Finite Element Equations Research Articles

A method for dynamic analysis and design of joined conical-cylindrical shells based on the model condensation

In the vibration analysis of joined conical-cylindrical shells, mode methods are widely used. However, from the practical results, boundary conditions affect significantly on the vibration behaviors of these structures. Therefore, the assumed modes may not obtain accurate results, which is terrible for structural design or vibration control. Finite element method (FEM) can be used to solve such problems, whereas the time and hardware costs are unacceptable, especially for the structural design and vibration control. The Craig-Bampton (C-B) method takes into account the advantages of both FEM and mode theory, and is very suitable for the dynamic analysis. This paper studies the advantages and feasibility of the C-B method in vibration analysis of joined conical-cylindrical shells. Using the eight-node super-parametric shell element and Hamilton's principle, the finite element equation of motion for the joined conical-cylindrical shell is established. The reduced FE model of the structure is obtained by using the C-B method. A process for efficient structural dynamic design is proposed. The correctness of the model reduction based on C-B method is verified through modal measurement experiments. In addition, some examples are given to illustrate the advantages of the C-B method in the optimization design and dynamic analysis of joined conical-cylindrical shell structures. Finally, a solution idea of coordinate transformation matrix is proposed when there are much more interfaces between substructures.

Hybrid Layer Modeling Method With Dual-Leakage Flux Paths for Heavily Saturated Iron-Cored Linear Permanent Magnet Synchronous Motors

This paper presents the dual-leakage hybrid layer modeling (DL-HLM) method for the linear permanent-magnet synchronous motors (LPMSMs) in a heavily saturated state. The proposed hybrid model consists of the nonlinear dual-leakage flux-tube model for the iron-cored armature where the geometric saliency exists, the Maxwell model for the PM track with uniform layers, and the hybrid input-output conversion method for the iteration between two models. As the minimum number of leakage flux paths, the dual-leakage flux-tube network is selected, considering the opposite-direction leakage fluxes generated by the flux-steering effect in heavily saturated iron-core teeth. The novel reluctance adaptation methods are also proposed, which allow the DL-HLM to accurately capture significant nonlinearities even with the minimum number of leakage flux paths, thereby correctly estimating motor forces in high-performance LPMSMs. The proposed DL-HLM is validated comparing to the equivalent finite element method (FEM) in terms of the magnetic fields in the working air-gap and motor force performances. The proposed modeling method estimates the magnetic fields and forces with an accuracy of higher than 95% even at significantly high saturation levels while simultaneously achieving multiple-orders-of-magnitude faster computation time as compared to the FEM.

A new, fast method for solving finite-element equations iteratively based on Gauss–Seidel

Solving large equation systems is the most time-consuming part of finite-element modelling – iterative techniques are favoured for models with numerous degrees of freedom where direct techniques have high storage requirements. Classical iterative techniques such as Gauss–Seidel (GS) are robust due to guaranteed convergence and algorithmic simplicity. Performance of iterative techniques chiefly depends on system scale and stiffness matrix properties – which are influenced by structural configuration. However, it is possible to adjust an iterative algorithm such that its speed is greatly enhanced for a certain class of structural configurations. This paper presents an adjusted GS solver, ‘constrained Gauss–Seidel’ (CGS), which has been formulated to solve typical multi-storey structures with an enhanced speed. The innovation in CGS originates from the adoption of a diaphragmatic relaxation mechanism that results in dividing equations into two groups to optimally deal with the different unknown types. In this paper, the concept and algorithm of the newly developed CGS method are elucidated. Then, 16 practical examples are solved to assess the solving speed of CGS against other iterative methods – GS and modified Gauss–Seidel (MGS, MGS*). The convergence speed of CGS attained 33 times, 3.7 times and 2 times those of GS, MGS and MGS*, respectively.

Study on the Cell Magnification Equivalent Method in Out-of-Plane Compression Simulations of Aluminum Honeycomb

The large scale and long calculation times are unavoidable problems in modeling honeycomb structures with large sizes and dense cells. The cell magnification equivalent is the main method to solve those problems. This study finds that honeycomb structures with the same thickness-to-length ratios have the same mechanical properties and energy absorption characteristics. The improved equivalent finite element models of honeycomb structures with the same thickness-to-length ratios were established and validated by experiments. Based on the validated finite element model of the equivalent honeycomb structures, the out-of-plane compression behaviors of honeycomb structures were analyzed by LS-DYNA software. The results show that the performance of honeycomb structures is not equivalent before and after cell magnification. Thus, the cell magnification results were further subjected to CORA (correlation analysis) to determine the magnification time and prove the accuracy of the cell magnification time through drop-weight impact tests. In addition, a first-order decay exponential function (ExpDec1) for predicting cell magnification time was obtained by analyzing the relationship between the cell wall length and the cell magnification time.

