HEAT TRANSFER CHARACTERISTICS OF CONDUCTIVE MATERIAL UNDER INNER NON-UNIFORM ELECTROMAGNETIC FIELDS

Electronic transport properties can be influenced by the applied electromagnetic fields in conductive materials. The change of the electron distribution function evoked by outfields obeys the Boltzmann equation. In this paper, a general law of heat conduction considering the non-uniform electromagnetic effect is developed from the Boltzmann equation. An analysis of the equation leads to the result that the electric field gradient and the magnetic gradient in the conductive material are responsible for the influences of electromagnetic fields on the heat conduction process. A physical model is established and finite element numerical simulation reveals that heat conduction can be increased or delayed by the different directions of the electric field gradient, and the existence of the magnetic gradient always hinders heat conduction.     

Tunability of Band Gaps in Two-Dimensional Phononic Crystals with Magnetorheological and Electrorheological Composites

The elastic wave propagation properties of phononic crystals(PnCs)composed of an elastic matrix embedded in magnetorheological and electrorheological elastomers are studied in this paper.The tunable band gaps and transmission spectra of these materials are calculated using the finite element method and supercell technology.The variations in the band gap characteristics with changes in the electric/magnetic fields are given.The numerical results show that the electric and magnetic fields can be used in combination to adjust the band gaps effectively.The start and stop frequencies of the band gap are obviously affected by the electric field,and the band gap width is regulated more significantly by the magnetic field.The widest and highest band gap can be obtained by combined application of the electric and magnetic fields.In addition,the band gaps can be moved to the low-frequency region by drilling holes in the PnC,which can also open or close new band gaps.These results indicate the possibility of multi-physical field regulation and design optimization of the elastic wave properties of intelligent PnCs.     

Construction of <Emphasis Type="Italic">n</Emphasis>-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.     

FUNDAMENTAL SOLUTION BASED GRADED ELEMENT MODEL FOR STEADY-STATE HEAT TRANSFER IN FGM

A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials (FGMs). The model can handle a spatially varying material property field of FGMs. In the proposed approach, a new variational functional is first constructed for generating corresponding finite element model. Then, a graded element is formulated based on two sets of independent temperature fields. One is known as intra-element temperature field defined within the element domain; the other is the so-called frame field defined on the element boundary only. The intra-element temperature field is constructed using the linear combination of fundamental solutions, while the independent frame field is separately used as the boundary interpolation functions of the element to ensure the field continuity over the interelement boundary. Due to the properties of fundamental solutions, the domain integrals appearing in the variational functional can be converted into boundary integrals which can significantly simplify the calculation of generalized element stiffness matrix. The proposed model can simulate the graded material properties naturally due to the use of the graded element in the finite element (FE) model. Moreover, it inherits all the advantages of the hybrid Trefftz finite element method (HT-FEM) over the conventional FEM and boundary element method (BEM). Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show a good numerical accuracy.     

Effect of Stress-Dependent Thermal Conductivity on Thermo-Mechanical Coupling Behavior in GaN-Based Nanofilm Under Pulse Heat Source

The thermal properties of a nanostructured semiconductor are affected by multi-physical fields,such as stress and electromagnetic fields,causing changes in temperature and strain distributions.In this work,the influence of stress-dependent thermal conductivity on the heat transfer behavior of a GaN-based nanofilm is investigated.The finite element method is adopted to simulate the temperature distribution in a prestressed nanofilm under heat pulses.Numerical results demonstrate the effect of stress field on the thermal conductivity of GaN-based nanofilm,namely,the prestress and the thermal stress lead to a change in the heat transfer behavior in the nanofilm.Under the same heat source,the peak temperature of the film with stress-dependent thermal conductivity is significantly lower than that of the film with a constant thermal conductivity and the maximum temperature difference can reach 8.2 K.These results could be useful for designing GaN-based semiconductor devices with higher reliability under multi-physical fields.     

Mixed time discontinuous space-time finite element method for convection diffusion equations

A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.     

DEFORMATION RIGIDITY OF ASSUMED STRESS MODES IN HYBRID ELEMENTS

The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.     

THE PERTURBATION FINITE ELEMENT METHOD FOR SOLVING THE PLANE PROBLEM IN CONSIDERATION OF LINEAR CREEP

In this paper, amethod (PFMC) for solving plane problem of linear creep is presented by using perturbation finite element. It can be used in plane problem in consideration of creep, such as reinforced concrete beam, prestressed concrete beam, reinforced concrete cylinder and reinforced concrete tunnel in elastic or visco-elastic medium, as well as underground building and so on. In the presented method, the assumption made in the general increment method that variables remain constant in a divtded time interval is not taken. The accuracy is improved and the length of time step becomes larger. The computer storage can be reduced and the calculating efficiency can be increased. Perturbation finite element formulae for four-node quadrilateral isoparametric element including reinforcement are established and five numerical examples are given. As contrasted with the analytical solution, the accuracy is satisfactory.     

