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.

Landscape Design Elements in Rehabilitation Environment Founded on Evidence-based Design

The concept and development history of rehabilitation environment were summarized in this study,principles and techniques of applying evidence-based design in the design of rehabilitation environment were analyzed,classification and functions of landscape elements in rehabilitation environment were particularly discussed.

Base force element method of complementary energy principle for large rotation problems

Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.

EFFECTS OF TRACE ELEMENTS ON THE OXIDATION OF LOW SEGREGATION Ni－Cr－Al BASED SUPERALLOYS

The oxidation behaviors of two kinds of low segregation Ht-Cr-Al based superalloys have been studied between 1000-1100℃, and compared with that of general Mt-Cr-Al based superalloys. The results indicated that the simultaneous additions of 0.1 wt% S and 0. 1 wt% Zr to low segregation alloys increase the oxidation rate of Al2O3-forming alloy and improve the scale adherence. The addition of 0.1 wt% Zr can ,minimize the negative effects of S on the adherence of Al2O3 scale. Low amounts of S(≤50 ppm wt) have no obviously negative effects on the adherence of Cr2O3 scale formed on one of the low segregation superalloys.

Application of control volume based finite element method for solving the black-oil fluid equations

This is the second paper of a series where we introduce a control volume based finite element method （CVFEM） to simulate multiphase flow in porous media. This is a fully conservative method able to deal with unstructured grids which can be used for representing any complexity of reservoir geometry and its geological objects in an accurate and efficient manner. In order to deal with the inherent heterogeneity of the reservoirs, all operations related to discretization are performed at the element level in a manner similar to classical finite element method （FEM）. Moreover, the proposed method can effectively reduce the so-called grid orientation effects. In the first paper of this series, we presented this method and its application for incompressible and immiscible two-phase flow simulation in homogeneous and heterogeneous porous media. In this paper, we evaluate the capability of the method in the solution of highly nonlinear and coupled partial differential equations by simulating hydrocarbon reservoirs using the black-oil model. Furthermore, the effect of grid orientation is investigated by simulating a benchmark waterflooding problem. The numerical results show that the formulation presented here is efficient and accurate for solving the bubble point and three-phase coning problems.

INFLUENCE OF ALLOYING ELEMENTS（Nb，Mo，V） ON MICROSTRUCTURE OF Ti_3Al BASE ALLOYS

The microstructures of Ti-14Al-21Nb and Ti-14Al-20Nb-2Mo-3.2V(wt%) alloys have been investikated by transmission electron microscopy(TEM).The phase constitution and the orientation relationship between α2and βwere identified by means of the selected area diffraction and the micro-diffraction techniques.Results show that,compared to Ti-14Al-21Nb,the alloying elements Mo and V can greatly increase the fraction of β phase and improve significantly the microstructures of Ti-14Al-20Nb-2Mo-3.2V.The ordered B2 structure is also evident in the residual βgrains of the latter alloy.

Finite element analysis of temperature field during multi-layer multi-pass weld-based rapid prototyping

During weld-bused rapid prototyping, the component experiences complex thermal process. In this paper, the temperature field evolution, thermal cycle characteristics, and temperature gradients of multi-layer multi-puss weld-based rapid prototyping are investigated using three-dimensional finite element models presented. The single-puss weld-bused rapid prototyping experiment is carried out. Thermal cycles calculated agree with experimental measurements. Furthermore, simulated results indicate that there exist the pre-heating effect of the fore layer and the post-heating effect of the rear layer in the multi-layer multi-pass weld-based rapid prototyping. In the first layer, the heat accumulates obviously. After the first layer, the dimension increase of the high temperature region behind the molten pool is not obvious. The heat diffusion condition in the first layer is the best, the heat diffusion condition in the second layer is the worst, and the heat diffusion conditions in the higher layers improve gradually.

Effects of Additional Elements on Microstructure and Precipitation Behaviour in Rapidly Solidified Al-Ti Base Alloys

Rapidly solidified Al-Ti base alloys were prepared by melt spinning at the cooling rate about 107 K/s. The melt-spun ribbons were used to observe the dricrostructures after heat treatment.In the supersaturated Al-Tl-Si alloy, age hardening occurred after 1 h anneal in the temperature range of 4000~500℃, which seems to be attributed to the precipitation of metastable Ll2- (Al,Si)3Ti phase. However. the microhardness was relatively low because of the low v/o and the insufflcient stability of precipitates. Thus. Cr was added to Al-Ti-Si alloys in order to stabilize the microstructures and to increase the v/o of precipitate5. As a result. the alIoys containing Cr were evaluated to possess the improved properties at the service temperature.

Hybrid Post-Processing Procedure for Displacement-Based Plane Elements

In the analysis of high-rise building, traditional displacement-based plane elements are often used to get the in-plane internal forces of the shear walls by stress integration. Limited by the singular problem produced by wall holes and the loss of precision induced by using differential method to derive strains, the displacement-based elements cannot always present accuracy enough for design. In this paper, the hybrid post-processing procedure based on the Hellinger-Reissner variational principle is used for improving the stress precision of two quadrilateral plane elements. In order to find the best stress field, three different forms are assumed for the displacement-based plane elements and with drilling DOF. Numerical results show that by using the proposed method, the accuracy of stress solutions of these two displacement-based plane elements can be improved.

