A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface

The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are obtained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bubble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under different parameters can be observed in our model, as demon- strated in our calculation results.

A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model

In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+
t2)is obtained,which is verified by the numerical results.

Feature Extraction and Recognition for Rolling Element Bearing Fault Utilizing Short-Time Fourier Transform and Non-negative Matrix Factorization

Due to the non-stationary characteristics of vibration signals acquired from rolling element bearing fault, thc time-frequency analysis is often applied to describe the local information of these unstable signals smartly. However, it is difficult to classitythe high dimensional feature matrix directly because of too large dimensions for many classifiers. This paper combines the concepts of time-frequency distribution（TFD） with non-negative matrix factorization（NMF）, and proposes a novel TFD matrix factorization method to enhance representation and identification of bearing fault. Throughout this method, the TFD of a vibration signal is firstly accomplished to describe the localized faults with short-time Fourier transform（STFT）. Then, the supervised NMF mapping is adopted to extract the fault features from TFD. Meanwhile, the fault samples can be clustered and recognized automatically by using the clustering property of NMF. The proposed method takes advantages of the NMF in the parts-based representation and the adaptive clustering. The localized fault features of interest can be extracted as well. To evaluate the performance of the proposed method, the 9 kinds of the bearing fault on a test bench is performed. The proposed method can effectively identify the fault severity and different fault types. Moreover, in comparison with the artificial neural network（ANN）, NMF yields 99.3% mean accuracy which is much superior to ANN. This research presents a simple and practical resolution for the fault diagnosis problem of rolling element bearing in high dimensional feature space.

A hybrid vertex-centered finite volume/element method for viscous incompressible flows on non-staggered unstructured meshes

This paper proposes a hybrid vertex-centered fi- nite volume/finite element method for solution of the two di- mensional （2D） incompressible Navier-Stokes equations on unstructured grids. An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling. The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by join- ing the centroid of cells sharing the common vertex. For the temporal integration of the momentum equations, an im- plicit second-order scheme is utilized to enhance the com- putational stability and eliminate the time step limit due to the diffusion term. The momentum equations are discretized by the vertex-centered finite volume method （FVM） and the pressure Poisson equation is solved by the Galerkin finite el- ement method （FEM）. The momentum interpolation is used to damp out the spurious pressure wiggles. The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both veloc- ity and pressure. The classic test cases, the lid-driven cavity flow, the skew cavity flow and the backward-facing step flow, show that numerical results are in good agreement with the published benchmark solutions.

Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis(SRFEA) with finite element limit analysis(FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety(FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis(1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.

A non-linear finite element model of human L4-L5 lumbar spinal segment with three-dimensional solid element ligaments

This paper establishes a non-linear finite element model (NFEM) of L4-L5 lumbar spinal segment with accurate three-dimensional solid ligaments and intervertebral disc. For the purpose, the intervertebral disc and surrounding ligaments are modeled with four-nodal three-dimensional tetrahedral elements with hyper-elastic material properties. Pure moment of 10 N·m without preload is applied to the upper vertebral body under the loading conditions of lateral bending, backward extension, torsion, and forward flexion, respectively. The simulate relationship curves between generalized forces and generalized displacement of the NFEM are compared with the in vitro experimental result curves to verify NFEM. The verified results show that: (1) The range of simulated motion is a good agreement with the in vitro experimental data; (2) The NFEM can more effectively reffect the actual mechanical properties than the FE model using cable and spring elements ligaments; (3) The NFEM can be used as the basis for further research on lumbar degenerative diseases.

Finite Element Simulation on the Spin-forming of the 3D Non-axisymmetric Thin-Walled Tubes

The roller movement trace for the 3D non-axisymmetric thin-walled tubes is a complex space curve. Besides the roller rotation caused by contact with the blank, the roller rotates around the workpiece together with the main spindle, and also moves simultaneously along the direction of the revolution radius. The method to correctly establish the finite element （FE） models of the metal spinning is based on the MSC. MARC software was introduced. The calculation formulas considering both the revolution and rotation of the roller were obtained by the mathematical deduction. The saving calculation points m should be a multiple of 4 for one revolution of the roller around the workpiece to obtain the maximum forming force for the spinning of the 3D non-axisymmetric thin-walled tubes. The simulation results conform well to the experimental ones for several spinning methods; the maximum error is less than ±15%.

