Elastodynamic Infinite Elements with Modified Bessel Shape Functions for Dynamic Soil-Structure Interaction

The paper is devoted to formulations of decay and mapped elastodynamic infinite elements, based on modified Bessel shape functions. These elements are appropriate for Soil-Structure Interaction （SSI） problems, solved in time or frequency domain and can be treated as a new form of the recently proposed Elastodynamic Infinite Elements with United Shape Functions （EIEUSF） infinite elements. The formulation of 2D Horizontal type Infinite Elements （HIE） is demonstrated here, but by similar techniques 2D Vertical （VIE） and 2D Comer （CIE） Infinite Elements can also be formulated. Using elastodynamic infinite elements is the easier and appropriate way to achieve an adequate simulation including basic aspects of Soil-Structure Interaction. Continuity along the artificial boundary （the line between finite and infinite elements） is discussed as well and the application of the proposed elastodynamic infinite elements in the Finite Element Method （FEM） is explained in brief. Finally, a numerical example shows the computational efficiency of the proposed infinite elements.

A NOVEL ELLIPSOIDAL ACOUSTIC INFINITE ELEMENT

A novel ellipsoidal acoustic infinite element is proposed. It is based a new pressure representation, which can describe and solve the ellipsoidal acoustic field more exactly. The shape functions of this novel acoustic infinite element are similar to the (Burnett's) method, while the weight functions are defined as the product of the complex conjugates of the shaped functions and an additional weighting factor. The code of this method is cheap to generate as for 1-D element because only 1-D integral needs to be numerical. Coupling with the standard finite element, this method provides a capability for very efficiently modeling acoustic fields surrounding structures of virtually any practical shape. This novel method was deduced in brief and the conclusion was kept in detail. To test the feasibility of this novel method efficiently,in the examples the infinite elements were considered,excluding the finite elements relative. This novel ellipsoidal acoustic infinite element can deduce the analytic solution of an oscillating sphere. The example of a prolate spheroid shows that the novel infinite element is superior to the boundary element and other acoustic infinite elements. Analytical and numerical results of these examples show that this novel method is feasible.

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

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

Analysis of ground vibrations due to underground trains by 2.5D finite/infinite element approach

The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains. The irregularities of the near field, including the tunnel structure and parts of the soil, are modeled by the finite elements, and the wave propagation properties of the far field extending to infinity are modeled by the infinite elements. One particular feature of the 2.5D approach is that it enables the computation of the three-dimensional response of the half-space, taking into account the load-moving effect, using only a two-dimensional profile. Although the 2.5D finite/infinite element approach shows a great advantage in studying the wave propagation caused by moving trains, attention should be given to the calculation aspects, such as the rules for mesh establishment, in order to avoid producing inaccurate or erroneous results. In this paper, some essential points for consideration in analysis are highlighted, along with techniques to enhance the speed of the calculations. All these observations should prove useful in making the 2.5D finite/infinite element approach an effective one.

On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions

This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite element method is explained in brief. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions.

Computing of the Anchor by the Method of Three-Dimension Point-Radiate Infinite Elements

On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node finite elements to compute the compression distortion of the prestressed anchorage segment. The results indicate that when the prestressed force acts on the anchorage head and segment, the stresses and the displacements in the rock around the anchorage head and segment concentrate on the zone center with the anchor axis, and they decrease with exponential forms. Therefore,the stresses and the displacement spindles are formed. The calculating results of the infinite element are close to the theoretical results. This indicates the method is right. This article introduces a new way to study the mechanism of prestressed anchors. The obtained results have an important role in the research of the anchor mechanism and engineering application.

Vehicle–track–tunnel dynamic interaction:a finite/infinite element modelling method

The aim of this study is to develop coupled matrix formulations to characterize the dynamic interaction between the vehicle,track,and tunnel.The vehicle–track coupled system is established in light of vehicle–track coupled dynamics theory.The physical characteristics and mechanical behavior of tunnel segments and rings are modeled by the finite element method,while the soil layers of the vehicle–track–tunnel(VTT)system are modeled as an assemblage of 3-D mapping infinite elements by satisfying the boundary conditions at the infinite area.With novelty,the tunnel components,such as rings and segments,have been coupled to the vehicle–track systems using a matrix coupling method for finite elements.The responses of sub-systems included in the VTT interaction are obtained simultaneously to guarantee the solution accuracy.To relieve the computer storage and save the CPU time for the large-scale VTT dynamics system with high degrees of freedoms,a cyclic calculation method is introduced.Apart from model validations,the necessity of considering the tunnel substructures such as rings and segments is demonstrated.In addition,the maximum number of elements in the tunnel segment is confirmed by numerical simulations.

Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method

The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.

INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS

The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.

THE ANALYSIS OF THIN WALLED COMPOSITE LAMINATED HELICOPTER ROTOR WITH HIERARCHICAL WARPING FUNCTIONS AND FINITE ELEMENT METHOD

In the present paper, a series of hierarchical warping functions is developed to analyze the static and dynamic problems of thin walled composite laminated helicopter rotors composed of several layers with single closed cell. This method is the development and extension of the traditional constrained warping theory of thin walled metallic beams, which had been proved very successful since 1940s. The warping distribution along the perimeter of each layer is expanded into a series of successively corrective warping functions with the traditional warping function caused by free torsion or free beading as the first term, and is assumed to be piecewise linear along the thickness direction of layers. The governing equations are derived based upon the variational principle of minimum potential energy for static analysis and Rayleigh Quotient for free vibration analysis. Then the hierarchical finite element method. is introduced to form a,. numerical algorithm. Both static and natural vibration problems of sample box beams axe analyzed with the present method to show the main mechanical behavior of the thin walled composite laminated helicopter rotor.