Enriched goal-oriented error estimation for fracture problems solved by continuum-based shell extended finite element method

An enriched goal-oriented error estimation method with extended degrees of freedom is developed to estimate the error in the continuum-based shell extended finite element method. It leads to high quality local error bounds in three-dimensional fracture mechanics simulation which involves enrichments to solve the singularity in crack tip. This enriched goal-oriented error estimation gives a chance to evaluate this continuum- based shell extended finite element method simulation. With comparisons of reliability to the stress intensity factor calculation in stretching and bending, the accuracy of the continuum-based shell extended finite element method simulation is evaluated, and the reason of error is discussed.

A RECTANGULAR ELEMENT OF THIN PLATES BASED UPON THE GENERALIZED VARIATIONAL PRINCIPLES

Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.

Mechanism of interaction relation between the rare-earth element Ce and impurity elements Pb and Bi in Ag-based filler metal

The mechanism of interaction relation between the rare-earth element Ce and elements Pb and Bi in Ag-based filler metal has been studied. The results show that the compounds CePb and CeBi with high melting point can be easily produced between these three elements in the filler metal, which greatly limited the formation of the isolated phase Pb or Bi and also eliminated the bad effect of impurity elements Pb and Bi on the spreading property of Ag-based filler metal. The metallurgical and quantum-mechanical bond formation analysis show that a strong chemical affinity was existed between the rare-earth element Ce and impurity elements Pb and Bi, which was proved by the XRD analysis results.

EFFECT OF RARE EARTH ELEMENT Er ON STRENGTHENING OF INTERFACE OF Ti（C，N） BASED CERMETS

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Finite Element Method Computations of the Acoustics of the Human Head Based on the Projection Based Interpolation Data

In this paper we present the Projection Based Interpolation (PBI) technique for construction of continuous approximation of MRI scan data of the human head. We utilize the result of the PBI algorithm to perform three dimensional (3D) Finite Element Method (FEM) simulations of the acoustics of the human head. The computational problem is a multi-physics problem modeled as acoustics coupled with linear elasticity. The computational grid contains tetrahedral finite elements with the number of equations and polynomial orders of approximation varying locally on finite element edges, faces, and interiors. We utilize our own out-of-core parallel direct solver for the solution of this multi-physics problem. The solver minimizes the memory usage by dumping out all local systems from all nodes of the entire elimination tree during the elimination phase.

Research Progress in Production Process of Molybdenum Disilicide Based Heating Elements in China

The molybdenum disilicide （MoSi2 ） based heating element is more and more important in modern industries relating to thermal treatment, melting and sintering due to its high working temperature. In China, the consumption of the MoSi2 heating element continues to increase with development and upgrading of industries. However, the MoSi2 heating element .from local manufacturers still has poor quality and thus results in waste of precious molybdenum resource. In this review, the recent research results of production process of MoSi2 heating elements were briefly summarized. The purity and particle size distribution of starting MoSi2 powder as well as the mixing and sintering processes were identified as major impact fators on the performance of MoSi2 heating elements. This review points out the improving direction for local MoSi2 heating elements.

THE ANALYTICAL SOLUTIONS BASED ON THE CONCEPT OF FINITE ELEMENT METHODS

On the basis of the concept of finite element methods, the rigorous analytical solutions of structural response in terms of the design variables are researched in this paper. The spatial trusses are taken as an example for the solution of the analytical expressions of the explicit displacements which are proved mathematically; then some conclusions are reached that are useful to structural sensitivity analysis and optimization. In the third part of the paper, a generalized geometric programming method is sugguested for the optimal model with the explicit displacement. Finally, the analytical solutions of the displacements of three trusses are given as examples.

Interaction Rule between Rare Earths and LowMelting Point Elements in Fe-,Cu-,AI-,Ni-Base Liquid Solutions

Interaction rule between representative RE and Sn, Sb, Pb, Cu, S, P low melting point elements respectively in Fe , Cu , Al , Ni base liquid solutions including totally 34 ternary and quarternary systems was investigated. For each system some thermodynamic properties were obtained, such as the standard free energies of equilibrium reactions, activity interaction coefficients etc ..

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method, The solution accuracy is further improved by implementing an adaptive meshing technique to generaie finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems tire： （a） a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and （b） a transient heat conduction analysis in a long plate subjected to moving heat source.

Research on Knowledge-based Connecting Elements Modeling

Steps of manipulation is required to complete the m od eling of the connection elements such as bolt, pin and the like in commerce CAD system. It leads to low efficiency, difficulty to assure the relative position, impossibility to express rules and knowledge. Based on the inner character analy sis of interpart, detail modification and assembly relation of mechanical connec ting element, the idea, which extends the feature modeling of part to the interp art feature modeling for assembly purpose, is presented, and virtual part based connecting element modeling is proposed. Virtual part is a complement set of lo cal modification of part to be connected. In assembly modeling, base part is mod ified by Boolean operation between base part and virtual part. The modeling and assembly is finished just in one operation, at the same time the rules and knowl edge of the connection elements are encapsulated through virtual part. According to this mechanism, a knowledge-based connecting elements rapid design module i s developed on commerce software package UG with satisfying results.

Adaptive nodeless variable finite elements with flux-based formulation for thermal-structural analysis

A nodeless variable element method with the fluxbased formulation is developed to analyze two-dimensional thermal-structural problems. The nodeless variable formula- tion provides accurate temperature distributions to yield more accurate thermal stress solutions. The flux-based formulation is used to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element meshes that can adapt and move along with the transient solution behavior. A version of a nearly optimal element size determination is proposed to provide high convergence rate of the predicted solutions. The combined procedure is evaluated by solving several thermal, structural, and thermal stress problems.