Comparison of perfectly matched layer and multi-transmitting formula artificial boundary condition based on hybrid finite element formulation

The theory of perfectly matched layer （PML） artificial boundary condition （ABC）, which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation （PDE） system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula （MTF） boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary.

A COMBINED HYBRID FINITE ELEMENT METHOD FOR PLATE BENDING PROBLEMS

In this paper, a combined hybrid method is applied to finite element discretization of plate bending problems. It is shown that the resultant schemes are stabilized, i.e., the convergence of the schemes is independent of inf-sup conditions and any other patch test. Based on this, two new series of plate elements are proposed.

Uniform analysis of a stabilized hybrid finite element method for Reissner-Mindlin plates

This paper presents a low order stabilized hybrid quadrilateral finite element method for ReissnerMindlin plates based on Hellinger-Reissner variational principle,which includes variables of displacements,shear stresses and bending moments.The approach uses continuous piecewise isoparametric bilinear interpolations for the approximations of the transverse displacement and rotation.The stabilization achieved by adding a stabilization term of least-squares to the original hybrid scheme,allows independent approximations of the stresses and moments.The stress approximation adopts a piecewise independent 4-parameter mode satisfying an accuracy-enhanced condition.The approximation of moments employs a piecewise-independent 5-parameter mode.This method can be viewed as a stabilized version of the hybrid finite element scheme proposed in [Carstensen C,Xie X,Yu G,et al.A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates.Comput Methods Appl Mech Engrg,2011,200:1161-1175],where the approximations of stresses and moments are required to satisfy an equilibrium criterion.A priori error analysis shows that the method is uniform with respect to the plate thickness t.Numerical experiments confirm the theoretical results.

Load identification in one dimensional structure based on hybrid finite element method

The new hybrid elements are proposed by combing modified Hermitian wavelet elements with ANASYS elements. Then hybrid elements are substituted into finite element formulations to solve the load identification. Transfer matrix can be constructed by using the inverse Newmark algorithm and hybrid finite element method. Loads can obtain through the responses and the transfer matrix. Load identification law was studied under different excitation cases in rod and Timoshenko beam.Regularization method is adopted to solve ill-posed inverse problem of load identification. Compared with ANSYS results,hybrid elements and HCSWI elements can accurately identify the applied load. Numerical results show that the algorithm of hybrid elements is effective. The accuracy of hybrid elements and HCSWI elements can be verified by comparing the load identification result of ANASYS elements with the experiment data. Hermitian wavelet finite element methods have high accuracy advantage but it is difficult to apply the engineering practice. In practical engineering, complex structure can be analyzed by using the hybrid finite element methods which can be obtained the high accuracy in the crucial component.

A NEW HYBRID QUADRILATERAL FINITE ELEMENT FOR MINDLIN PLATE

In this paper a new quadrilateral plate element concerning the effect of transverse shear strain has been presented. It is derived from the hybrid finite element model based on the principles of virtual work. The outstanding advantage of this element is to use more rational trial functions of the displacements. For this reason, every variety of plate deformation can be simulated really whilc the least degrees of freedom is employed.A wide range of numerical tests was conducted and the results illustrate that this element has a very wide application scope to the thickness of plates and satisfactory accuracy can be obtained by coarse mesh for all kinds of examples.

A New Classification Method of Stress Modes in Hybrid Stress Finite Element

The paper presents a new method for classifying the stress modes in hybrid stress finite element in terms of natural stress modes in finite element and the rank analysis of matrix G in forming element It reveals the relation among the different assumed stress field, and gives the general method in forming stress field Comparing with the method of eigenvalue analysis, the new method is more efficient

MIXED HYBRID PENALTY FINITE ELEMENT METHOD AND ITS APPLICATION

The penalty and hybrid methods are being much used in dealing with the general incompatible element, With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower, and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element is extremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together. And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element. That is to say, they are optimal to each other.Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degreesof freedom are given on each corner -- one displacement and tworotations), the calculating formula of the element stiffness matrix is almost the same as that of the old triangle element for plate bending with nine degrees of freedom But it is converged to true solution with arbitrary irregrlar triangle subdivision. If the true solution u?H3 with this method the linear and quadratic rates of convergence are obtianed for three bending moments and for the displacement and two rotations respectively.

