulate and predict springback responses to changes in the processing parameters. A particle swarm optimization （PSO） algorithm was used to optimize the weights and thresholds of the neural network model. The neural network was trained using available FEM simulation data. The results showed that a more accurate prediction of s!oringback can be acquired using the FEM-PSONN model.展开更多
Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh...Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh independently of f luid motion, and the container fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free su rface without producing undesirable distortion of the computational mesh. The fi nite element method and finite difference method are used spacewise and timewise , respectively. A numerical example involving either forced horizontal oscillati on or forced pitching oscillation of the fluid filled container is presented to illustrate the effectiveness and the robustness of the method. In additi on, this work can be extended for the fluid structure interaction problems.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.10971203,11271340,and 11101381)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O（h^2） for both the original variable u in H1 （Ω） norm and the flux p = u in H（div, Ω） norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O（h^3） are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.
基金supported by the National Natural Science Foundation of China(Grant Nos.51890912,51979025 and 52011530189).
文摘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.
文摘高位滑坡对建筑集群的冲击破坏时常导致严重的人员伤亡,基于光滑粒子流体动力学-离散元法-有限元法(smoothed particle hydrodynamics-discrete element method-finite element method,SPH-DEM-FEM)耦合的数值模型,开展了高位滑坡对框架结构建筑群的冲击过程、建筑结构破坏机理、冲击力时程与框架柱关键点应力和弯矩等动力机制研究。研究结果表明:SPH-DEM-FEM耦合数值方法能够有效地模拟碎石土滑坡中土(SPH)石(DEM)混合物的抛射弹跳、爬高绕流冲击运动过程。考虑了常规建筑垂直、平行于滑坡流向的三排建筑组合布局,位于滑坡近端的纵向排列建筑表现为连续性倾倒破坏,横向排列的建筑则呈现整体倾倒破坏;因前排建筑群对滑坡冲击能量的耗散及滑坡自身摩擦耗能,位于滑坡后端建筑表现为引流面墙体和前排柱发生局部破坏,结构保持稳定,损毁程度依次为上游无建筑缓冲耗能的建筑>有横向排列的建筑>有纵向排列的建筑;纵向、横向排列的建筑冲击力衰减幅度分别31%、21%。横向框架建筑整体倾倒的损毁机制表现为框架柱的直接剪断或节点塑形铰链失效;纵向框架建筑连续性倾倒的损毁机制表现为前排框架柱的失效引起后排框架柱轴向压力和极限弯矩增加,持续冲击荷载超过其极限弯矩致使后排框架柱发生弯曲破坏,最终结构倾倒。系统能量在动能、内能和摩擦耗能间转化,其中摩擦耗能占65.5%,结构耗能占23.6%,动能快速下降与内能急剧增加是建筑破坏的关键特征。
文摘Curved beams with complex geometries are vital in numerous engineering applications,where precise vibration analysis is crucial for ensuring safe and effective designs.Traditional finite element methods(FEMs) often struggle to accurately represent the dynamic characteristics of these structures due to the limitations in their shape function approximations.To overcome this challenge,the current study introduces an innovative finite element(FE)-based technique for the undamped vibrational analysis of curved beams with arbitrary curvature,employing explicitly derived interpolation functions.Initially,the exact interpolation functions are developed for circular are elements with the force method.These functions facilitate the creation of a highly accurate stiffness matrix,which is validated against the benchmark examples.To accommodate arbitrary curvature,a systematic transformation technique is established to approximate the intricate curves with a series of circular arcs.The numerical findings indicate that increasing the number of arc segments enhances accuracy,approaching the exact solutions.The analysis of free vibrations is conducted for both circular and non-circular beams.Mass matrices are derived using two methods:lumped mass and consistent mass,where the latter is based on the interpolation functions.The effectiveness of the proposed method is confirmed through the comparisons with the existing literature,demonstrating strong agreement.Finally,several practical cases involving beams with diverse curvature profiles are analyzed.Both natural frequencies and mode shapes are determined,providing significant insights into the dynamic behavior of these structures.This research offers a dependable and efficient analytical framework for the vibrational analysis of complex curved beams,with promising implications for structural and mechanical engineering.
基金supported by the National Natural Science Foundation of China(Grant Nos.42272338 and 41827807)Department of Transportation of Zhejiang Province,China(Grant No.202213).
文摘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.
基金Project(50175034) supported by the National Natural Science Foundation of China
文摘In the incremental sheet forming （ISF） process, springback is a very important factor that affects the quality of parts. Predicting and controlling springback accurately is essential for the design of the toolpath for ISF. A three-dimensional elasto-plastic finite element model （FEM） was developed to simulate the process and the simulated results were compared with those from the experiment. The springback angle was found to be in accordance with the experimental result, proving the FEM to be effective. A coupled artificial neural networks （ANN） and finite element method technique was developed to simulate and predict springback responses to changes in the processing parameters. A particle swarm optimization （PSO） algorithm was used to optimize the weights and thresholds of the neural network model. The neural network was trained using available FEM simulation data. The results showed that a more accurate prediction of s!oringback can be acquired using the FEM-PSONN model.
文摘Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh independently of f luid motion, and the container fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free su rface without producing undesirable distortion of the computational mesh. The fi nite element method and finite difference method are used spacewise and timewise , respectively. A numerical example involving either forced horizontal oscillati on or forced pitching oscillation of the fluid filled container is presented to illustrate the effectiveness and the robustness of the method. In additi on, this work can be extended for the fluid structure interaction problems.
