Combined Finite Element Method Research Articles

Numerical Solution of Burger's Type Equation Using Finite Element Collocation method with Strang Splitting

The nonlinear Burgers equation, which has a convection term, a viscosity term and a time dependent term in its structure, has been splitted according to the time term and then has been solved by finite element collocation method using cubic B-spline bases. By splitting the equation U_{t}+UU_{x}=vU_{xx} two simpler sub problems U_{t}+UU_{x}=0 and U_{t}-vU_{xx}=0 have been obtained. A discretization process has been performed for each of these sub-problems and the stability analyzes have been carried out by Fourier (von Neumann) series method. Then, both sub-problems have been solved using the Strang splitting technique to obtain numerical results. To see the effectiveness of the present method, which is a combination of finite element method and Strang splitting technique, we have calculated the frequently used error norms ‖e‖₁, L₂ and L_{∞} in the literature and have made a comparison between exact and a numerical solution.

A smooth contact algorithm for the combined finite discrete element method

From its inception, the combined finite discrete element method has used a distributed potential contact force algorithm to resolve interaction between finite elements. The contact interaction algorithm relies on evaluation of the contact force potential field. The problem with existing algorithms is that the potential field introduces artificial numerical non-smoothness in the contact force. This work introduces a smooth potential field based on the finite element topology, and a generalized contact interaction law is constructed on top of the smooth potential field. A number of validation cases for the proposed algorithm, considering different shapes of discrete elements, are presented, and detailed aspects of the proposed contact interaction law are tested with numerical examples.

Stress State Measurement and Result Analysis of Car Wheels

The stress state of the car wheel is one of the guiding design indicators for the wheel structure. This paper uses the combination of finite element method and bench test to study the stress state of the wheel when driving straight. Through the finite element simulation of bending fatigue and radial fatigue, the position of dangerous points during the use of the wheel is obtained. The location of the dangerous point is used as the strain measuring point, and the test bench is built. The strain gauge is used to measure the strain of these points in the straight running condition, and the test results are analyzed. The results show that when the vehicle is traveling straight, the tire will have a greater impact on the load of the wheel. The squeezing deformation between the tire and the wheel, as well as the positive and negative rotation, will have an effect on the stress state of the wheel. The maximum strain of the wheel appears on the inside of the wheel rim, the rim is in contact with the tire and along the circumference of the wheel. The strain near the center of the wheel is small. Different loads have no effect on the variation of wheel strain, but have an effect on the maximum and minimum peaks.

Structural Damage Recognition Based on the Finite Element Method and Quantum Particle Swarm Optimization Algorithm

Structural damage recognition is always the concerned focus in many fields like aerospace, petroleum and petrochemical industry, industrial production and civil life. For damage recognition in complex structure or structural interior, especially somewhere sensors can’t go, minor damage is often hard identified by not only traditional nondestructive testing methods like ultrasonic testing, radiographic testing, magnetic particle testing, penetrant testing, eddy current testing, but also the current popular ultrasonic guided wave based on the piezoelectric wafer, electromagnetic acoustic transducer or magnetostrictive sensor, which is mainly because the response signals are always affected by many structural features. In this article, the advanced global search algorithm, quantum particle swarm optimization algorithm is first combined with the finite element method to accurately recognize the structural damage based on the conductance-frequency spectrum resulted from electromechanical impedance method. Meanwhile, the objective function is designed to compare the difference of peak frequency variations in the experiment and finite element calculation respectively. By adopting the stiffness reduction method of the elements near the structural damage, the identification efficiency is largely improved for no need to repeatedly partition the model grid. And after multiple iteration optimization of the artificial intelligence algorithm - quantum particle swarm optimization algorithm, the identification error of damage parameters including location and degree can be reduced to below 4 percent. Therefore, the combination of finite element method and quantum particle swarm optimization algorithm is quite effective for guaranteeing high accuracy and efficiency for damage parameters’ recognition in complex structures

Fluid\u2013structure interaction of flexible submerged vegetation stems and kinetic turbine blades