INCREMENTAL ANALYSIS FOR NONLINEAR RUBBER-LIKE MATERIALS BY HYBRID STRESS FINITE ELEMENT

In this paper, on the basis of the incremental Reissner variational principle.a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible Mooney rubber-like materials. The corrected terms of the non-equilibrium force and the incompressibility deviation are considered in the formulation. The computed values of numerical example agree very closely with the exact solution.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces

In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence.

A hybridized weak Galerkin finite element scheme for the Stokes equations

In this paper a hybridized weak Galerkin(HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced.The WG method uses weak functions and their weak derivatives which are defined as distributions.Weak functions and weak derivatives can be approximated by piecewise polynomials with various degrees.Different combination of polynomial spaces leads to different WG finite element methods,which makes WG methods highly flexible and efficient in practical computation.A Lagrange multiplier is introduced to provide a numerical approximation for certain derivatives of the exact solution.With this new feature,the HWG method can be used to deal with jumps of the functions and their flux easily.Optimal order error estimates are established for the corresponding HWG finite element approximations for both primal variables and the Lagrange multiplier.A Schur complement formulation of the HWG method is derived for implementation purpose.The validity of the theoretical results is demonstrated in numerical tests.

Dynamic analysis and experimental study of vibro-acoustic system with uncertainties at middle frequencies

To take into account the influence of uncetainties on the dynamic response of the vibro-acousitc structure, a hybrid modeling technique combining the finite element method（FE）and the statistic energy analysis（SEA） is proposed to analyze vibro-acoustics responses with uncertainties at middle frequencies. The mid-frequency dynamic response of the framework-plate structure with uncertainties is studied based on the hybrid FE-SEA method and the Monte Carlo（MC）simulation is performed so as to provide a benchmark comparison with the hybrid method. The energy response of the framework-plate structure matches well with the MC simulation results, which validates the effectiveness of the hybrid FE-SEA method considering both the complexity of the vibro-acoustic structure and the uncertainties in mid-frequency vibro-acousitc analysis. Based on the hybrid method, a vibroacoustic model of a construction machinery cab with random properties is established, and the excitations of the model are measured by experiments. The responses of the sound pressure level of the cab and the vibration power spectrum density of the front windscreen are calculated and compared with those of the experiment. At middle frequencies, the results have a good consistency with the tests and the prediction error is less than 3. 5dB.

Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method

Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara's 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h^(1+min){α,1}) is established for both the displacement approximation in H^1-norm and the stress approximation in L^2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.

An analytical approach to reconstruction of axisymmetric defects in pipelines using T(0,1)guided waves

Torsional guided waves have been widely utilized to inspect the surface corrosion in pipelines due to their simple displacement behaviors and the ability of longrange transmission.Especially,the torsional mode T(0,1),which is the first order of torsional guided waves,plays the irreplaceable position and role,mainly because of its non-dispersion characteristic property.However,one of the most pressing challenges faced in modern quality inspection is to detect the surface defects in pipelines with a high level of accuracy.Taking into account this situation,a quantitative reconstruction method using the torsional guided wave T(0,1)is proposed in this paper.The methodology for defect reconstruction consists of three steps.First,the reflection coefficients of the guided wave T(0,1)scattered by different sizes of axisymmetric defects are calculated using the developed hybrid finite element method(HFEM).Then,applying the boundary integral equation(BIE)and Born approximation,the Fourier transform of the surface defect profile can be analytically derived as the correlative product of reflection coefficients of the torsional guided wave T(0,1)and the fundamental solution of the intact pipeline in the frequency domain.Finally,reconstruction of defects is precisely performed by the inverse Fourier transform of the product in the frequency domain.Numerical experiments show that the proposed approach is suitable for the detection of surface defects with arbitrary shapes.Meanwhile,the effects of the depth and width of surface defects on the accuracy of defect reconstruction are investigated.It is noted that the reconstructive error is less than 10%,providing that the defect depth is no more than one half of the pipe thickness.