Three-Dimensional Modeling of Marine Controlled Source Electromagnetic Using a New High-Order Finite Element Method With an Absorption Boundary Condition

The marine controlled source electromagnetic method (MCSEM) is widely used in marine oil, gas exploration and deep structures investigation because of its low cost and high efficiency. In this paper, a high-precision forward algorithm for 3D modeling for MCSEM is proposed. Unstructured meshes are used to discretize the model domain, and local mesh refinement techniques are applied, which is conducive to simulating complex terrains and targets. The application of electric dipole discrete technology can load wire excitation sources with arbitrarily complex spatial shapes, which can simulate more realistic electromagnetic field distribution of marine controllable sources electromagnetic in actual exploration. Absorption boundary conditions based on real number and exponential stretching techniques are introduced to improve the numerical solution accuracy. To improve the efficiency of solving, the open-source massively parallel solver (MUMPS) based on the multifrontal algorithm is used to solve the finite element equations. Finally, some typical geoelectric models are designed to verify the correctness and effectiveness of the proposed algorithm. The calculation results show that higher order finite elements bring about higher accuracy. In addition, the loading of absorption boundary conditions is simple and effective than conventional Dirichlet boundary conditions.

A stochastic finite element scheme for solving partial differential equations defined on random domains

This paper proposes a novel stochastic finite element scheme to solve partial differential equations defined on random domains. A geometric mapping algorithm first transforms the random domain into a reference domain. By combining the mesh topology (i.e. the node numbering and the element numbering) of the reference domain and random nodal coordinates of the random domain, random meshes of the original problem are obtained by only one mesh of the reference domain. In this way, the original problem is still discretized and solved on the random domain instead of the reference domain. A random isoparametric mapping of random meshes is then proposed to generate the stochastic finite element equation of the original problem. We adopt a weak-intrusive method to solve the obtained stochastic finite element equation. In this method, the unknown stochastic solution is decoupled into a sum of the products of random variables and deterministic vectors. Deterministic vectors are computed by solving deterministic finite element equations, and corresponding random variables are solved by a proposed sampling method. The computational effort of the proposed method does not increase dramatically as the stochastic dimension increases and it can solve high-dimensional stochastic problems with low computational effort, thus the proposed method avoids the curse of dimensionality successfully. Four numerical examples are given to demonstrate the good performance of the proposed method.

A FEM-DFN model for the interaction and propagation of multi-cluster fractures during variable fluid-viscosity injection in layered shale oil reservoir

To investigate the height growth of multi-cluster fractures during variable fluid-viscosity fracturing in a layered shale oil reservoir, a two-dimensional finite element method (FEM)-discrete fracture network (DFN) model coupled with flow, stress and damage is proposed. A traction-separation law is used to describe the mixed-mode response of the damaged adhesive fractures, and the cubic law is used to describe the fluid flow within the fractures. The rock deformation is controlled by the in-situ stress, fracture cohesion and fluid pressure on the hydraulic fracture surface. The coupled finite element equations are solved by the explicit time difference method. The effects of the fracturing treatment parameters including fluid viscosity, pumping rate and cluster spacing on the geometries of multi-fractures are investigated. The results show that variable fluid-viscosity injection can improve the complexity of the fracture network and height of the main fractures simultaneously. The pumping rate of 15 m 3 /min, variable fluid-viscosity of 3-9-21-36-45 mPa s with a cluster spacing of 7.5 m is the ideal treatment strategy. The field application shows that the peak daily production of the application well with the optimized injection procedure of variable fluid-viscosity fracturing is 171 tons (about 2.85 times that of the adjacent well), which is the highest daily production record of a single shale oil well in China, marking a strategic breakthrough of commercial shale oil production in the Jiyang Depression, Shengli Oilfield. The variable fluid-viscosity fracturing technique is proved to be very effective for improving shale oil production.