A fluid–structure interaction (FSI) methodology is presented for simulating elastic bodies embedded and/or encapsulating viscous incompressible fluid. The fluid solver is based on finite volume and the large eddy simulation approach to account for turbulent flow. The structural dynamic solver is based on the combined finite element method–discrete element method (FEM-DEM). The two solvers are tied up using an immersed boundary method (IBM) iterative algorithm to improve information transfer between the two solvers. The FSI solver is applied to submerged vegetation stems and blades of small-scale horizontal axis kinetic turbines. Both bodies are slender and of cylinder-like shape. While the stem mostly experiences a dominant drag force, the blade experiences a dominant lift force. Following verification cases of a single-stem deformation and a spinning Magnus blade in laminar flows, vegetation flexible stems and flexible rotor blades are analysed, while they are embedded in turbulent flow. It is shown that the single stem’s flexibility has higher effect on the flow as compared to the rigid stem than when in a dense vegetation patch. Making a marine kinetic turbine rotor flexible has the potential of significantly reducing the power production due to undesired twisting and bending of the blades. These studies point to the importance of FSI in flow problems where there is a noticeable deflection of a cylinder-shaped body and the capability of coupling FEM-DEM with flow solver through IBM.

Drying Technology Assisted by Nonthermal Pulsed Filamentary Microplasma Treatment: Theory and Practice

Nonthermal pulsed filamentary microplasma treatment for drying is a nonthermal technology with promising perspectives to dehydrate plant agricultural materials. The modified set of Luikov’s equations for heat, mass and pressure transfer, has been used to analyze nonthermal pulsed filamentary microplasma treatment effects. The finite element method in combination with the step-by-step finite-difference method for a coupled system of differential equations in partial derivatives was used for numerical simulation of heat, humidity and pressure potentials transfer. The drying time of samples treated by nonthermal pulsed filamentary microplasma treatment assisted by thermionic emission was reduced up to 20.6% (5 kV/cm; 1200 discharges) in comparison to intact tissue. The effect of the obtained approach is very useful for studying process mechanisms and for explaining nonthermal pulsed filamentary microplasma treatment effects. Refined transfer kinetic coefficients from a set of equations based on experimental drying curve can be used for the quantitative determination of thermodynamic coefficients. The agreement of the simulation data with the analytical equation and experimental results is satisfactory (discrepancy less than 3%). Obtained results showed that the proposed model with the refined transfer kinetic coefficients adequately describe the experimental data.

An improved FE-Meshfree method for solving steady seepage problems

An improved FE-Meshfree method, formulated as a combination of finite element method (FEM) and radial point interpolation method (RPIM), has been proposed in this paper, aiming for obtaining a more accurate and robust solution for steady seepage problems. Two main aspects are mainly investigated: firstly, the traditional cell-based discretization and assembly procedure as normally seen in FEM is replaced by a support domain based one, which potentially improves the computed results with a higher tolerance with the mesh distortion; secondly, an adaptation procedure of inserting extra field nodes on the boundaries/interfaces is proposed and incorporated, which shows an improved computational accuracy and stability. The superiority of the method is demonstrated via some applications to both confined and unconfined seepage problems.

Mathematical Modeling of Magnetic Fields of Actuators with Hape Memory Effect by a Combined Finite Element Method and Fundamental Solutions with Point Magnetic Moments

Mathematical Modeling of Magnetic Fields of Actuators with Hape Memory Effect by a Combined Finite Element Method and Fundamental Solutions with Point Magnetic Moments

Application of the inverse method in the 3 ω method for measuring the thermal conductivity of thin films