Simulation of three-dimensional tension-induced cracks based on cracking potential function-incorporated extended finite element method

In the finite element method,the numerical simulation of three-dimensional crack propagation is relatively rare,and it is often realized by commercial programs.In addition to the geometric complexity,the determination of the cracking direction constitutes a great challenge.In most cases,the local stress state provides the fundamental criterion to judge the presence of cracks and the direction of crack propagation.However,in the case of three-dimensional analysis,the coordination relationship between grid elements due to occurrence of cracks becomes a difficult problem for this method.In this paper,based on the extended finite element method,the stress-related function field is introduced into the calculation domain,and then the boundary value problem of the function is solved.Subsequently,the envelope surface of all propagation directions can be obtained at one time.At last,the possible surface can be selected as the direction of crack development.Based on the aforementioned procedure,such method greatly reduces the programming complexity of tracking the crack propagation.As a suitable method for simulating tension-induced failure,it can simulate multiple cracks simultaneously.

Mixed Finite Element Formats of any Order Based on Bubble Functions for Stationary Stokes Problem

Mixed element formats of any order based on bubble functions for the stationary Stokes problem are derived in triangular and tetrahedral meshes and the convergence of these formats are proved.

THE h-p VERSION OF THE INFINITE ELEMENT METHOD AND ITS APPLICATION

The paper investigates the h-p version of the infinite element method. An exponential conver gence can be abtained by a small amount of computing work.

Research on the acoustic scattering function and coherence properties from rough seafloor based on finite element model

Acoustic scattering from a rough sea bottom is recognized as a main source of reverberation. In this study, scattering properties from a layered bottom were exploited based on the finite element model. The scattering strength and loss from the layered rough seabed were investigated by ensembling the realizations of rough interface. They were found to be dependent on the thickness of sediment, and interference was significant in the case of thin sediment. Through verification of the finite element model, the scattering loss could be evaluated using the Eckart model with a proper sound speed in the thick sediment. The multiple scattering effect on the sound field was also exploited. It revealed that the effect depended strongly on the bottom type.

Mapping-Based 3D Hexahedral Finite Element Mesh Generation Method

Mapping mesh generation is widely applied in pre-processes of Finite Element Method （FEM）. In this study, the basic 3D mapping equations by Lagrange interpolating function are founded. Based these equations, a mapping pattern library, which maps essential configurations e.g. line, circle, rotary body, sphere etc. to hexahedral FEM mesh, has been built. Then available FEM mesh will be generated by clipping and assembling the mapped essential objects. Study case illustrates that the proposed method is simple and efficient to generate valid FEM mesh for complex 3D engineering structure.

ESTIMATES ON THE FINITE ELEMENT APPROXIMATIONS OF A QUADRATIC FUNCTIONAL

This paper gives some estimates of a quadratic functional related with Rie- mann Hypothesis.

A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization

The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.

Construction of Finite Element Multiscaling Function with Three Coefficients

The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.

Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

Advancements in manufacturing technology,including the rapid development of additive manufacturing(AM),allow the fabrication of complex functionally graded material(FGM)sectioned beams.Portions of these beams may be made from different materials with possibly different gradients of material properties.The present work proposes models to investigate the free vibration of FGM sectioned beams based on onedimensional(1D)finite element analysis.For this purpose,a sample beam is divided into discrete elements,and the total energy stored in each element during vibration is computed by considering either the Timoshenko or Euler-Bernoulli beam theory.Then,Hamilton’s principle is used to derive the equations of motion for the beam.The effects of material properties and dimensions of FGM sections on the beam’s natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model(TM).The presented model is validated by comparison with three-dimensional(3D)finite element simulations of the first three mode shapes of the beam.

Mapping relationship analysis of welding assembly properties for thin-walled parts with finite element and machine learning algorithm

The finite element(FE)-based simulation of welding characteristics was carried out to explore the relationship among welding assembly properties for the parallel T-shaped thin-walled parts of an antenna structure.The effects of welding direction,clamping,fixture release time,fixed constraints,and welding sequences on these properties were analyzed,and the mapping relationship among welding characteristics was thoroughly examined.Different machine learning algorithms,including the generalized regression neural network(GRNN),wavelet neural network(WNN),and fuzzy neural network(FNN),are used to predict the multiple welding properties of thin-walled parts to mirror their variation trend and verify the correctness of the mapping relationship.Compared with those from GRNN and WNN,the maximum mean relative errors for the predicted values of deformation,temperature,and residual stress with FNN were less than 4.8%,1.4%,and 4.4%,respectively.These results indicate that FNN generated the best predicted welding characteristics.Analysis under various welding conditions also shows a mapping relationship among welding deformation,temperature,and residual stress over a period of time.This finding further provides a paramount basis for the control of welding assembly errors of an antenna structure in the future.