Infinite Elements Research Articles

Nonlinear soil deformability effects on the seismic damage mechanisms of brick and stone masonry arch bridges

Masonry arch bridges, which were generally built using brick and stone materials, still form a significant part of the highway and railway networks in the World. The subsoil deformability may considerably affect seismic damage mechanics of masonry arch bridges. The paper investigates the effects of nonlinear foundation soil behavior on the seismic damage mechanisms of brick and stone semicircular masonry arch bridges. Direct soil-structure interaction (SSI) approach is taken into account in the 3 D finite element models of the masonry arch bridge-foundation-soil interaction systems including contact, finite and infinite elements. Nonlinear behaviors of masonry units and homogenous soil domain are modeled using the Concrete Damage Plasticity (CDP) and Mohr-Coulomb failure criteria. The selected ground motion is matched and deconvoluted for hard and medium soil domains. Seismic damage mechanisms of brick and stone masonry arch bridges subjected to combined longitudinal and vertical deconvolved ground motion components are obtained for hard, medium, and partially hard and medium soil domains and are compared with each other.

Numerical and experimental analysis on the vibration and radiated noise of the cylinder washing machine

The radiated noise of washing machines plays a pivotal role in user experience. Several studies have provided evidence that the low-frequency vibration of washing machine makes great contributions to its radiated noise. Unlike high-frequency noise, low-frequency noise decreases slowly and its wavelength is longer, so it can easily pass through obstacles and bring out a far-reaching impact on human health. Recently researchers pay intense attention to decease the low-frequency noise caused by household washing machines. The infinite element method (IFEM) is relatively simple and practical in simulating infinite region among numeric methods in acoustic computing with low frequency. Besides, IFEM could be coupled well with FEM and has high computational efficiency in low-frequency domain. Accordingly, our work introduces FE-IFEM into the prediction on the radiated noise of the washing machine. In this work, we analyze the dynamic characteristics and accurately estimate the radiated noise based on FE-IFEM. Firstly, the finite element model of washing machine is established and the natural frequency is measured to ensure the reliability of the model. Furthermore, the rigid-flexiblecoupling dynamic model is constructed to analyze the vibration and the vibration response test is carried out to verify the estimates of dynamic analysis. Finally, the radiated noise of the washing machine is calculated by using FE-IFEM and the noise experiment is performed. The simulation results are compared with the results obtained from the experiment and we conclude that the simulation estimates are in good agreement with the measured results. The maximum error obtained by this method is less than 6 dB. It indicates that FE-IFEM is an appropriate choice for predicting the radiated noise of washing machines in the low-frequency domain.

Characteristics of wave propagation through rock mass slopes with weak structural planes and their impacts on the seismic response characteristics of slopes: a case study in the middle reaches of Jinsha River

Time-frequency joint analysis was used to investigate the seismic response of rock slopes containing weak structural planes. Four three-dimensional finite element models containing infinite element boundaries were modelled: homogeneous slope, anti-dip slope, bedding slope, and block slope models. The material of the models was elastic material. The influence of the structural planes on the seismic responses of the slopes was systematically analyzed. The results of time-frequency joint analysis show that the structural planes impact the propagation characteristics of the waves and the dynamic amplification effect of the slopes. The wave propagation characteristics and peak ground acceleration distribution of the block slope model are more complex than those of the other models. The influence of structural planes on the amplification effect of the slopes is discussed. Additionally, according to frequency-domain analysis, structural planes have a small impact on the natural frequencies and the peak Fourier spectrum amplitude distribution of the slope but have a significant influence on its dynamic deformation characteristics. The natural frequencies of slopes can be obtained by using modal analysis and Fourier spectrum analysis. The relationships between the natural frequencies of the slopes and their dynamic deformation characteristics were analyzed; in particular, the impacts of low-order and high-order natural frequency on the deformation of the surficial slope were investigated. The applicability of the energy spectrum in the evaluation of the dynamic deformation characteristics of slopes was discussed. The effects of structural planes on the seismic failure mode of the slopes are identified according to the analyses of the dynamic responses of the slopes.

