A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

Finite Element Method Simulation of Wellbore Stability under Different Operating and Geomechanical Conditions

The variation of the principal stress of formations with the working and geo-mechanical conditions can trigger wellbore instabilities and adversely affect the well completion.A finite element model,based on the theory of poro-elasticity and the Mohr-Coulomb rock damage criterion,is used here to analyze such a risk.The changes in wellbore stability before and after reservoir acidification are simulated for different pressure differences.The results indicate that the risk of wellbore instability grows with an increase in the production-pressure difference regardless of whether acidification is completed or not;the same is true for the instability area.After acidizing,the changes in the main geomechanical parameters(i.e.,elastic modulus,Poisson’s ratio,and rock strength)cause the maximum wellbore instability coefficient to increase.

Finite Element Analysis of Coronal Shear Fractures of the Femoral Neck: Displacement of the Femoral Head and Effect of Osteosynthetic Implants

Coronal shear fractures of the femoral neck (CSFF) are the most challenging to treat among proximal femur fractures, directly affecting the life expectancy of patients with osteoporosis. However, an adequate osteosynthesis method has not been elucidated yet. This study investigated the displacement direction of the femoral head fragment and its effect on the bone using finite element method. A finite element model for CSFF was developed from CT image data of a patient with osteoporosis using Mechanical Finder (ver. 11). Subsequently, finite element analyses were performed on six osteosynthesis models under maximum load applied during walking. The compressive stresses, tensile stresses, and compressive strains of each model were examined. The results suggested that the compressive and tensile stress distributions were concentrated on the anterior side of the femoral neck. Compressive strain distribution in the femoral head and neck was concentrated in four areas: at the tip of the blade or lag screw, the anteroinferior side of the blade or lag screw near the fracture site, and the upper right and lower left near the junction of the blade or lag screw and nail. Thus, the distribution of both these stresses revealed that the femoral head fragment was prone to anterior and inferior displacement. Distribution of compressive strains revealed the direction of the stress exerted by the osteosynthetic implant on the bone. The same results were observed in all osteosynthetic implants;thus, the findings could lay the foundation for developing methods for placing osteosynthetic implants less prone to displacement and the osteosynthetic implants themselves. In particular, the study provides insight into the optimal treatment of CSFF.

Gradient Recovery Based Two-Grid Finite Element Method for Parabolic Integro-Differential Optimal Control Problems

In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results.

THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D

For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.

A Deep Learning Approach to Shape Optimization Problems for Flexoelectric Materials Using the Isogeometric Finite Element Method

A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.

In silico optimization of actuation performance in dielectric elastomercomposites via integrated finite element modeling and deep learning

Dielectric elastomers(DEs)require balanced electric actuation performance and mechanical integrity under applied voltages.Incorporating high dielectric particles as fillers provides extensive design space to optimize concentration,morphology,and distribution for improved actuation performance and material modulus.This study presents an integrated framework combining finite element modeling(FEM)and deep learning to optimize the microstructure of DE composites.FEM first calculates actuation performance and the effective modulus across varied filler combinations,with these data used to train a convolutional neural network(CNN).Integrating the CNN into a multi-objective genetic algorithm generates designs with enhanced actuation performance and material modulus compared to the conventional optimization approach based on FEM approach within the same time.This framework harnesses artificial intelligence to navigate vast design possibilities,enabling optimized microstructures for high-performance DE composites.

Multi-scale Modeling and Finite Element Analyses of Thermal Conductivity of 3D C/SiC Composites Fabricating by Flexible-Oriented Woven Process

Thermal conductivity is one of the most significant criterion of three-dimensional carbon fiber-reinforced SiC matrix composites(3D C/SiC).Represent volume element(RVE)models of microscale,void/matrix and mesoscale proposed in this work are used to simulate the thermal conductivity behaviors of the 3D C/SiC composites.An entirely new process is introduced to weave the preform with three-dimensional orthogonal architecture.The 3D steady-state analysis step is created for assessing the thermal conductivity behaviors of the composites by applying periodic temperature boundary conditions.Three RVE models of cuboid,hexagonal and fiber random distribution are respectively developed to comparatively study the influence of fiber package pattern on the thermal conductivities at the microscale.Besides,the effect of void morphology on the thermal conductivity of the matrix is analyzed by the void/matrix models.The prediction results at the mesoscale correspond closely to the experimental values.The effect of the porosities and fiber volume fractions on the thermal conductivities is also taken into consideration.The multi-scale models mentioned in this paper can be used to predict the thermal conductivity behaviors of other composites with complex structures.