The Effect of Machining Parameters on the Temperature Distribution in Metal Cutting Operation

This study presents numerical solution by using coupling model between computational fluid dynamic (CFD), and finite element method (FEM) to predicted the temperature distribution through cutting tool. In this study ANSYS/Explicit dynamic used to solve finite element equations in cutting zone. Machining simulations were conducted using Aluminum (AL) and High speed steel (HSS) as a workpeice and tool material respectively. Depth of cut varied from 1.5 mm to 2.5 mm and a cutting speed varied from 6m/s to 10m/s have been considered in the simulations. The CFD model solve by using ANSYS/fluent to find the temperature distribution at the tool surface by using finite volume method. The simulation explained the influence of depth of cut, and cutting speed on cutting temperature. For all simulations, the rake angle is fixed (6°). The rise or reduction in temperature as a result of the various cutting parameters was also estimated and discussed. After solving the problem, it was discovered that the temperature at the tip (tool-work piece contact area) was the highest and gradually decreased towards the surface, and that the results showed a major influence of cutting speed on the temperature generated in the machined models and a very small influence of depth of cut on the workpiece temperature.

The scaled boundary finite element method for dispersive wave propagation in higher‐order continua

AbstractThe classical theory of elasticity relies on the perfect structure of matter. No matter how small a medium is, it always stays homogeneous—but the reality is different. Even though the classical continuum mechanics suffices well for describing phenomena that evolve at super‐microscopic scales, it ceases to reproduce reasonable responses when the size effects are pronounced. It is due to the local constitutive equations of classical continuum mechanics, which are devoid of any length scales associated with the underlying microstructure. The gradient‐dependent theory of elasticity redresses this shortcoming by incorporating the kinematic quantities of the corresponding representative volume element by enriching the differential equations with higher‐order spatial and temporal derivatives. In this study, the scaled boundary finite element method is formulated for the equations of motion with higher‐order inertia terms. To this end, the semi‐discretized scaled boundary finite element equations of the medium are derived by introducing the scaled boundary transformation of geometry to the gradient‐enriched equations of motion and applying the Galerkin method of weighted residuals. It is shown that the well‐established available solution methods are incapable of handling the frequency‐domain representation of the derived formulation. Accordingly, a numerical solution method based on the shooting technique is proposed. The solution procedure is formulated for general numerical integration schemes via the infinite Taylor series. The evolution of the impedance‐diffusion matrix and contribution of inter‐subdomain forces and tractions are extracted. Four different numerical integration methods are employed to describe the solution procedure. In addition, a comparison regarding their computational efficiency is presented. For the sake of verification, the scaled boundary finite element solutions of three numerical examples are compared with reference solutions that are obtained using finite element models with extremely fine meshes. The convergence trends are also presented for both ‐ and ‐refinement methods. The results demonstrate the capability of the proposed formulation in reproducing accurate responses.

Extending the Incidence Angle of Shear Vertical Wave Electromagnetic Acoustic Transducer with Horizontal Magnetization.

Angled shear vertical (SV) waves have been successfully employed in the non-destructive testing of welds, pipes, and railways. Non-contact meander-line coil electromagnetic acoustic transducers (EMAT) have many benefits in generating angled SV waves. The most important benefit is that the incidence angle of an SV wave can be controlled by the excitation frequency. However, the incidence angle of a traditional SV-wave EMAT is reported to be under 45 degrees in many cases. In this work, such cases are tested, and the problems of the received signal at large incidence angles are found to be due to wave interference and small signal amplitudes. An equivalent finite element (FE) model is established to analyze the problem, and the main reason is found to be the head wave. An alternative configuration of angled SV-wave EMAT with horizontal magnetization is proposed to reduce the influence of the head wave. Finally, the results from simulations and experiments show that the proposed EMAT has a larger signal amplitude and significantly reduced interference in large-incidence angle scenarios. Moreover, an incidence angle of an SV wave of up to 60 degrees can be achieved, which will help improve the performance and capability of nondestructive testing.

A robust Moore–Penrose pseudoinverse-based static finite-element solver for simulating non-local fracture in solids