Planar nano-materials generally refer to samples that are extremely thin in the direction of thickness, such as nanofilms, graphene, and superlattice. They are of great importance in various fields, including transistors, thermoelectrics, and optoelectronics, etc. In practice, materials’ thermal transport characteristics often play a crucial role in applications. More importantly, due to the confinement in the direction of thickness, the mechanisms of thermal transport process in planar nano-materials become very different from those at the macroscale. For example, the effective lattice thermal conductivities of nanofilms are always highly dependent on their thickness, since phonon coherence, ballistic transport, and boundary scattering effects could occur in this case. Therefore, probing thermal transport properties of planar materials has been a research hotspot in both the research and industrial communities. The 3 ω method has been proven to be a powerful tool that can measure the thermal conductivities of planar materials effectively. Particularly for a thin film on a substrate, the differential 3 ω method was developed. In this scheme, it is necessary to determine the thermal properties of substrate materials in the first step. Thus, a reference sample should be measured in addition to the target sample, which not only increases the complexity of measurement but also reduces the measurement accuracy of the thin film’s thermal transport properties. In the present work, we used the numerical simulations to demonstrate that in the 3 ω method the combination of finite element method (FEM) and inverse problem method can derive the thermal properties of thin film and substrate simultaneously. It was found that the thermal conductivities could be determined accurately despite the cutoff frequency of measurement, whereas the thermal diffusivities’ accuracy could be improved with increasing cutoff frequency of measurement. Furthermore, as a test, the thermal conductivities of silicon dioxide (SiO2) thin film on the silicon (Si) substrate were measured using the method above. In our experiments, the thickness of Si substrate was 450 μm, and the thickness of SiO2 thin film was 950 nm. The frequency of driving current was set from 100 to 5000 Hz (the cutoff frequency). The trust region reflective method was adopted in the fitting process. Moreover, it was found that the measurement uncertainty of temperature rise was less than 1% and thus its influence on the uncertainties of measured thermal properties could be ignored. As a result, the major uncertainties of thermal conductivity measurement came from measuring the thickness of SiO2 thin film. The thermal conductivity of Si substrate was 142.1 W/(m K) with a relative error equal to approximately 2%, and the thermal conductivity of SiO2 thin film was 1.01 W/(m K) with a relative error equal to approximately 2%, which could agree well with the reported value in literature. In summary, the present work demonstrated that the combination of FEM and inverse method could be employed for thermal properties measurement, and thus analytical models are not always necessary. For future work, the methodology presented in this paper can be extended to deal with the measurement of thermal transport properties of irregular-shape thin flakes on a substrate.

On the numerical eigenmode analysis of acoustically lined ducts with uniform mean flow

The present work concerns the numerical eigenmode analysis of acoustically lined ducts of any constant cross-sectional shape in the presence of mean flow. The duct is lined with bulk-reactive porous material, which is separated from the flow channel by a perforated panel. A combined wave and finite element (WFE) method is introduced to investigate the effects of uniform mean flow on the eigenmodes and eigenvalues of the lined ducts. The proposed method is validated against analytical solutions for a simple case. A convergence rate of Se4 for eigenvalues can be reached for Mach number up to 0.8, with Se being the mesh size. In this study, the eigenmodes of a lined duct are divided into air-borne modes and lining-borne modes. The air-borne modes propagate mostly in the air domain, while the lining-borne modes can propagate in both air domain and porous domain. The effect of Mach number on the axial wavenumbers and mode shapes are analysed. It is found that, for air-borne modes, Mach number will strongly affect their wavenumbers, while its effect on the mode shape is marginal. On the contrary, for the lining-borne modes, Mach number has small effect on the wavenumber, but its effect on the mode shape is significant. Specifically, even the mode properties can be changed from a lining-borne mode to an air-borne mode for some left-travelling lining-borne mode. The transmission loss (TL) of a lined duct with three typical Mach numbers is calculated by the mode matching method. It is found that up-flow will generally increase TL of lined duct, compared with the case of no flow; while down-flow will generally decrease TL. In both situations, the peak frequency does not show significant change.

Thermo-hydro-mechanical modeling of fault discontinuities using zero-thickness interface element

Abstract In this paper, a coupled thermo-hydro-mechanical (THM) simulation in a faulted deformable porous medium is presented. This model involves solving the mass conservation, linear momentum balance, and energy balance equations which are derived from the Biot's consolidation theory. Fluid pore pressure, solid displacement, and temperature are chosen as initial variables in these equations, and the finite element method in combination with the interface element is used for spatial discretization of continuous and discontinuities (fault) parts of the medium to solve the equations. The main purpose of this study is providing precise formulations, applicability, and ability of the triple-node zero-thickness interface element in THM modeling of faults. It should be noted that the system of equations is solved using a computer code written in Matlab program. In order to verify the developed method, simulations of index problems such as Mandel's problem, and coupled modeling of a faulted porous medium and a faulted aquifer are presented. The modeling results obtained from the developed method show a very good agreement with those by other modeling methods, which indicates its accuracy.