Modularized and Parametric Modeling Technology for Finite Element Simulations of Underground Engineering under Complicated Geological Conditions

The surrounding geological conditions and supporting structures of underground engineering are often updated during construction,and these updates require repeated numerical modeling.To improve the numerical modeling efficiency of underground engineering,a modularized and parametric modeling cloud server is developed by using Python codes.The basic framework of the cloud server is as follows:input the modeling parameters into the web platform,implement Rhino software and FLAC3D software to model and run simulations in the cloud server,and return the simulation results to the web platform.The modeling program can automatically generate instructions that can run the modeling process in Rhino based on the input modeling parameters.The main modules of the modeling program include modeling the 3D geological structures,the underground engineering structures,and the supporting structures as well as meshing the geometric models.In particular,various cross-sections of underground caverns are crafted as parametricmodules in themodeling program.Themodularized and parametric modeling program is used for a finite element simulation of the underground powerhouse of the Shuangjiangkou Hydropower Station.This complicatedmodel is rapidly generated for the simulation,and the simulation results are reasonable.Thus,this modularized and parametric modeling program is applicable for three-dimensional finite element simulations and analyses.

Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal

The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.

Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

Collapse Behavior of Pipe-Framed Greenhouses with and without Reinforcement under Snow Loading:A 3-D Finite Element Analysis

The present paper first investigates the collapse behavior of a conventional pipe-framed greenhouse under snow loading based on a 3-D finite element analysis,in which both geometrical and material non-linearities are considered.Three snow load distribution patterns related to the wind-driven snow particle movement are used in the analysis.It is found that snow load distribution affects the deformation and collapse behavior of the pipe-framed greenhouse significantly.The results obtained in this study are consistent with the actual damage observed.Next,discussion is made of the effects of reinforcements by adding members to the basic frame on the strength of the whole structure,in which seven kinds of reinforcement methods are examined.A buckling analysis is also carried out.The results indicate that the most effective reinforcement method depends on the snow load distribution pattern.

A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent Singularities

The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.

Contribution to the Full 3D Finite Element Modelling of a Hybrid Stepping Motor with and without Current in the Coils

The paper presents our contribution to the full 3D finite element modelling of a hybrid stepping motor using COMSOL Multiphysics software. This type of four-phase motor has a permanent magnet interposed between the two identical and coaxial half stators. The calculation of the field with or without current in the windings (respectively with or without permanent magnet) is done using a mixed formulation with strong coupling. In addition, the local high saturation of the ferromagnetic material and the radial and axial components of the magnetic flux are taken into account. The results obtained make it possible to clearly observe, as a function of the intensity of the bus current or the remanent induction, the saturation zones, the lines, the orientations and the magnetic flux densities. 3D finite element modelling provide more accurate numerical data on the magnetic field through multiphysics analysis. This analysis considers the actual operating conditions and leads to the design of an optimized machine structure, with or without current in the windings and/or permanent magnet.

Multiscale Finite Element Method for Coupling Analysis of Heterogeneous Magneto-Electro-Elastic Structures in Thermal Environment

Magneto-electro-elastic (MEE) materials, a new type of composite intelligent materials, exhibit excellent multifield coupling effects. Due to the heterogeneity of the materials, it is challenging to use the traditional finite element method (FEM) for mechanical analysis. Additionally, the MEE materials are often in a complex service environment, especially under the influence of the thermal field with thermoelectric and thermomagnetic effects, which affect its mechanical properties. Therefore, this paper proposes the efficient multiscale computational method for the multifield coupling problem of heterogeneous MEE structures under the thermal environment. The method constructs a multi-physics field with numerical base functions (the displacement, electric potential, and magnetic potential multiscale base functions). It equates a single cell of heterogeneous MEE materials to a macroscopic unit and supplements the macroscopic model with a microscopic model. This allows the problem to be solved directly on a macroscopic scale. Finally, the numerical simulation results demonstrate that compared with the traditional FEM, the multiscale finite element method (MsFEM) can achieve the purpose of ensuring accuracy and reducing the degree of freedom, and significantly improving the calculation efficiency.

Stress Distributions Created by Short and Regular Implants Placed in the Anterior Maxilla at Different Angles: A Finite Element Analysis

Although short implants are seen as alternative treatments that require additional surgical techniques in posterior region, they can be applied to anterior maxilla and various studies are required on this subject. The purpose of this study was to examine and compare the peak von Mises stress distributions in the crown, implant and abutment by using finite element analysis (FEA). Besides, a comparison of the implant-abutment connection types in the short implant with the FEA method was established. A short implant (4 × 5 mm) with a taper-lock connection and a regular implant (4 × 9 mm) with a screw connection were used in maxillary central incisor tooth area. Three different titanium abutments with 0?, 15? and 25? angles were used for abutments. In addition, in order to determine whether the stress change in short implants is due to the length of the implant-abutment connection, a screw was designed for a short implant and it was also evaluated in the same three angles. A total of three groups and nine models were generated. 114.6N load was applied to the cingulum area of the crown at an angle of 135? to the long axis of the crowns. A torque load of 25 Ncm was applied to the regular and short implant screw. Von Mises stress distributions of implants, abutments and crowns were evaluated by using FEA. Increased angle in implants increased von Mises stress values of implant, abutment and crown. Screw connection was found higher at all angles in short implants. Close values were found at different angles in taper-lock short implant crowns. The length and the angle in the bone of implant with the type of implant-abutment connection results in the accumulated stress values. Clinical Implications Taper implant-abutment connection system was found to be more promising in terms of stress accumulation in crowns. Although the amount of stress on the abutment increased due to the length of the implant in short implants, taper implant-abutment connection system slightly reduced related to this increase.

