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.

Cross-sectional warping and precision of the first-order shear deformation theory for vibrations of transversely functionally graded curved beams

The warping may become an important factor for the precise transverse vibrations of curved beams.Thus,the first aim of this study is to specify the structural design parameters where the influence of cross-sectional warping becomes great and the first-order shear deformation theory lacks the precision necessary.The outof-plane vibrations of the first-order shear deformation theory are compared with the warping-included vibrations as the curvature and/or thickness increase for symmetric and asymmetric transversely-functionally graded(TFG)curved beams.The second aim is to determine the influence of design parameters on the vibrations.The circular/exact elliptical beams are formed via curved mixed finite elements(MFEs)based on the exact curvature and length.The stress-free conditions are satisfied on three-dimensional(3D)constitutive equations.The variation of functionally graded(FG)material constituents is considered based on the power-law dependence.The cross-sectional warping deformations are defined over a displacement-type FE formulation.The warping-included MFEs(W-MFEs)provide satisfactory 3D structural characteristics with smaller degrees of freedom(DOFs)compared with the brick FEs.The Newmark method is used for the forced vibrations.

Early Clinical and Functional Outcome of Primary Total Knee Replacement with Posterior Cruciate Substituting Prosthesis for Primary Knee Osteoarthritis Using 2011 Knee Society Score

Background: Primary knee Osteoarthritis (OA) is the commonest articular disease in middle age and elderly people. Primary total knee replacement (TKR) is a known world-wide standard and definitive treatment of primary knee OA following failed adequate non-operative management. It is of clinical importance to assess the clinical and functional outcome of TKR to prognosticate the severity of primary knee OA. The new (2011) knee society scoring system (nKSS) is both surgeons and patients’ assessment tool for the treatment outcome of TKR. Study Design: Prospective interventional analytical study. Aim and Objective: The aim of the study was to determine early clinical and functional outcome of primary total knee replacement in patients with primary knee osteoarthritis using nKSS. The objectives were: 1) To determine the pre-operative nKSS and post operative nKSS;2) To determine relationships between pre-operative nKSS and post operative nKSS at 6 weeks, 3, 6, 9 and 12 months;3) To determine the complication rates in patients undergoing primary TKR in the study centre. Methods: A prospective interventional study of 59 patients aged 51 to 70 years who had 67 Total Knee Replacements (TKRs) participated in the study between November 2015 to June 2018 at National Orthopaedics Hospital, Lagos, Nigeria. Patients’ sociodemographic data, pre-operative and post-operative nKSS system were recorded at 6 weeks, 3, 6, 9 and 12 months during follow up. The data were analyzed using Statistical Package for Social Science (SPSS). Results: There were 41 females and 18 males (M:F = 1:2.3). There were total of 67 TKRs with 31 right TKRs, 20 left TKRs and 8 staged bilateral TKRs. The participants’ age ranged from 51 to 70 years with the mean age of 59.5 (±8.5) years. Four patients did not complete the study due to various reasons. The remaining 55 participants completed the study period with progressive improvement of their post-operative nKSS at 6 weeks, 3, 6, 9 and 12 months post-operatively when compared with pre-operative nKSS (P value 0.5). Conclusion: This study revealed improved early clinical and functional outcome of primary total knee replacement in primary knee osteoarthritis using nKSS in all the studied patients. There is no significant negative effect of lower pre-operative nKSS (and its components) on the post-operative nKSS outcome.

Research on Stoichiometry of Early-spring Herbs Functional Group in the Subtropical Artificial Wetland

[Objective]The aim was to carry out stoichiometry on the early-spring herbs functional group in subtropical artificial wetland.[Method]UV-Vis spectrophotometer was used for the determination of nitrate-nitrogen,ammonium nitrogen and phosphorus concentrations.Potassium persulfate absorptiometry was used for the measurement of total N content,while the flame photometer was used to detect the potassium and sodium concentration in plants.All the nutrient determination of plant samples were repeated for four times.[Result]The four nutrient concentrations in almost all samples were in the normal range of natural plant nutrition concentrations;in early-spring herbs functional groups,different species showed diversity on the nutrient concentrations;plant height had no significant effect on the nutrient concentrations in plants;the nutrient concentrations of non-grass group plants were higher than that of grass group plants;the nutrient concentrations of the annual herb were higher than that of perennial herbs.[Conclusion]The study had provided basis for the understanding of the effects of changes in nutritional conditions on species diversity,community structure and succession of the system.