In this work, we develop a pseudoinverse-based static finite-element solver to model the elastic deformation and non-local brittle fracture of solids. The pseudoinverse of the finite-element stiffness matrix is calculated using a QR decomposition-based method which is faster than using the traditional approach based on the singular value decomposition method. This new finite-element framework has two advantages: (1) the finite-element equations can still be solved even when the finite-element stiffness matrix is singular, and (2) there is no need for introducing an artificial elastic rest energy or viscous regularization for the sole purpose of keeping the finite-element stiffness matrix non-singular in order to solve the finite-element equations. We also show that the proposed method is robust in solving chosen boundary value problems involving the elastic deformation and abrupt non-local mode I and mixed-mode brittle fracture of solids when compared to the traditional element kill method where a small but finite residual stiffness is maintained at a material in order to prevent the finite-element stiffness matrix from being singular. Hence, this proposed method allows the modeling of separation/fragmentation of solids when fracture occurs.Finally, we use the new computational framework to model the fracture of PMMA beam samples at room temperature. By calibrating the material parameters in the constitutive theory using analytical methods and fitting to a Mode I fracture experiment force–displacement response, we show that our newly-proposed computational method is able to predict the experimental fracture loci and crack propagation characteristics in PMMA beam samples undergoing mixed-mode fracture conditions to good accord.

Exothermic chemical reaction of magneto-convective nanofluid flow in a square cavity

• The convective flow of Ferric Oxide-water nanofluid inside a square cavity is quantitatively explored. • The experiment was conducted in a hydromagnetic field and exothermic chemical process. • The finite element method has been employed in the numerical simulation. • The finite element method has been employed in the numerical simulation. • The heat transfer characteristics are analyzed for the presence of the magnetic field. • Heat transfer is studied in relation to the Frank-Kamenetskii number. We investigate the unsteady laminar convective magnetohydrodynamic nanofluids flow in a square cavity driven by an exothermic chemical reaction. Because exothermic chemical reactions are intrinsic in nanofluidic flow applications, we consider this exothermic chemical reaction in the analysis, which is governed by Arrhenius kinetics energy. A water-based nanofluid containing iron oxide (Fe 3 O 4 ) nanoparticles is employed in the simulation. The square cavity is accurately propounded by a combination of suitable heating and flow conditions. The left vertical wall of the enclosure is considered a higher unevenly heated wall, the right vertical wall of the domain is considered a relatively cool constant temperature, and the upper and lower walls are considered insulating walls. Each wall assumes a no-slip condition. The nanofluid governing equations are transformed into the non-dimensional set of equations using similarity analysis and then modified into finite element equations. Galerkin's method in finite element analysis is used to obtain the results of the problem. The results show that the Rayleigh number, the Frank-Kamenetsky number, and the nanosolid volume ratio all have significant effects on the convective flow regime, and the average Nusselt number increases with these parameters. Due to the greater value of the Rayleigh number ( Ra = 10 6 ), the average Nusselt number increased to 75.92%, and heat generation due to a strongly exothermic reaction (higher Frank-Kamenetskii number) can blow up the bounded solution. The water-Fe 3 O 4 nanofluid achieves a greater rate of heat transfer (maximum 22.65%) than that of the base fluid.

Dynamic response of FG-CNTRC beams subjected to a moving mass

This article presents the forced vibration of composite beams reinforced by single-walled carbon nanotubes (SWCNTs) and subjected to a moving mass. Considering the distribution of carbon nanotubes such as uniform (UD-CNT), functionally graded Λ (FGΛ-CNT) and X (FGX-CNT), three different beams are studied. Based on a third-order shear deformation theory (TSDT), the motion equations of the beams are derived using Hamilton's principle. Including mass interaction forces, the motion equations are transformed into a finite element equation in which a two-node beam element with eight degrees of freedom is utilized. To improve the efficiency of the beam element, the transverse shear rotation is employed as an independent variable in the derivation of the beam element. The vibration characteristics, including the dynamic magnification factors and the time histories for mid-span deflections are computed by using the Newmark method. Numerical result reveal that the vibration of the beams is clearly influenced of the CNT reinforcement, and the dynamic magnification is significantly decreased by increasing the CNT volume fraction. It is also shown that the FGX-CNT beam is the best in dynamic resistance in terms of the lowest dynamic deflection and dynamic magnification factors. The effects of the total volume fraction and the moving load velocity on the dynamic behaviour of the functionally graded carbon nanotube reinforced composites (FG-CNTRC) beams are examined in detail and highlighted.