Finite element analysis of stress at implant-bone interface of dental implants with different structures

The effect of structure,elastic modulus and thickness of lower modulus layer in porous titanium implants on the stress distribution at the implant-bone interface was investigated.Three-dimensional finite element models of different titanium implants were constructed.The structures of the implants included the whole lower modulus style （No.1）,bio-mimetic style （No.2）,the whole lower modulus style in cancellous bone （No.3） and the whole dense style No.4.The stress distributions at bone-implant interface under static loading were analyzed using Ansys Workbench 10.0 software.The results indicated that the distribution of interface stress is strongly depended on the structure of the implants.The maximum stresses in cancellous bone and root region of implant No.2 are lower than those in the other three implants.A decrease in the modulus of the low modulus layer facilitates the interface stress transferring.Increasing the thickness of the low modulus layer can reduce the stress and induce a more uniform stress distribution at the interface.Among the four implants,biomimetic style implant No.2 is superior in transferring implant-bone interface stress to surrounding bones.

Grain statistics effect on deformation behavior in asymmetric rolling of pure copper foil by crystal plasticity finite element model

The grain statistics effect was investigated through asymmetric rolling of pure copper foil by a realistic polycrystalline aggregates model and crystal plasticity element finite model.A polycrystalline aggregate model was generated and a crystal plasticity-based finite element model was developed for each grain and the specimen as a whole.The crystal plasticity model itself is rate dependent and accounts for local dissipative hardening effects and the original orientation of each grain was generated based on the orientation distribution function（ODF）.The deformation behaviors,including inhomogeneous material flow,decrease of contact press and roll force with the increase of grain size for the constant size of specimens,were studied.It is revealed that when the specimens are composed of only a few grains across thickness,the grains with different sizes,shapes and orientations are unevenly distributed in the specimen and each grain plays a significant role in micro-scale plastic deformation and leads to inhomogeneous deformation and the scatter of experimental and simulation results.The slip system activity was examined and the predicted results are consistent with the surface layer model.The slip band is strictly influenced by the misorientation of neighbor grain with consideration of slip system activity.Furthermore,it is found that the decrease of roll force and the most active of slip system in surface grains are caused by the increase of free surface grain effect when the grain size is increased.The results of the physical experiment and simulation provide a basic understanding of micro-scaled plastic deformation behavior in asymmetric foil rolling.

Finite element analysis of the free-damped beam-stiffened plate

A finite element model is presented for free-damped beam-stiffened plates. The nodes of the plate elements are treated as master-nodes, and the corresponding nodes of the beam elements are considered as slave-nodes. The stiffness and mass matrices of the elements are developed. Based on the analysis of the dynamic properties of the structures, modal loss factors are predicted by the modal strain energy method. Finally, an example is given to compare the results obtained from the proposed method with the results of the ANSYS software. The results show that the method in this paper is computationally efficient, simple and feasible with high precision and engineering practicability.

Study on hot deformation behavior of homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy using a combination of strain-compensated Arrhenius constitutive model and finite element simulation method

Isothermal hot compression experiments were conducted on homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy to investigate hot deformation behavior at the temperature range of 673-773 K and the strain rate range of 0.001-1 s^(-1)by using a Gleeble-1500D thermo mechanical simulator.Metallographic characterization on samples deformed to true strain of 0.70 illustrates the occurrence of flow localization and/or microcrack at deformation conditions of 673 K/0.01 s^(-1),673 K/1 s^(-1)and 698 K/1 s^(-1),indicating that these three deformation conditions should be excluded during hot working of homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy.Based on the measured true stress-strain data,the strain-compensated Arrhenius constitutive model was constructed and then incorporated into UHARD subroutine of ABAQUS software to study hot deformation process of homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy.By comparison with measured force-displacement curves,the predicted results can describe well the rheological behavior of homogenized Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy,verifying the validity of finite element simulation of hot compression process with this complicated constitutive model.Numerical results demonstrate that the distribution of values of material parameters(α,n,Q and ln A)within deformed sample is inhomogeneous.This issue is directly correlated to the uneven distribution of equivalent plastic strain due to the friction effect.Moreover,at a given temperature the increase of strain rate would result in the decrease of equivalent plastic strain within the central region of deformed sample,which hinders the occurrence of dynamic recrystallization(DRX).