Applying set optimization to weak efficiency

Set-valued extensions of vector-valued functions are used to investigate the relations between weak efficiency and variational inequalities (both Stampacchia and Minty type) which allows to apply the complete lattice framework from set optimization. Since the seminal work of Giannessi, it has been a challenge to generalize scalar results to the vector case. In this effort, some notions of generalized derivatives for vector-valued functions have been introduced, either in the form of set-valued functions or introducing appropriate notions of infinite elements in vector spaces. Switching the focus to set optimization in conlinear spaces, we propose a Dini-type derivative, that keeps the same set-valued form of the optimization problem.

Development of High-Order Infinite Element Method for Bending Analysis of Mindlin–Reissner Plates

An approach is presented for solving plate bending problems using a high-order infinite element method (IEM) based on Mindlin–Reissner plate theory. In the proposed approach, the computational domain is partitioned into multiple layers of geometrically similar virtual elements which use only the data of the boundary nodes. Based on the similarity, a reduction process is developed to eliminate virtual elements and overcome the problem that the conventional reduction process cannot be directly applied. Several examples of plate bending problems with complicated geometries are reported to illustrate the applicability of the proposed approach and the results are compared with those obtained using ABAQUS software. Finally, the bending behavior of a rectangular plate with a central crack is analyzed to demonstrate that the stress intensity factor (SIF) obtained using the high-order PIEM converges faster and closer than low-order PIEM to the analytical solution.

Axisymmetric BEM analysis of one-layered transversely isotropic halfspace with cavity subject to external loads

This paper presents an axisymmetric boundary element analysis of one-layered transversely isotropic material of halfspace extent with either ellipsoidal or spherical cavity. This analysis uses the fundamental solution of a transversely isotropic bi-material fullspace subject to the body force uniformly concentrated at a circular ring. The finite and infinite boundary elements are, respectively, used to discretize the finite and semi-infinite regions of the external boundary and the finite boundary elements are used to discretize the internal boundary. Different types of the integrals in the discretized boundary integral equations are efficiently calculated. An improved traction recovered method is applied to calculate the stresses on the boundary. Using one set of BEM mesh, a total of 12 case studies are calculated for the elastic fields of the one-layered transversely isotropic solid by uniform traction on the external horizontal boundary. The solid has either an ellipsoidal, a spherical, or none cavity in the upper layer. Four combinations of two transversely isotropic metals are adopted for the one-layered solid. One metal is the stiff zinc and the other is the soft magnesium. The displacements for the cases with magnesium as the upper layer are larger than those with zinc as the upper layer. Besides, the effects of the lower solid materials to the displacements are limited. The BEM results also reveal the variations of the displacements and stresses within the halfspace with or without cavities for different cases.

3D Forward Modeling of Seepage Self-potential Using Finite-infinite Element Coupling Method

The streaming potential in porous media is one of the main constituents of the self-potential. It has attracted special attention in environmental and engineering geophysics. Forward modeling of streaming potentials could be the foundation of corresponding data inversion and interpretation, and improving the application effect of the self-potential method. The traditional finite element method has a large subdivision area and computational quantity, and the artificial boundary condition is not suitable for complex models. The Helmholtz-Smoluchowski equation is introduced for evaluating the streaming potential. Then three new shape functions of the multidirectional mapping infinite elements are proposed and the finite-infinite element coupling method is deduced for reducing the subdivision scale and improving both the calculation efficiency and accuracy. The correctness and validity of the new coupled method are verified by a resistive model in homogeneous half-space. Besides, a seepage model with complex terrain and a landfill model with dynamic leakages are modeled using the improved coupled method. The results show that the accuracy of the improved coupled method is superior to the unimproved coupled method, and is better than the finite element method. Also, the coupled method has better adaptability to complex models and is suitable for the accurate simulation of dynamic multi-source seepage models.

