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This paper aims to analyze the influence of rotated anisotropy on the stability of slope, the random finite element method is used in this study.

The random field is generated by the discrete cosine transform (DCT) method, which can generate random field with different rotated angles conveniently.

Two idealized slopes are analyzed; it is observed that the rotated angle significantly affects the slope failure risk. The two examples support the conclusion that when the orientation of the layers is nearly perpendicular to the slip surface, the slope is in a relative stable condition. The results of heterogeneous slope with two clay layers demonstrate that the rotated angle of lower layer mainly controls the failure mechanism of the slope, and the rotated angle of upper layer exhibits a significant influence on the probability of slope failure.

The method for rotated anisotropy random field generation based on the DCT has a simple expression with few parameters and is convenient for implementation and practical application. The proposed method and the results obtained are useful for analyzing the stability of the heterogeneous slopes in engineering projects.

For gravity dams built on foundations with directional joint sets, the seepage in the foundation possesses anisotropic characteristics and may have adverse effects on the foundation stability. A methodology for system reliability analysis of gravity dam foundations considering anisotropic seepage and multiple sliding surfaces is proposed in this paper.

Anisotropic seepages in dam foundations are simulated using finite element method (FEM) with the equivalent continuum model (ECM), and their effect on dam foundation stability is involved by uplift pressures acting on the potential sliding surfaces. The system failure probability of the dam foundation is efficiently estimated using Monte Carlo method (MCM) combined with response surface method (RSM).

The case study shows that it is necessary to consider the possibly adverse effect of anisotropic seepage on foundation stability of gravity dams and the deterministic analysis of the foundation stability may be misleading. The system reliability analysis of the dam foundation is justified, as the uncertainties in shear strength parameters of the foundation rocks and joint sets as well as aperture, connectivity and spacing of the joint sets are quantified and the system effect of the multiple potential sliding surfaces on the foundation reliability is reasonably considered.

(1) A methodology is proposed for efficient system reliability analysis of foundation stability of gravity dams considering anisotropic seepage and multiple sliding surfaces (2) The influence of anisotropic seepage on the stability of gravity dam foundation  is revealed (3) The influence of estimation errors of RSMs on the system reliability assessment of dam foundation is investigated.

A finite volume scheme for diffusion equations on non-rectangular meshes is proposed in [Deyuan Li, Hongshou Shui, Minjun Tang, J. Numer. Meth. Comput. Appl., 1(4)(1980)217–224 (in Chinese)], which is the so-called nine point scheme on structured quadrilateral meshes. The scheme has both cell-centered unknowns and vertex unknowns which are usually expressed as a linear weighted interpolation of the cell-centered unknowns. The critical factor to obtain the optimal accuracy for the scheme is the reconstruction of vertex unknowns. However, when the mesh deformation is severe or the diffusion tensor is discontinuous, the accuracy of the scheme is not satisfactory, and the author hope to improve this scheme.

The authors propose an explicit weighted vertex interpolation algorithm which allows arbitrary diffusion tensors and does not depend on the location of discontinuity. Both the derivation of the scheme and that of vertex reconstruction algorithm satisfy the linearity preserving criterion which requires that a discretization scheme should be exact on linear solutions. The vertex interpolation algorithm can be easily extended to 3 D case.

Numerical results show that it maintain optimal convergence rates for the solution and flux on 2 D and 3 D meshes in case that the diffusion tensor is taken to be anisotropic, at times heterogeneous, and/or discontinuous.

This paper proposes a linearity preserving and explicit weighted vertex interpolation algorithm for cell-centered finite volume approximations of diffusion equations on general grids. The proposed finite volume scheme with the new interpolation algorithm allows arbitrary continuous or discontinuous diffusion tensors; the final scheme is applicable to arbitrary polygonal grids, which may have concave cells or degenerate ones with hanging nodes. The final scheme has second-order convergence rate for the approximate solution and higher than first-order accuracy for the flux on 2 D and 3 D meshes. The explicit weighted interpolation algorithm is easy to implement in three dimensions in case that the diffusion tensor is continuous or discontinuous.

The ordinary vector hysteresis stop model with constant threshold values is not able to prohibit the hysteretic property after the saturation correctly. This paper aims to develop an improved vector hysteresis stop model with threshold surfaces. This advanced anisotropic vector hysteresis stop model can represent the magnetic saturation properties and the hysteresis losses under alternating and rotating magnetizations.

By integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model, the anisotropy of the permeability of an electrical steel sheet can be represented. Instead of the commonly used constant threshold value for plastic elements of the hysteresis model, threshold surfaces are applied to the stop hysterons. The threshold surfaces can be derived directly from measured alternating major loops of the material sample. By saturated polarization, the constructed threshold surfaces are vanishing. In this way, the reversible magnetic flux density is in the same direction of the applied magnetic flux density. Thus, the saturation properties are satisfied.

Analyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows that the clockwise (CW) and counter-CW (CCW) rotational hysteresis losses decrease by saturated flux density. At this state, instead of the domain wall motion, the magnetization rotation is dominant in the material. As a result, the hysteresis losses, which are related to the domain wall motion, are vanished near the saturation. In one stop operator, the plastic element represents the hysteresis part of the model. Integrating threshold surface into the plastic element, the hysteresis part can be modified to zero near the saturation to represent the saturation properties.

The results of this work demonstrate that the presented vector hysteresis stop model allows simulation of anisotropic hysteresis effects, alternating and rotating hysteresis losses. The parameters of the hysteresis model are determined by comparing the measured and modeled minor loops in different alternating magnetization directions. With the identified parameters, the proposed model is excited with rotated excitations in CW and CCW directions. The rotated hysteresis losses, derived from the model, are then compared with those experimentally measured. The modified vector stop model can significantly improve the accuracy of representing hysteresis saturations and losses.

The purpose of this paper is to investigate the effect of anisotropy in terms of a single parameter indicating strengthening or weakening in the tangential direction in composite disc with hyperbolically varying thickness introduced presumably by processing or due to alignment of dispersed reinforcements during flow of the matrix.

Mathematical model to describe steady-state creep behavior in an anisotropic rotating disc made of Al-SiCp composite containing 30 vol% of SiC particles. The creep behavior of the composite has been described by Sherby's law. The creep parameters in the law have been determined using the regression equations developed on the basis of available experimental results in the literature. Stress and strain rate distributions for isotropic disc (a=1) have been compared with those obtained for anisotropic composites with characteristic parameters a=0.7 and 1.3.

The study revealed that the change in the stresses by anisotropy in composite disc is relatively small while anisotropy introduces significant change in the strain rates. It is concluded that the radial strain rate always remained compressive for the isotropic composite as well as the anisotropic disc with a greater than unity (a=1.3). However, it becomes tensile in the middle region of the disc when it is less than unity (a=0.7). If a is reduced from 1.3 to 0.7, the variation of tensile strain rate in the tangential direction remains similar, but the magnitude reduces, i.e. the strength in tangential direction is enhanced.

This study puts forward an analytical framework for the analysis of creep stresses and creep rates in an anisotropic rotating disc with hyperbolically varying thickness.

This study aims to simulate the dendritic growth in Stokes flow by iteratively coupling a domain and boundary type meshless method.

A preconditioned phase-field model for dendritic solidification of a pure supercooled melt is solved by the strong-form space-time adaptive approach based on dynamic quadtree domain decomposition. The domain-type space discretisation relies on monomial augmented polyharmonic splines interpolation. The forward Euler scheme is used for time evolution. The boundary-type meshless method solves the Stokes flow around the dendrite based on the collocation of the moving and fixed flow boundaries with the regularised Stokes flow fundamental solution. Both approaches are iteratively coupled at the moving solid–liquid interface. The solution procedure ensures computationally efficient and accurate calculations. The novel approach is numerically implemented for a 2D case.

The solution procedure reflects the advantages of both meshless methods. Domain one is not sensitive to the dendrite orientation and boundary one reduces the dimensionality of the flow field solution. The procedure results agree well with the reference results obtained by the classical numerical methods. Directions for selecting the appropriate free parameters which yield the highest accuracy and computational efficiency are presented.

A combination of boundary- and domain-type meshless methods is used to simulate dendritic solidification with the influence of fluid flow efficiently.

Non-oriented electrical steel presents anisotropic behaviour. Modelling such anisotropic behaviour has become a necessity for accurate design of electrical machines. The main aim of this study is to model the magnetic anisotropy in the non-oriented electrical steel sheet of grade M400-50A using a phenomenological hysteresis model.