Elastoplastic response of functionally graded cemented carbides due to thermal loading

Finite dement formulations are used to simulate the evolution of the elastoplastic response of functionally graded cemented carbides （FGCC） due to thermal loading. The geometry of specimens is an axisymmetric solid cylinder with a two-dimensional gradient. The elastoplastic constitutive relationship is developed by constraint factors. Numerical results show that compressive stresses occur in the surface zone and tensile stresses in the cobalt rich zone when the temperature drops from the initial stress-free temperature of 800 to 0℃. The maximum value of the surface compressive stress is 254 MPa and the maximum value of the tensile stress is 252 MPa in the cobalt rich zones. When the cobalt concentration difference in the specimens is equal to or greater than 0.3, there is pronounced plastic flow in cobalt rich zone. When the temperature heats up from 0 to 800 ℃, the total plastic strain reaches 0.001 4. Plastic flow has a significant effect on the reduction of thermal stress concentration.

Tensile Shock Physics in Compressible Thermoviscoelastic Solid Medium

This paper addresses tensile shock physics in thermoviscoelastic (TVE) solids without memory. The mathematical model is derived using conservation and balance laws (CBL) of classical continuum mechanics (CCM), incorporating the contravariant second Piola-Kirchhoff stress tensor, the covariant Green’s strain tensor, and its rates up to order n. This mathematical model permits the study of finite deformation and finite strain compressible deformation physics with an ordered rate dissipation mechanism. Constitutive theories are derived using conjugate pairs in entropy inequality and the representation theorem. The resulting mathematical model is both thermodynamically and mathematically consistent and has closure. The solution of the initial value problems (IVPs) describing evolutions is obtained using a variationally consistent space-time coupled finite element method, derived using space-time residual functional in which the local approximations are in hpk higher-order scalar product spaces. This permits accurate description problem physics over the discretization and also permits precise a posteriori computation of the space-time residual functional, an accurate measure of the accuracy of the computed solution. Model problem studies are presented to demonstrate tensile shock formation, propagation, reflection, and interaction. A unique feature of this research is that tensile shocks can only exist in solid matter, as their existence requires a medium to be elastic (presence of strain), which is only possible in a solid medium. In tensile shock physics, a decrease in the density of the medium caused by tensile waves leads to shock formation ahead of the wave. In contrast, in compressive shocks, an increase in density and the corresponding compressive waves result in the formation of compression shocks behind of the wave. Although these are two similar phenomena, they are inherently different in nature. To our knowledge, this work has not been reported in the published literature.

Local pointwise convergence of the 3D finite element

For an elliptic problem with variable coefficients in three dimensions,this article discusses local pointwise convergence of the three-dimensional(3D)finite element.First,the Green's function and the derivative Green's function are introduced.Secondly,some relationship of norms such as L^(2)-norms,W^(1,∞)-norms,and negative-norms in locally smooth subsets of the domainΩis derived.Finally,local pointwise convergence properties of the finite element approximation are obtained.

Finite Element Implementation of the Exponential Drucker-Prager Plasticity Model for Adhesive Joints

This paper deals with the numerical implementation of the exponential Drucker-Parger plasticitymodel in the commercial finite element software,ABAQUS,via user subroutine UMAT for adhesive joint simulations.The influence of hydrostatic pressure on adhesive strength was investigated by a modified Arcan fixture designed particularly to induce a different state of hydrostatic pressure within an adhesive layer.The developed user subroutine UMAT,which utilizes an associated plastic flow during a plastic deformation,can provide a good agreement between the simulations and the experimental data.Better numerical stability at highly positive hydrostatic pressure loads for a very high order of exponential function can also be achieved compared to when a non-associated flow is used.

The Trace Elements are Bounded by Organic Functional Groups in Coal:A Studying Result Based on FTIR Analysis

The relationship between trace elements in coal and organic functional groups of coal, also some of aromatic structure, was investigated by using curve fitting of infrared spectra. Cluster analysis was also performed according to the degree of affinity of organic groups to the trace elements. The results show that there is a possibility that trace elements, especially LREE, were bound to peripheral organic functional groups of middle rank coal macromolecule. The most possible functional group that binds trace element is the hydroxyl, and to the less degree, the asymmetric -CH3 and 〉CH2 stretching, -CH3 stretching, etc. The degree of affinity of trace elements to different functional groups varies. The tendency obeys the natural structural changing law of trace elements-- the periodic law. The deviation of some trace elements from this regular trend is attributed to the deviation of intrinsic ＂confusion degree＂ （conventional molar entropy） of the matter system of coal basin, which is affected by the inner and outer factors during the evolution.

Active vibration control of functionally graded beams with piezoelectric layers based on higher order shear deformation theory

This paper reports on a study of active vibration control of functionally graded beams with upper and lower surface-bonded piezoelectric layers. The model is based on higher-order shear deformation theory and implemented using the finite element method （FEM）. The proprieties of the functionally graded beam （FGB） are graded along the thickness direction. The piezoelectric actuator provides a damping effect on the FGB by means of a velocity feedback control algorithm. A Matlab program has been developed for the FGB model and compared with ANSYS APDL. Using Newmark＇s method numerical solutions are obtained for the dynamic equations of FGB with piezoelectric layers. Numerical results show the effects of the constituent volume fraction and the influence the feedback control gain on the frequency and dynamic response of FGBs.