Influences of earthquake input models on nonlinear seismic performances of minaret-foundation-soil interaction systems

Minarets, which are tall and slender structures, are important elements of mosques. Seismic performances of minarets can be strongly affected by the nonlinear dynamic soil-structure interaction and earthquake input mechanism models. The present paper investigates the influences of different earthquake input mechanism models on the nonlinear seismic performances of tall and slender minarets considering nonlinearity of both soil and structure behaviors. Three different minaret types constructed with concrete, masonry brick and stone materials are selected for the applications. Direct soil-structure interaction (SSI) approach is taken into account in the 3D finite element models of the minaret-foundation-soil interaction systems. Tie contact between the soil and foundation interfaces and infinite elements on the far sides of the soil domain are utilized in the 3D models. Nonlinear behaviors of masonry and concrete units, and homogenous soil domain are modeled using Concrete Damage Plasticity (CDP) and Mohr-Coulomb failure criteria. The standard rigid-base free, massless-foundation free, massed-foundation free and massed-foundation deconvolved earthquake input models are considered in the nonlinear seismic analyses. Three different earthquake records are selected for the nonlinear analyses and they are matched to the target response spectrum with return period of 475 years. The deconvolved ground motions at the rigid half-space bedrock are calculated from the matched records using the equivalent linear frequency domain analyses. Frequency and mode shapes, displacements, drift ratios, tensile strain and stress propagation patterns and damage ratios of brick, stone and concrete minaret models subjected to combined horizontal and vertical ground motions are determined for four earthquake input mechanism models and compared with each other.

Formula omitted]–graded identities and central polynomials of the Grassmann algebra

Let F be an infinite field of characteristic p different from 2 and let E be the Grassmann algebra generated by an infinite dimensional vector space L over F. In this paper we provide, for any odd prime q, a finite basis for the Tq-ideal of the Zq-graded polynomial identities for E and a basis for the Tq-space of graded central polynomials for E, for any Zq-grading on E such that L is homogeneous in the grading. Moreover, we prove that the set of all graded central polynomials of E is not finitely generated as a Tq-space, if p>2. In the non-homogeneous case such bases are also described when at least one non-neutral component has infinite many homogeneous elements of the basis of L in the respective grading.

Enhancement of energy density in novel Ba0.67Sr0.33TiO3 nanorod array nanocomposites

The majority of the previously reported nanocomposites obtainable with higher energy density (>15 J cm−3) relies strongly on much higher breakdown strength (>4000 kV cm−1). The operation of capacitors in such higher applied electric field brings challenges because of the substantially increased the failure probability. In this study we explored the dispersibility and the orientation of fillers in nanocomposites as they play vital roles in the energy density. Based on the infinite element modulation results, an original design of 1–3 type composite structure was employed in the current study. This design adopts the one-dimensional (110)-oriented monodispersed barium strontium titanate Ba0.67Sr0.33TiO3 (BST) nanorod array as fillers embedded in the three-dimensional poly (−vinylidene fluoride) (PVDF) polymer matrix. With these originally designed BST/PVDF nanocomposites, we have demonstrated a significant enhancement of energy density at a lower applied electric field. For example, an energy density of 13.10 J cm−3 at electric field of 3400 kV cm−1 can be obtained, an enhancement of 3 times larger than that of bare PVDF. Moreover, the discharge efficiency is maintained at 69% at 3400 kV cm−1. The high performance of this originally designed nanacomposite demonstrated its potential application in the next generation energy storage devices.

Experimental Determination and Modeling of Drying Process of Woody Biomass

Birch is a kind of readily available woody biomass resource, which can be used to crush and manufacture fuel particles and animal bedding. One of the important aspects during the production system is the drying of biomass prior to storage or processing. Moisture migration in wood is a particularly important factor in determining the drying process. The objectives of this study are to investigate the drying characteristics of Birch and develop a model to simulate moisture diffusion in Birch during the drying process. Experiments were conducted in a controlled environment chamber. Different temperatures and relative humidity were set to simulate the different drying conditions. The mechanism of moisture movement in Birch samples during the drying process was represented by a diffusion model according to Fick’s second law. A computer program in Matlab software was developed to simulate the infinite element model. Moisture diffusivity of Birch was determined by minimising the sum of squares of the residuals between experimental results and numerically predicted data. Results showed that the moisture diffusion coefficients of Birch ranged from 1.2×10−7m2/hr to 9.6×10−7m2/hr with temperature varying from 20°C to 60°C. And the trend of diffusion coefficient versus temperature was in accordance with the Arrhenius equation.