The well-known phenomenological vector Jiles–Atherton hysteresis model is modified to correctly model the typical anisotropic behaviour of the non-oriented electrical steel sheet, which is not described correctly by the original vector Jiles–Atherton model. The modification to the vector model is implemented through the anhysteretic magnetization. Instead of the commonly used classical Langevin function, the authors introduced 2D bi-cubic spline to represent the anhysteretic magnetization for modelling the magnetic anisotropy.

The proposed model is found to yield good agreement with the measurement data. Comparisons are done between the original vector model and the proposed model. Another comparison is also made between the results obtained considering two different modifications to the anhysteretic magnetization.

The paper presents an original method to model the anhysteretic magnetization based on projections of the anhysteretic magnetization in the principal axis, and apply such modification to the vector Jiles–Atherton model to account for the magnetic anisotropy. The replacement of the classical Langevin function with the spline resulted in better fitting. The proposed model could be used in the numerical analysis of magnetic field in an electrical application.

The purpose of this paper is to propose a suitable motion control method for omni‐directional mobile robots (OMRs) based on anisotropy.

A dynamic modeling method for OMRs based on the theory of vehicle dynamics is proposed. By analyzing the driving torque acting on each axis while the robot moves in different directions, the dynamic anisotropy of OMRs is analyzed. The characteristics of dynamic anisotropies and kinematic anisotropies are introduced into the fuzzy sliding mode control (FSMC) system to coordinate the driving torque as a factor of influence.

A combination of the anisotropy and FSMC method produces coordinated motion for the multi‐axis system of OMRs, especially in the initial process of motion. The proposed control system is insensitive to parametric vibrations and external disturbances, and the chattering is apparently decreased. Simulations and experiments have proven that an effective motion tracking can be achieved by using the proposed motion control method.

In order to obtain a clearer analysis of the anisotropy influence during the acceleration process, only the case of translation motion is discussed here. Future work could be done on cases where there are both translation and rotation motions.

The proposed motion control method is applied successfully to achieve effective motion control for OMRs, which is suitable for any kind of OMR.

The novel concept of dynamic anisotropy of OMRs is proposed. By introducing the anisotropy as an influential factor into the FSMC system, a new motion control method suitable for OMRs is proposed.

Microstructure-sensitive design (MSD), for optimal performance of engineering components that are sensitive to material anisotropy, has largely been confined to the realm of theory. The purpose of this paper is to insert the MSD framework into a finite element environment in order to arrive at a practical tool for improved selection and design of materials for critical engineering situations.

This study applies the recently developed Hybrid Bishop-Hill (HBH) model to map the yield surface of anisotropic oxygen free electronic copper. Combining this information with the detailed local stresses determined via finite element analysis (FEA), a “configurational yield stress” is determined for the entire component. By varying the material choice/processing conditions and selecting the directionality of anisotropy, an optimal configuration is found.

The paper provides a new FEA-based framework for MSD for yield-limited situations. The approach identified optimal directionality and processing configurations for three engineering situations that are particularly sensitive to material anisotropy.

The microstructure design space for this study is limited to a selection of eight copper materials produced by a range of processing methods, but is generalizable to many materials that exhibit anisotropic behavior.

The introduction of MSD methodology into a finite element environment is a first step toward a comprehensive designer toolkit for exploiting the anisotropy of general materials (such as metals) in a way that is routinely undertaken in the world of fiber-based composite materials. While the gains are not as sizeable (due to the less-extreme anisotropy), in many applications they may be extremely important.

The purpose of this paper is to help high frequency circuit designers understand how to choose the best permittivity value for a laminate material for accurate modeling.

In this paper, experimental measurements of the performance of simple circuits are compared to various mathematical and software models.

Higher permittivity values were obtained using samples with bonded copper foil compared to samples etched free of foil. These higher values yielded better agreement between measured and modelled performance using current automated design software. High profile foil on thin laminates was found to increase the surface impedance of the conductor and change the propagation constant and apparent permittivity of the laminate by 15 percent or more. It was also demonstrated that, under some circumstances, the anisotropy of the substrate could result in differences in measured and modelled performance.

Only a limited number of circuit laminate materials were closely examined. Future work should include a wider variety of laminates.

The paper details the magnitude of the effects of test method, conductor profile and substrate anisotropy on the values of a material's permittivity best suited for circuit design purposes.