STUDY ON PARAMETERS FOR TOPOLOGICAL VARIABLES FIELD INTERPOLATED BY MOVING LEAST SQUARE APPROXIMATION

This paper presents a new approach to the structural topology optimization of continuum structures. Material-point independent variables are presented to illustrate the existence condition,or inexistence of the material points and their vicinity instead of elements or nodes in popular topology optimization methods. Topological variables field is constructed by moving least square approximation which is used as a shape function in the meshless method. Combined with finite element analyses,not only checkerboard patterns and mesh-dependence phenomena are overcome by this continuous and smooth topological variables field,but also the locations and numbers of topological variables can be arbitrary. Parameters including the number of quadrature points,scaling parameter,weight function and so on upon optimum topological configurations are discussed. Two classic topology optimization problems are solved successfully by the proposed method. The method is found robust and no numerical instabilities are found with proper parameters.     

A hybrid-stress element based on Hamilton principle

A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.     

A coupled continuous and discontinuous finite element method for the incompressible flows

In this paper, we develop a coupled continuous Galerkin and discontinuous Galerkin finite element method based on a split scheme to solve the incompressible Navier–Stokes equations. In order to use the equal order interpolation functions for velocity and pressure, we decouple the original Navier–Stokes equations and obtain three distinct equations through the split method, which are nonlinear hyperbolic, elliptic, and Helmholtz equations, respectively. The hybrid method combines the merits of discontinuous Galerkin (DG) and finite element method (FEM). Therefore, DG is concerned to accomplish the spatial discretization of the nonlinear hyperbolic equation to avoid using the stabilization approaches that appeared in FEM. Moreover, FEM is utilized to deal with the Poisson and Helmholtz equations to reduce the computational cost compared with DG. As for the temporal discretization, a second‐order stiffly stable approach is employed. Several typical benchmarks, namely, the Poiseuille flow, the backward‐facing step flow, and the flow around the cylinder with a wide range of Reynolds numbers, are considered to demonstrate and validate the feasibility, accuracy, and efficiency of this coupled method. Copyright © 2016 John Wiley & Sons, Ltd.     

Twinned Finite Plane Deformations Generated by Prescribed Rotation Fields

In previous work, it has been shown that any suitably smooth plane proper-orthogonal tensor field can serve as a rotation tensor for generating a plane finite deformation. In this paper, this previous analysis is used to study plane finite twin deformations. We show that given a defined smooth curve which separates two arbitrarily prescribed rotation fields, a twin deformation field can be generated in a neighborhood surrounding such curve. Examples are presented for cases where the Jacobian of the finite deformation field is discontinuous or continuous across the defined curve. Twinning in an elastic region is also analyzed in some detail.     

H 1 space-time discontinuous finite element method for convection-diffusion equations

An H~1 space-time discontinuous Galerkin (STDG) scheme for convectiondiffusion equations in one spatial dimension is constructed and analyzed. This method is formulated by combining the H~1 Galerkin method and the space-time discontinuous finite element method that is discontinuous in time and continuous in space. The existence and the uniqueness of the approximate solution are proved. The convergence of the scheme is analyzed by using the techniques in the finite difference and finite element methods. An optimal a-priori error estimate in the L~∞ (H~1 ) norm is derived. The numerical exper- iments are presented to verify the theoretical results.     

Hybrid Equilibrium Finite Elements for Wave Diffraction Problems

Hybrid equilibrium finite elements based on the direct approximation of the domain stress and boundary displacement fields are presented. The structure is divided into a far field, which is considered as an infinite super element, and a near field, which is in turn discretized into finite elements. The displacements in the domains of typical finite elements are obtained from the assumed domain stress field by using the dynamic equilibrium equations. The Helmholtz equation is satisfied in the domain of the infinite super element, and the domain stress fields are associated with elastic and compatible displacements. The resulting governing system is symmetric, sparse, and, if well done, positive. Numerical applications are presented to illustrate the performance of the formulation     

A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes

Recently, a discontinuous Galerkin method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution of the Helmholtz equation in the mid-frequency regime. This method was fully developed however only for regular meshes, and demonstrated only for interior Helmholtz problems. In this paper, we extend it to irregular meshes and exterior Helmholtz problems in order to expand its scope to practical acoustic scattering problems. We report preliminary results for two-dimensional short wave problems that highlight the superior performance of this discontinuous Galerkin method over the standard finite element method.     