Directional interpolation infinite element for dynamic problems in saturated porous media

In this study, a directional interpolation infinite element suited to a saturated porous medium is presented to account for dynamic problems with semi-infinite or infinite domain. By employing the Galerkin method, the element property matrixes for a two-dimensional space are given. Using the governing differential equations for wave propagation in the saturated porous media, the analytical solutions for one-dimensional wave propagation are derived in detail. Then the shape functions for the infinite element based on the analytical solutions are formulated and the dynamic stiffness matrix is presented in analytical form is presented. As a result, a fully coupled 2D infinite element for the analysis of dynamic problems in unbounded saturated porous media is presented. The effectiveness and accuracy of the proposed element is well demonstrated by a comparison of the numerical results with known analytical solutions for 1D and 2D wave propagation problems. The results highlight that the proposed directional interpolation infinite element is useful and effective for addressing the dynamic problems with semi-infinite or infinite domain, with consideration of both compression and shear waves.

Spectral Stochastic Infinite Element Method in Vibroacoustics

A novel method to solve exterior Helmholtz problems in the case of multipole excitation and random input data is developed. The infinite element method is applied to compute the sound pressure field in the exterior fluid domain. The consideration of random input data leads to a stochastic infinite element formulation. The generalized polynomial chaos expansion of the random data results in the spectral stochastic infinite element method. As a solution technique, the non-intrusive collocation method is chosen. The performance of the spectral stochastic infinite element method is demonstrated for a time-harmonic problem and an eigenfrequency study.

2.5D self-potential forward modeling by natural-infinite element coupling method

The self-potential method is an effective method for time-lapse monitoring of underground fluxes, in particular of contaminants. High efficiency and precise forward modeling are necessary for data interpretation and inversion. The natural element method is a new meshless numerical modeling method based on Voronoi diagram, Delaunay triangulation, and natural neighborhood interpolation, where the model nodes are arranged flexibly without grid constraints. However, adding boundary conditions is cumbersome for multi-source models. The infinite element method is an effective numerical method for truncated boundary problems without loading boundary conditions. A new numerical modeling approach is proposed by the coupling of natural elements and infinite elements and applied to redox self-potential models which are multi-source models. The numerical result shows the global stiffness matrix of the new coupled method is sparse, symmetric and independent of the position of field sources, which is helpful to improve forward modeling efficiency. The new method has high precision and is suitable for multi-source models.

Influence of the Position of Artificial Boundary on Computation Accuracy of Conjugated Infinite Element for a Finite Length Cylindrical Shell

Structural finite element coupled with the conjugated infinite element method is an efficient numerical technique for solving the acoustic radiation problem due to the vibration of underwater objects. However, for large complex structures, the total acoustic mesh would become very large if the artificial boundary is too far away from the structural wetted surface. Thus, the calculation time can become too long to confine the application of the conjugated infinite element method. On the other hand, if the artificial boundary is close to the structural wetted surface, it will lead to computation accuracy losing due to the near-field effects. Consequently, it is essential to present some guidelines based on the physical mechanism of structural acoustics to choose a suitable artificial boundary that optimizes calculation accuracy and efficiency. In present work, the evanescent wave theory of an infinite length cylindrical shell is adopted to theoretically analyze the decay characteristic of evanescent waves in near field. Then, the effect of the position of artificial boundary on computation accuracy of conjugated infinite element for a finite length ring-stiffened cylindrical shell is numerically investigated. Results suggested that for the cylindrical shell mentioned in this study, the artificial boundary can be placed at least 0.4 times the acoustic wavelength away from the structural wetted surface. What’s more, for high frequencies or large-scale structures, the required non-dimensional distance between the artificial boundary and the structural wetted surface increases.

Elements Generating a Proper Normal Subgroup of the Cremona Group

Abstract Consider an algebraically closed field ${\textbf{k}}$, and let $\textsf{Cr}_2({\textbf{k}})$ be the Cremona group of all birational transformations of the projective plane over ${\textbf{k}}$. We characterize infinite order elements $g\in \textsf{Cr}_2({\textbf{k}})$ having a power $g^n$, $n\neq 0$, generating a proper normal subgroup of $\textsf{Cr}_2({\textbf{k}})$.