Combine experimental and FEM analysis of adhesive bonded single lap joint with Al-alloy flat adherends and pre-embedded artificial defects

Adhesive bonded lap joint is considered to be better substitute to riveted or welded joints for aerospace, marine and structural applications. It is due to the ability to develop relatively lower stress concentration and fatigue severity in highly dynamic environment. In real practice, there are defects present in the joint interface that decide the strength and durability of the component. Hence, it is required to understand the joint strength with different defect geometries. In this paper, a combined experimental and finite element method is conducted to evaluate the strength of lap joint of Al-alloy flat plate, pre-embedded with defects of various geometries: square, rectangle, circular and elliptical. The results of experimental and FEM analysis are converging, and indicate the clear variation of strength due to different type of defects. It encourages further analysis.

A combined finite element method for parabolic equations posted in domains with rough boundaries

In this paper, we consider the solution of parabolic equations posted in domains with rough boundaries using the combined finite element procedure proposed in Xu et al. [A combined finite element method for elliptic problems posted in domains with rough boundaries, J. Comput. Appl. Math. 336 (2018), pp. 235–248] in space and backward-Euler scheme in time. We first prove error estimates for elliptic projection operator for both and by the dual argument which depend on the elliptic auxiliary problem, and then energy error estimates of semi-discrete and fully discrete schemes which have convergence rates about and , where s>0, respectively. Numerical results are provided for parabolic equations in domains with non-oscillating or oscillating boundaries to verify the theoretical findings.

A free, square, point-loaded ice sheet: A finite element-discrete element approach

Deflection of a free, thin, square, elastic, point-loaded ice sheet is studied. A three-dimensional, combined finite element-discrete element method (FEM-DEM) is applied. Examined is a set of square, self-similar (plan view) ice sheet samples with the side lengths of L=20, 40, 80, and 160 m; thicknesses of h=0.5, 1.0, and 1.5 m; and the average discrete element sizes of l=2h and 3h. The samples are generated and meshed via a centroidal Voronoi tessellation procedure. Each mesh is unstructured and consists of convex polyhedra as the discrete elements and a Delaunay-triangulated, in-plane beam lattice of co-rotational, viscously damped Timoshenko beam finite elements. Two load cases are considered: a sheet sample subjected to i) a vertical, centrally applied point load; and ii) a vertical point load on an edge. In both load cases, a good agreement is found between the deflections computed with the FEM-DEM approach and with FEM. Maximum, non-dimensionalized deflections w¯max (w¯max=q/Fz, where q=q(wmax) is an approximate, resultant reaction force due to the buoyancy, wmax the computed maximum deflection, and Fz the applied point load) scale, in each load case, either by a power-law, w¯max∝hm1(L), or exponentially, w¯max∝10m2(h)L, depending on whether computed over h (for each L) or vice versa. The exponents m1 and m2 are not constants, but functions of L and h, respectively, and approximately equal in either load case. In-plane size estimates are sought for an FEM-DEM sheet sample to represent either a) an infinite, elastic, point-loaded ice sheet; or b) a semi-infinite, elastic, point-loaded (with the load on the free edge) ice sheet with a free edge. A free, square, point-loaded FEM-DEM sheet sample well approximates both a) and b), if L/2>≈5lch, where lch denotes a characteristic length.

Springback simulation analysis of angle shape forming of springs based on orthogonal experiment method

The springback phenomenon in the angle shape forming process of spring affects the efficiency and accuracy of spring machine adjustment. In this paper, the angle shape forming process and springback process of SWOSC-V material are simulated by finite element analysis software ABAQUS, and orthogonal experiments are designed. According to the simulation results, the importance order and changing trend of each parameter are determined, and the parameters of minimum springback angle and springback law are obtained. It provides a reference for practical application. It is proved that the combination of finite element method and orthogonal experiment can improve the efficiency of finding the springback law.

Analysis on the heat storage unit through a Y-shaped fin for solidification of NEPCM

The primary goal of current research is the expedition of the discharging process with the use of Al2O3-nanoparticles and Y-shaped fins. The nanoparticle can be dispersed in a PCM to eliminate the limitations of them. Newton-Raphson scheme with a combination of Finite element method were implemented to discuss the novel outcomes of the present analysis. A powerful numerical approach is involved in simulating time-dependent phenomena in a complex geometry. Outcomes prove that dispersing nanoparticles is a good way of enhancing the discharge rate. As the radius of nanoparticle augments up to 20 nm, total energy decreases and profile has been converged in lower time. A comparison reveals that the outputs have excellent agreement with the experimental results.