A sensitivity analysis on the parameter of the GLS method for a second‐gradient theory of incompressible flow

Using a non‐conforming C⁰‐interior penalty method and the Galerkin least‐square approach, we develop a continuous–discontinuous Galerkin finite element method for discretizing fourth‐order incompressible flow problems. The formulation is weakly coercive for spaces that fail to satisfy the inf‐sup condition and consider discontinuous basis functions for the pressure field. We consider the results of a stability analysis through a lemma which indicates that there exists an optimal or quasi‐optimal least‐square stability parameter that depends on the polynomial degree used to interpolate the velocity and pressure fields, and on the geometry of the finite element in the mesh. We provide several numerical experiments illustrating such dependence, as well as the robustness of the method to deal with arbitrary basis functions for velocity and pressure, and the ability to stabilize large pressure gradients. We believe the results provided in this paper contribute for establishing a paradigm for future studies of the parameter of the Galerkin least square method for second‐gradient theory of incompressible flow problems. Copyright © 2015 John Wiley & Sons, Ltd.     

水下声波传播过程的时域间断Galerkin有限元方法

本文构建了声压波动方程的改进时域间断Galerkin有限元方法.传统时域连续有限元方法在计算高梯度、强间断特征水中声波传播问题时往往会出现虚假数值振荡现象,这些数值振荡会影响正常波动的计算精度.为了解决这一问题,本文通过引入人工阻尼的方式构建了改进的时域间断Galerkin有限元方法,并针对具有高梯度、强间断特征的多障碍物复杂边界和层合液体介质声传播问题进行了计算.计算结果表明,与传统时域连续方法如N ew mark方法计算结果对比,所发展方法能较好地消除高梯度和强间断声压力波传播过程中虚假的数值振荡,具有较高的计算精度.问题的求解为进一步流固声耦合问题的研究奠定了基础.     

Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation

The extended finite element method (X-FEM) is a numerical method for modeling strong (displacement) as well as weak (strain) discontinuities within a standard finite element framework. In the X-FEM, special functions are added to the finite element approximation using the framework of partition of unity. For crack modeling in isotropic linear elasticity, a discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are used to account for the crack. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence quasi-static crack propagation simulations can be carried out without remeshing. In this paper, we discuss some of the key issues in the X-FEM and describe its implementation within a general-purpose finite element code. The finite element program Dynaflow™ is considered in this study and the implementation for modeling 2-d cracks in isotropic and bimaterial media is described. In particular, the array-allocation for enriched degrees of freedom, use of geometric-based queries for carrying out nodal enrichment and mesh partitioning, and the assembly procedure for the discrete equations are presented. We place particular emphasis on the design of a computer code to enable the modeling of discontinuous phenomena within a finite element framework.     

数值流形方法及其在岩石力学中的应用

数值流形方法是目前岩石力学分析的主要方法之一.该方法起源于不连续变形分析,主要用于统一求解连续和非连续问题,其核心技术是在分析时采用了双重网格:数学网格提供的节点形成求解域的有限覆盖和权函数;而物理网格为求解的积分域.数学网格被用来建立数学覆盖,数学覆盖与物理网格的交集定义为物理覆盖,由物理覆盖的交集形成流形单元.流形方法的优点在于它使用了独立的数学和物理网格,具有和有限元明显不同的定义形式,且数学网格对于同一问题不同的求解精度的需求可以很方便地细化.由于该方法考虑了块体运动学,可以模拟节理岩体裂隙的开裂和闭合过程,因而在岩石力学中得到了广泛应用,近年来许多学者对该方法进行了研究.本文简要叙述了节理岩体的数值方法从连续到非连续的发展过程,详细地介绍了数值流形方法的组成和数值流形方法在岩石力学及其相关领域的研究和发展概况,最后就作者所关心的一些问题,如三维问题的数值流形方法、数值流形方法在物理非线性问题和裂纹扩展问题中的应用、相关的耦合方法等进行了探讨.     

discontinuous galerkin method for discontinuous temperature field problems

针对不连续温度场问题建立了一种间断Galerkin有限元方法，该方法的主要特点是允 许插值函数在单元边界上存在跳变. 在建立有限元方程时，通过在单元边界上引入数值通量 项和稳定性项来处理间断效应，并且数值通量可以直接由接触热阻的定义式导出. 数值算例 表明该方法可以很方便且准确地捕捉到结构内部由于接触热阻而引起的温度跳变，同时在局 部高梯度温度场的模拟方面也比常规连续Galerkin有限元方法效率明显要高. 该方法也为研 究由接触热阻引起的温度场与应力场之间的耦合问题提供了一种新的数值模拟手段.