3D MCSEM modeling based on domain-decomposition finite-element method

Domain decomposition approach is effective in converting large modeling problems into many small ones, so that the parallel computation can be easily facilitated and the memory consumption can be largely reduced. In this paper, we developed a domain-decomposition method for 3D time-domain marine controlled-source (MCSEM) modeling based on Dual-Primal Finite-Element Tearing and Interconnecting technique (FETI-DP). We use tetrahedral grids to do the spatial discretization first and then partition the mesh into subdomains. In each subdomain, the finite-element equations are independently constructed using the first-order vector shape functions and boundary conditions. To build the interconnections among these subdomains, we establish the interface equation for the Lagrange multipliers that are used as the boundary conditions for the subdomains. After solving the equations, the electric field for all subdomains can be obtained from the Lagrange multipliers. For the time discretization, we use unconditionally stable backward Euler scheme. We validate our algorithm by comparing with a semi-analytical solutions for a uniform half-space model under the ocean. Numerical experiments show that compared to the conventional finite-element method, our domain-decomposed method can save large amount of memory, render it possible to run 3D MCSEM modeling in small computational equipment.

Nonlinear dynamic analysis of galloping of a single iced conductor with four degrees of freedom based on curved beam theory

Based on the nonlinear strain-displacement relationship of spatial curved beam theory, a finite element model for galloping analysis of iced transmission lines is established, which involves three translational degrees of freedom (DOF) and one rotational degree of freedom for each node. Considering the aerodynamic nonlinearity and the geometric nonlinearity of large amplitude motions of the iced transmission line, the nonlinear dynamic finite element equation is presented by using the virtual work principle. The equation is transformed into the sub-space according to the mode superposition method and a time integration algorithm is also performed in the sub-space. Then, the element independence and modal convergence are researched. Finally, the influence of aerodynamic forces on structural frequency is analyzed. The numerical results show that aerodynamic forces will greatly affect the torsional frequency of the transmission line, which accurately reflects the dynamic characteristics of transmission lines. Furthermore, the galloping calculation of the transmission line has reliable accuracy by using 4-DOF (per node) elements for the iced conductor. On the other hand, the model can predict the actual galloping response of the transmission line, which is convenient for the implementation of subsequent control design.

Analysis of noise attenuation for offshore platform silencer in duct with flow

Recently, the NORSOK standards, which regulate noise and vibration on offshore platforms, were strengthened by prohibiting the use of glass wool for environmental and safety reasons. In addition, the use of sound-absorbing materials in panels and silencers was prohibited. Therefore, developing a silencer that does not use sound-absorbing materials is necessary. In this study, a bandgap expressed by acoustic characteristics of a periodic structure was applied to develop a silencer without sound-absorbing materials. The bandgap is formed in a frequency range in which propagation of acoustic waves is suppressed by setting a specific distance between single units based on periodic structural theory. The designed silencer evaluates the noise attenuation effect of the periodic structure based on a fluid-structure coupling finite-element equation for a plane wave in a stationary medium. In addition, the silencer model was selected by analyzing the regenerated noise originating from the periodic structure in the flow duct. This flow noise is used to analyze the propagation of sound waves based on the FW-H equation. This is achieved by employing the Lighthill acoustic analogy to predict the flow-induced sound pressure. Furthermore, compressed air was injected at the end of the duct in the flow noise experiment to perform measurements. The results from the acoustic and flow noise experiments were compared to confirm the effect of the flow in the duct on noise generation. Moreover, the flow noise analysis based on the flow velocity elucidated the effect of the periodic structure on the flow. In addition, the analysis results were used to investigate its performance of the silencer with the periodic rod arrangement considering the flow noise in the duct and predict its acoustic characteristics in the bandgap frequency range.

Iterative solver with folded preconditioner for finite element simulation of magnetotelluric fields

We propose an iterative solver with a folded preconditioner for large sparse systems of linear algebraic equations (SLAEs), which are obtained as a result of a vector finite element approximation of electromagnetic fields in magnetotelluric problems. The solver is based on the computational scheme of the Conjugate A-Orthogonal Conjugate Residual method (COCR), diagonal preconditioner, and residual smoothing. To build a finite element approximation, the primary-secondary field approach is used. To construct a preconditioner, we use a matrix, the elements of which are the weights of the representation of gradients of nodal basis functions as a linear combination of edge basis functions. For Dublin Test Model 1 in a wide frequency range from 0.0001 Hz to 10 Hz, we compare the accuracy and computational efficiency of our code with the results of other authors, as well as compare the computational efficiency of the proposed diagonal folded preconditioned (DFP) COCR solver with other solvers. It is shown that the apparent resistivities obtained on the coarsest mesh with our code differ by no more than a few percent from the solution on a finer mesh and from some solutions obtained by other authors using the finite element, finite difference, and integral equation methods. The computational time required for our code is 8 times less than the minimum time presented by other authors (with a corresponding recalculation of the performance of the computers used). It is also shown that the DFP COCR solver practically does not increase the number of iterations at low frequencies and its computational time is about 20 times less than the time required for the COCR solver with a standard diagonal preconditioner. A comparison of the DFP COCR solver with the Parallel Direct Sparse solver (PARDISO) shows that even at low and medium frequencies, the computational time of the DFP COCR solver is about 20 times less than the computational time of the PARDISO, and at high frequencies this difference reaches already 50 times.