Seismic Isolation Effect of Non-Water Reacted Two-Component Polymeric Material Coating on Tunnels

An isolation layer is one of the countermeasures to promote the anti-seismic performance of tunnels. A newly invented polymeric material, non-water reacted two-component polymeric material (NRTCPM), is superior in impermeability and construction efficiency. In this study, covering a tunnel with NRTCPM coating to mitigate the damage caused by an earthquake is discussed, and an Impact Resonance Test (IRT) is firstly used to obtain the damping ratios and dynamic elastic modulus of NRTCPM. By using infinite element boundary, eight dynamic numerical modelsare made to study the isolation effects based on different density, Poisson’s ratio, dynamic elastic modulus and thickness of isolation layer values. Three different conditions are explored in this paper, namely (1) no NRTCPM layer coating around tunnel; (2) different densities, Poisson’s ratios and dynamic elastic moduli of a polymeric layer; and (3) various thicknesses of polymeric isolation layers around the lining. Tensile and compressive stresses are compared under these different conditions. The results show that retrofitting tunnel lining with this material has a good effect on seismic isolation. An optimum density and thickness of the NRTCPM layer is suggested considering cost and strength.

Boundary element formulation of axisymmetric problems in vertically non-homogeneous solids subject to normal traction

This paper presents an efficient and accurate boundary element method (BEM) for the elastic analysis of axisymmetric problems in vertically non-homogeneous solids without or with cavity. This BEM uses the fundamental solution of the elastic field in a multilayered elastic solid induced by the body force uniformly concentrated at a circular ring. This solution is also called Yue's solution. The effective integration methods are used for dealing with the integrals in the discretized boundary integral equations. The discretization of the boundary surface uses one-dimensional boundary elements. It also adopts the infinite boundary element to take into account the influence of a far-field region on the boundary surface. Numerical verifications of displacements and stresses for three benchmark problems are conducted, which gives the excellent agreement with previously published results. Case studies are presented to numerically illustrate the influences of both vertically non-homogeneous elastic material properties and spherical cavity on the elastic fields induced by uniform tractions on the boundary surface. These numerical results show that this new BEM is a fast and simple numerical algorithm for accurately computing the axisymmetric elastic fields in vertically non-homogeneous solids with or without cavity induced by normal tractions.

Analysis of scattering by finite sonic crystals in free field with infinite elements and normal modes

Acoustic exterior problems are in this paper solved numerically using the Astley-Leis infinite element method (IFEM). Normal modes can be determined thanks to the frequency independence of the system matrices. Convergence properties of the harmonic sound pressure solution as well as of normal mode eigenvalues are investigated for two-dimensional elliptical computational domains to estimate the essential requirements of accuracy. A relationship between the half-axis ratio of the ellipses and the eigenvalues is identified. By solving half-space problems, symmetry of the computational domains is utilized, which is shown for the first time for frequency-independent normal modes in exterior acoustics. This paper discusses applicability of the modes in the example of sonic crystals—periodic arrays of scatterers, in this context denoted as acoustic meta-atoms—that have recently attracted attention for their possible use as noise barriers. It can be shown that the sound-insulating effect of finite sonic crystals and individual meta-atoms in the free field can be related to normal modes in exterior acoustics. With the help of this approach, the absorption by Helmholtz resonators and due to a boundary admittance inside are studied. This work provides a new point of view and physical insights into the effects and underlying physics of sound insulation by finite sonic crystals and acoustic meta-atoms in free field. Although it is not the intention of this article to optimize the arrays, the method of normal modes in exterior acoustics is presented as an appropriate and novel tool for their dimensioning and design.

The numerical manifold method for exterior problems

The numerical manifold method (NMM), a Galerkin-type numerical method, has been successful in the solution of problems with finite definition domains, yet it has never been applied to problems with unbounded domains, or exterior problems. This study aims to fill the big gap by constructing infinite patches, together with the finite patches, to cover the unbounded domain. The local approximations of infinite patches can take the asymptotic estimations of the solutions at infinity, which are available for all those well-established boundary value problems. Compared with the infinite element methods in the finite element method (FEM), the construction of the trial functions by NMM is more elegant in theory and more systematical in methodology, resulting in more accurate solutions. Some typical examples in potential and half-space elasticity problems are investigated to illustrate the applicability and accuracy of the proposed method.