A Two-Level Preconditioning Technique for Wire Antennas Attached with Dielectric Objects

An iterative solution of linear systems is studied,which arises from the discretization of a wire antennas attached with dielectric objects by the hybrid finite-element method and the method of moment （hybrid FEM-MoM）.It is efficient to model such electromagnetic problems by hybrid FEM-MoM,since it takes both the advantages of FEM＇s and MoM＇s ability.But the resulted linear systems are complicated,and it is hard to be solved by Krylov subspace methods alone,so a two-level preconditioning technique will be studied and applied to accelerate the convergence rate of the Krylov subspace methods.Numerical results show the effectiveness of the proposed two-level preconditioning technique.

THE CONVERGENCE FOR NODAL EXPANSION METHOD

In this paper, we prove the convergence of the nodal expansion method, a new numerical method for partial differential equations and provide the error estimates of approximation solution.

A NEW HYBRIDIZED MIXED WEAK GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC PROBLEMS

In this paper,a new hybridized mixed formulation of weak Galerkin method is studied for a second order elliptic problem.This method is designed by approximate some operators with discontinuous piecewise polynomials in a shape regular finite element partition.Some discrete inequalities are presented on discontinuous spaces and optimal order error estimations are established.Some numerical results are reported to show super convergence and confirm the theory of the mixed weak Galerkin method.

Effect of planet pin position errors on the fatigue reliability of large aviation planetary systems

Planet pin position errors significantly affect the mechanical behavior of planetary transmissions at both the power-sharing level and the gear tooth meshing level,and its tolerance properties are one of the key design elements that determine the fatigue reliability of large aviation planetary systems.The dangerous stress response of planetary systems with error excitation is analyzed according to the hybrid finite element method,and the weakening mechanism of large-size carrier flexibility to this error excitation is also analyzed.In the simulation and analysis process,the Monte Carlo method was combined to take into account the randomness of planet pin position errors and the coupling mechanism among the error individuals,which provides effective load input information for the fatigue reliability evaluation model of planetary systems.In addition,a simulation test of gear teeth bending fatigue intensity was conducted using a power flow enclosed gear rotational tester,providing the corresponding intensity input information for the reliability model.Finally,under the framework of stress-intensity interference theory,the computational logic of total formula is extended to establish a fatigue reliability evaluation model of planetary systems that can simultaneously consider the failure correlation and load bearing time-sequence properties of potential failure units,and the mathematical mapping of planet pin positional tolerance to planetary systems fatigue reliability was developed based on this model.Accordingly,the upper limit of planet pin positional tolerance zone can be determined at the early design stage according to the specific reliability index requirements,thus maximizing the balance between reliability and economy.

Fluid-structure interaction simulation of pathological mitral valve dynamics in a coupled mitral valve-left ventricle model

Background Understanding the interaction between the mitral valve(MV)and the left ventricle(LV)is very important in assessing cardiac pump function,especially when the MV is dysfunctional.Such dysfunction is a major medical problem owing to the essential role of the MV in cardiac pump function.Computational modelling can provide new approaches to gain insight into the functions of the MV and LV.Methods In this study,a previously developed LV-MV model was used to study cardiac dynamics of MV leaflets under normal and pathological conditions,including hypertrophic cardiomyopathy(HOCM)and calcification of the valve.The coupled LV-MV model was implemented using a hybrid immersed boundary/finite element method to enable assessment of MV haemodynamic performance.Constitutive parameters of the HOCM and calcified valves were inversely determined from published experimental data.The LV compensation mechanism was further studied in the case of the calcified MV.Results Our results showed that MV dynamics and LV pump function could be greatly affected by MV pathology.For example,the HOCM case showed bulged MV leaflets at the systole owing to low stiffness,and the calcified MV was associated with impaired diastolic filling and much-reduced stroke volume.We further demonstrated that either increasing the LV filling pressure or increasing myocardial contractility could enable a calcified valve to achieve near-normal pump function.Conclusion The modelling approach developed in this study may deepen our understanding of the interactions between the MV and the LV and help in risk stratification of heart valve disease and in silico treatment planning by exploring intrinsic compensation mechanisms.