Nonlinear finite element analysis of three implant-abutment interface designs

The objective of this study was to investigate the mechanical characteristics of implant-abutment interface design in a dental implant system, using nonlinear finite element analysis （FEA） method. This finite element simulation study was applied on three commonly used commercial dental implant systems： model I, the reduced-diameter 3i implant system （West Palm Beach, FL, USA） with a hex and a 12-point double internal hexagonal connection; model II, the Semados implant system （Bego, Bremen, Germany） with combination of a conical （45° taper） and internal hexagonal connection; and model III, the Br,~nemark implant system （Nobel Biocare, Gothenburg, Sweden） with external hexagonal connection. In simulation, a force of 170 N with 45°oblique to the longitudinal axis of the implant was loaded to the top surface of the abutment. It has been found from the strength and stiffness analysis that the 3i implant system has the lowest maximum yon Mises stress, prirlcipal stress and displacement, while the Br^nemark implant system has the highest. It was concluded from our preliminary study using nonlinear FEA that the reduced-diameter 3i implant system with a hex and a 12-point double internal hexagonal connection had a better stress distribution, and produced a smaller displacement than the other two implant systems.

Element nodal computation-based radial integration BEM for non-homogeneous problems

This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial in-tegral which is used to transform domain integrals to equivalent boundary integrals is carried out on the basis of elemental nodes. As a result, the computational time spent in evaluating domain integrals can be saved considerably in comparison with the conventional RIBEM. Three numerical examples are given to demonstrate the correctness and computational efficiency of the proposed approach.

COMPACTLY SUPPORTED NON-TENSOR PRODUCT FORM TWO-DIMENSION WAVELET FINITE ELEMENT

Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.

Elemental Concentrations in Biological Samples of Coronavirus Disease (COVID-19) and Other Pulmonary Disease Patients

Background: Recently, Coronavirus Disease 2019 (COVID-19) has been affected by the extreme acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and has developed important global health anxiety. At this time, the treatment options for this disease are only moderately successful. Smoking has been related to COVID-19 and its mortality, and it has the potential to affect bacteriological and viral conversion, clinical effects, and treatment outcomes. Methods: The aim of this study was to determine the relationship between critical essential trace {zinc (Zn), iron (Fe), and copper (Cu)} and toxic {cadmium (Cd) and nickel (Ni)} elements in human biological samples such as scalp hair, serum, saliva, blood, nasal fluid, and sputum of smoking and nonsmoking male COVID-19 patients (n = 139, age range 25 - 38 years) from Hyderabad, Pakistan. For comparative purposes, the biological specimens of referent persons (n = 83), pulmonary Tuberculosis (T.B) patients (n = 67), Pneumonia (n = 56) of the same age groups were also be analyzed. Microwave oven mediated digestion method was employed, and digestion of samples was carried out with the help of 2:1 mixture solution of HNO3 (65%) and H2O2 (30%). Atomic absorption spectrometry was employed for the determination of elemental concentrations from the microwave oven employed digested samples. Results: The found average of essential elements (Zn, Fe, and Cu) in biological specimens of smoker and nonsmoker male COVID-19, T.B, and Pneumonia patients was found to lower, whilst cadmium and nickel were found to be higher when compared with samples from referents (p < 0.001). Conclusions: Improved elemental (Cu, Fe, Zn) concentrations may also decrease the risk of bacterial co-infection by enhancing the mucociliary clearance and respiratory epithelial barrier function, in addition to providing direct antibacterial effects against S. pneumoniae. Our findings also suggest that higher Cd and Ni concentrations are linked to cigarette smoking, which could lead to COVID-19 and other lung-infected diseased recurrences. However, further clinical and experimental research is required.

INFLUENCE OF NON-PROCESS ELEMENTS ON REED PULP'S CHARACTERS DURING OXYGEN DELIGNIFICATION

A series of Reed Pulps were prepared in which the level of Non-Process Elements(NPEs), including calcium, manganese,copper,iron were seclectively enriched and depleted, these pulps were then oxygen delignification,and the pulps were characterized according to kappa number,viscosity,brightness. The results indicated that the enrichment of NPEs have an important effulence on delignification,pulp viscosity and brightness, iron is the most harmful during oxygen delignification but manganese is just like a kind of aid and can enhance brightness and delignification.

Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.