Finite element approaching analysis of load localization and identification for smart structures

PurposeThe purpose of this paper is to propose a numerical approaching analysis method combining the sequential unconstrained minimization technique and finite element method to identify the loading condition and geometry of smart structures accurately.Design/methodology/approachA new load identification model is built and the finite element approaching method is proposed by the combination of finite element method and optimization technique.FindingsThe approaching algorithm has good convergence and fast approximation speed; the accuracy can meet the engineering requirements. The approaching model is simple, and the precision is controllable and it can be used to solve the load identification problem of the smart material structure.Originality/valueIn view of the cited papers, the information sensed by the smart structure is limited, discrete and contains certain errors. How to derive the cause from the limited, error-containing discrete information is an important problem that needs to be solved by the self-diagnosis function. A load identification model based on structural displacement response is established and a numerical approximation method is proposed by combining the finite element method with the optimization technique; the load magnitude and position of the structure are identified according to the displacement measurement values of the internal finite point in the structure under the load condition.

Research on rhenium–iridium alloy coating on microgroove molds in precision glass molding

There is an increasing demand for microgrooves in optical systems with a pitch at wave length level. Precision glass molding (PGM) is one of the most efficient methods for fabricating microgrooves on glass surface. Nickel–phosphorus (Ni–P) exhibits excellent cutting properties and is developed as the mold material for glass microgrooves. However, the phosphorus in Ni–P mold tends to diffuse into the glass during the PGM process at high temperatures, which may reduce the optical performance of the molded glass microgroove component. In addition, the atomic diffusion increases the interface friction coefficient between the glass and the mold, resulting in the decrease of molding accuracy of the microgroove array. To solve these problems, a rhenium–iridium (Re–Ir) alloy coating is deposited on the surface of the Ni–P microgroove mold by ion sputtering. In this paper, the surface roughness of the mold before and after coating with Re–Ir alloy coating is investigated. The mechanical properties of Ni–P and the Re–Ir alloy coating are obtained using a combination of finite element method (FEM) and experimental tests. The mold deformation after heating to the molding temperature is analyzed. The results show that the mechanical properties of the Ni–P mold surface can be strengthened after being plated with Re–Ir alloy coating, the Re–Ir coating isolates the diffusion of phosphorus from the Ni–P mold, and improve the forming accuracy of glass microgrooves.

Ultrawide band gap design of phononic crystals based on topological optimization

In this paper, based on the combined finite element method and bidirectional evolutionary structural optimization algorithm, we perform the topological optimization of phononic crystals to obtain ultrawide band gap between two special adjacent bands for both the in-plane and out-of-plane wave modes. The influences of matrix/scatter materials, material volume fraction, and initial topological design on the unit cell optimization are discussed in detail. The results show that the strategy proposed in this paper is effective and efficient to obtain better optimization results under the similar optimization condition, solutions with ultrawide band gaps can be easily obtained within 30 iterations. Several new patterns for phononic band gap crystals with optimized band gaps are presented. This work provides useful guidance in topological optimization design of phononic crystals.

Dynamic mechanical behavior analysis of deep water drilling riser under hard hang-off evacuation conditions

A dynamic analysis model for a drilling riser under hard hang-off conditions was established, and the model was solved by finite element method in combination with the Newmark β method and verified by comparing the results with similar researches. The influences of evacuation and current speeds, the desired track of the drilling platform, the weight of lower marine riser package (LMRP) and the length of the hang-off drilling riser on drilling riser deformation and bending moment were analyzed. Results indicate that the most fragile part of riser is the upper joint on the top end and the platform speed and track direction are key operable parameters during the emergency evacuation; keeping the platform moving a little faster than the surface current speed especially with a heavy LMRP is favorable for reducing the deformation of the riser; the desired track of drilling platform is along the ocean current; recycling the riser helps reduce the deformation but harms the upper joint of the riser. These results can provide a basis for making evacuation plans of the platform, provide a theoretical guarantee for the safety of the hard hang-off riser, and serve as a reference for the production and installation of the riser.