Electromechanical study of graphene reinforced lead-free functionally graded tile for vibration energy harvesting

This study focuses on the electromechanical analysis of functionally graded graphene reinforced piezoelectric composite (FG-GRPC) structures in order to identify circuit metrics such as voltage and power. The graphene platelets (GPLs) scatter evenly and parallelly in each graphene platelets reinforced piezoelectric composite (GRPC) tile. The effective modulus of elasticity for the GRPC tile is calculated by the Halpin-Tsai (HT) parallel model. The rule of the mixture (ROM) is employed to estimate the effective mass density, poisson’s ratio, and piezoelectric properties of GRPC structure. A simple power law distribution is responsible for the spatial disparity in composition over the thickness to generate FG-GRPC structural tiles. The first-order shear deformation theory and Hamilton’s principle are used to derive the governing finite element equations for the FG-GRPC plates. The impact of external resistance, frequency, volume fraction, piezoelectric characteristics, and geometry of the tile on the circuit metrics of FG-GRPC structures are thoroughly examined. Our results reveal that the circuit metrics of FG-GRPC plates are significantly enhanced due to consideration of material grading exponent and a small quantity of GPLs. This article will provide the necessary physical insights for modeling the electromechanical coupling in multipurpose piezoelectric materials, devices, and large-scale systems, allowing them to be used in industrial applications such as pressure sensors, miniature ultrasonic motors, fuel injectors, active controllers, and robotic systems.

A universal elastoplastic equivalent method for sandwich panels and its application in plastic forming

Based on Hill’48 yield criterion, a simple and universal elastoplastic equivalent method for sandwich panels was proposed. In this method, the core of sandwich panel was equivalent to an orthotropic homogeneous panel, and the elastoplastic parameters of equivalent sandwich model were quickly obtained by uniaxial tensile and pure shear numerical simulations of the mesoscopic sandwich model utilizing user-defined material subroutine (UMAT). The equivalent elastoplastic parameters of brazed aluminum honeycomb panels (BAHPs) with core heights of 9 mm (BAHP-H9) and 12 mm (BAHP-H12) were obtained, which were proved to be effective by comparison with analytical solutions and analysis of numerical simulation results. Then, the effectiveness of elastoplastic equivalent method was further demonstrated by comparing the numerical simulation results of multi-point forming (MPF) for the mesoscopic and equivalent finite element (FE) model of BAHPs. Finally, MPF experiments of cylindrical BAHPs under different target forming radii were carried out. The results showed that the elastoplastic equivalent method could be effectively applied to the plastic forming of sandwich panels.

Influence of location junction on ion transfer behavior in conical nanopores with bipolar polyelectrolyte brushes

A bipolar ion diode consists of two positively and negatively charged surfaces that show the distribution of specific ions under different applied voltages. One of the most important electrokinetic phenomena occurring in bipolar nanopores is ionic current rectification (ICR). ICR in nanopores occur when, by applying a voltage to both ends of a nanochannel, the system exhibits non-linear current-voltage behavior or diode-like behavior, in other words, ionic current occurs in a specific direction. In modeling bipolar soft nanochannels, it is usually assumed that the properties of the soft layer and the electrolyte are the same, which is not true for soft layers with high charge densities. In the present work, the effect of sharp and wide aperture radius of nanochannels on ionic current rectification in bipolar nanochannels by coating polyelectrolytic layer with conical geometry in different values of soft layer lengths was studied. For this purpose, by adopting a numerical calculation approach Finite element, Poisson-Nernst-Planck and Navier-Stokes equations were solved for steady-state by considering different permeability values, diffusion coefficient, and dynamic viscosity for polyelectrolyte and electrolyte In general, it can be concluded that the bipolar conical nanopore has a higher ICR than the cylinder geometry with the same average radius If the junction is at the tip of the nanopore. For example, when the mole concentration was equal to c0=50mM, the ICR for the bipolar conical nanopore with a soft layer with an optimal junction at the tip of the nanopore reached 45, while in the bipolar cylindrical nanopore at best (the optimal junction in the middle of the nanopore) reached 25.