A New Non-uniform Beam Element and Its Application to Buckling Analysis for Framed Structures

The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the non-linear analysis and the static condensation. Based on the interpolation theory, the displacement fields of the three-node non-uniform Euler-Bernoulli beam element were constructed at first: the quintic Hermite interpolation polynomial was used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then,based on the basic assumptions of non-uniform Euler-Bernoulli beam whose section properties were continuously varying along its centroidal axis, the linear and geometric stiffness matrices of the three-node non-uniform beam element were derived according to the nonlinear finite element theory. Finally,the degrees of freedom ( DOFs) of the middle node of the element were eliminated using the static condensation method, and a new two-node non-uniform beam element including axial-force effect was obtained. The results indicate that each bar needs to be meshed with only one element could get a fairly accurate solution when it is applied to the stability analyses.

Review: Recent Developments in the Non-Probabilistic Finite Element Analysis

Generally, the finite element analysis of a structure is completed under deterministic inputs.However,uncertainties corresponding to geometrical dimensions,material properties, boundary conditions cannot be neglected in engineering applications. The probabilistic methods are the most popular techniques to handle these uncertain parameters but subjective results could be obtained if insufficient information is unavailable. Non-probabilistic methods can be alternatively employed,which has led to the procedures for nonprobabilistic finite element analysis. Each non-probabilistic finite element analysis method consists of two individual parts,including the core algorithm and pre-processing procedure. In this context,three types of algorithms and two typical pre-processing procedures as well as their effectiveness are described in detail,based on which novel hybrid algorithms can be conceived for the specific problems and the future work in this research field can be fostered.

Uniform Convergence for Finite Volume Element Method for Non-selfadjoint and Indefinite Elliptic Problems

In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.

Analysis of the Influence of Parafunctional Loads on the Bone-Prosthesis System: A Non-Linear Finite Element Analysis

The present study evaluates the effects of occlusal loading on an implant-supported dental implant with external hexagon dental implant-abutment systems, using the finite element method analysis. Tensile analyses were performed to simulate different axial and obliquous masticatory loads. The influence of the variations in the contouring conditions of the interfaces was analyzed to weigh the osseointegration with linear and non-linear cases, by means of a parametric design. The geometry selected to place the prostheses was a jaw section, considering the properties of the set of cortical and trabecular bones. The results show that for non-linear contour conditions, the stress presents smaller value distributions and signals a different place in the screw-implant interface as the factor of the greater weight in this study. The location indicated that von Mises stress concentrations are not exclusive to the contact regions studied, moving to an area that is not in direct contact with the non-linear contact interfaces. In addition, the direction of load with an angle of 15 degrees presented the highest values of von Mises stress.

Line-element based nonlinear adaptive piecewise compensating correction for LVDT sensors

In order to solve the linear variable differential transformer （LVDT） displacement sensor nonlinearity of overall range and extend its working range, a novel line-element based adaptively seg- menting method for piecewise compensating correction was proposed. According to the mechanical structure of LVDT, the output equation was calculated, and then the theoretic nonlinear source of output was analyzed. By the proposed line-element adaptive segmentation method, the nonlinear output of LVDT was divided into linear and nonlinear regions with a given threshold. Then the com- pensating correction function was designed for nonlinear parts employing polynomial regression tech- nique. The simulation of LVDT validates the feasibility of proposed scheme, and the results of cali- bration and testing experiments fully prove that the proposed method has higher accuracy than the state-of-art correction algorithms.

Finite element analysis of anchor plates using non-coaxial models

The non-coaxial model simulating the non-coincidence between the principal stresses and the principal plastic strain rates is employed within the framework of finite element method（FEM） to predict the behaviors of anchors embedded in granular material.The non-coaxial model is developed based on the non-coaxial yield vertex theory,and the elastic and conventional coaxial plastic deformations are simulated by using elasto-perfectly plastic Drucker-Prager yield function according to the original yield vertex theory.Both the horizontal and vertical anchors with various embedment depths are considered.Different anchor shapes and soil friction and dilation angles are also taken into account.The predictions indicate that the use of non-coaxial models leads to softer responses,compared with those using conventional coaxial models.Besides,the predicted ultimate pulling capacities are the same for both coaxial and non-coaxial models.The non-coaxial influences increase with the increasing embedment depths,and circular anchors lead to larger non-coaxial influences than strip anchors.In view of the fact that the design of anchors is mainly determined by their displacements,ignoring the non-coaxiality in finite element numerical analysis can lead to unsafe results.

A STABILIZED MIXED FINITE ELEMENT FORMULATION FOR THE NON-STATIONARY INCOMPRESSIBLE BOUSSINESQ EQUATIONS

In this study, we employ mixed finite element （MFE） method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence, uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.