Buckling analysis of functionally graded plates partially resting on elastic foundation using the differential quadrature element method

We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.

Optimization design and residual thermal stress analysis of PDC functionally graded materials

The distribution of thermal stresses in functionally graded polycrystalline diamond compact (PDC) and in single coating of PDC are analyzed respectively by thermo-mechanical finite element analysis (FEA). It is shown that they each have a remarkable stress concentration at the edge of the interfaces. The diamond coatings usually suffer premature failure because of spallation, distortion or defects such as cracks near the interface due to these excessive residual stresses. Results showed that the axial tensile stress in FGM coating is reduced from 840 MPa to 229 MPa compared with single coating, and that the shear stress is reduced from 671 MPa to 471 MPa. Therefore, the single coating is more prone to spallation and cracking than the FGM coating. The effects of the volume compositional distribution factor (n) and the number of the graded layers (L) on the thermal stresses in FGM coating are also discussed respectively. Modelling results showed that the optimum value of the compositional distribution factor is 1.2, and that the best number of the graded layers is 6.

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.

Finite Element Analysis of Shrinkage in the Interface of Functionally Graded Concrete Segment Used in Shield Tunneling

In functionally graded materials (FGM), the problem of interface stability caused by the volume deformation is commonly regarded as the key factor for its performance. Based on test results, in terms of finite element method (FEM) this paper analyzed problems in the shrinkage of functionally graded material interface of shield concrete segment, which was designed and produced by the principle of functionally graded materials. In the analysis model, the total shrinkage of concrete was converted into the thermal shrinkage by means of the method of 'Equivalent Temperature Difference'. Consequently, the shrinkage stress of interface layer was calculated and compared with the bond strength of interface layer. The results indicated that the volume deformation of two-phase materials of functionally graded concrete (FGC) segment, which were the concrete cover and the concrete structure layer, showed better compatibility and the tension stress of interface layer, which was resulted from the shrinkage of concrete and calculated by ANSYS, was less than the bond strength of interface layer. Therefore, the interface stability of functionally graded concrete segment was good and the sliding deformation of interface layer would not generate.

CONVERGENCE RATES IN THE LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS

The author discusses necessary and sufficient conditions of the complete con- vergence for sums of B-valued independent but not necessarily identically distributed r.v.'s in Banach space of type p, and obtains characterization of Banach space of type p in terms of the complete convergence. A series of classical results on iid real valued r.v.'s are ex- tended. As application authors give the analogous results for randomly indexed sums.

ESTIMATES ON THE FINITE ELEMENT APPROXIMATIONS OF A QUADRATIC FUNCTIONAL

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

ON THE SELECTION OF SHAPE FUNCTION SPACES OF TRIANGULAR PLATE ELEMENTS

Using the method of undetermined coefficients, we construct a set of shape function spaces of nine-node triangular plate elements converging for any meshes, which generalize Spect's element and Veubeke's element.

Problems and Countermeasures of Taihu Port Farm in Jingzhou City after Function Reform of Running the Society

Deepening function reform of running the society of state-owned farm is an important strategic plan made by the Party Central Committee and the State Council,and is also ' hard bone' bitten by fully implementing the strategy of rural revitalization and promoting the modernization of agriculture and countryside. In this paper,the problems of Taihu Port Farm in Jingzhou City after function reform of running the society are systematically and comprehensively analyzed via field research,and corresponding countermeasures are proposed. The research could provide beneficial reference and experience reference for deepening function reform of running the society of current state-owned farm.

Design and Synthesis of Ti-ZrO_2 Functionally Graded Materials

Functionally graded materials (FGMs) based on titanium-zirconia system have been prepared by powder metallurgical method. The graded interlayer number and the compositional distribution have been designed by elastic finite element method. The interfacial microstructure between layers, the combining state of phases between Ti and ZrO2 have been investigated by means of XRD (X-ray diffraction), SEM (scanning electron microscope), EDS (energy dispersive spectrometer) and so on. The co-existing region of Ti and ZrO2 has been determined by thermodynamic calculation to control the sintering atmosphere. The experimental results show that the joint between Ti and ZrO2 phases is physical in this composite and ZrO2 mainly exists as tetragonal phase. The microstructure of Ti-ZrO2 system FGM exhibits a transition from a zirconia particle dispersion in a titanium matrix to an inverse dispersion of titanium in zirconia. The gradient structure of titanium and zirconia can relieve thermal stress.

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.