A two-scale method for identifying mechanical parameters of composite materials with periodic configuration

In this paper, a two-scale method （TSM） is presented for identifying the mechanics parameters such as stiffness and strength of composite materials with small periodic configuration. Firstly, a formulation is briefly given for two-scale analysis （TSA） of the composite materials. And then a two-scale computation formulation of strains and stresses is developed by displacement solution with orthotropic material coefficients for three kinds of such composites structures, i.e., the tension column with a square cross section, the bending cantilever with a rectangular cross section and the torsion column with a circle cross section. The strength formulas for the three kinds of structures are derived and the TSM procedure is discussed. Finally the numerical results of stiffness and strength are presented and compared with experimental data. It shows that the TSM method in this paper is feasible and valid for predicting both the stiffness and the strength of the composite materials with periodic configuration.

Computational multiscale methods for granular materials

The fine-scale heterogeneity of granular material is characterized by its polydisperse microstructure with randomness and no periodicity. To predict the mechanical response of the material as the microstructure evolves, it is demonstrated to develop computational multiscale methods using discrete particle assembly-Cosserat continuum modeling in micro- and macro- scales,respectively. The computational homogenization method and the bridge scale method along the concurrent scale linking approach are briefly introduced. Based on the weak form of the Hu-Washizu variational principle, the mixed finite element procedure of gradient Cosserat continuum in the frame of the second-order homogenization scheme is developed. The meso-mechanically informed anisotropic damage of effective Cosserat continuum is characterized and identified and the microscopic mechanisms of macroscopic damage phenomenon are revealed. c 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi： 10.1063/2.1301101]

The Multi-scale Method for Solving Nonlinear Time Space Fractional Partial Differential Equations

In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.

Dynamic thermo-mechanical coupled response of random particulate composites:A statistical two-scale method

This paper focuses on the dynamic thermo-mechanical coupled response of random particulate composite materials. Both the inertia term and coupling term are considered in the dynamic coupled problem. The formulation of the problem by a statistical second-order two-scale （SSOTS） analysis method and the algorithm procedure based on the finite-element difference method are presented. Numerical results of coupled cases are compared with those of uncoupled cases. It shows that the coupling effects on temperature, thermal flux, displacement, and stresses are very distinct, and the micro- characteristics of particles affect the coupling effect of the random composites. Furthermore, the coupling effect causes a lag in the variations of temperature, thermal flux, displacement, and stresses.

Two-scale finite element method for piezoelectric problem in periodic structure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.

MULTI-SCALE METHODS FOR INVERSE MODELING IN 1-D MOS CAPACITOR

In this paper, we investigate multi-scale methods for the inverse modeling in 1-D Metal-Oxide-Silicon (MOS) capacitor. First, the mathematical model of the device is given and the numerical simulation for the forward problem of the model is implemented using finite element method with adaptive moving mesh. Then numerical analysis of these parameters in the model for the inverse problem is presented. Some matrix analysis tools are applied to explore the parameters' sensitivities. And third, the parameters are extracted using Levenberg-Marquardt optimization method. The essential difficulty arises from the effect of multi-scale physical difference of the parameters. We explore the relationship between the parameters' sensitivities and the sequence for optimization, which can seriously affect the final inverse modeling results. An optimal sequence can efficiently overcome the multi-scale problem of these parameters. Numerical experiments show the efficiency of the proposed methods.

STRAIGHTFORWARD MULTI-SCALE BOUNDARY ELEMENT METHOD FOR GLOBAL/LOCAL MECHANICAL ANALYSIS OF ELASTIC HETEROGENEOUS MATERIAL

A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.

A scaled boundary node method applied to two-dimensional crack problems

A boundary-type meshless method called the scaled boundary node method （SBNM） is developed to directly evaluate mixed mode stress intensity factors （SIFs） without extra post-processing. The SBNM combines the scaled boundary equations with the moving Kriging （MK） interpolation to retain the dimensionality advantage of the former and the meshless attribute of the latter. As a result, the SBNM requires only a set of scattered nodes on the boundary, and the displacement field is approximated by using the MK interpolation technique, which possesses the 5 function property. This makes the developed method efficient and straightforward in imposing the essential boundary conditions, and no special treatment techniques are required. Besides, the SBNM works by weakening the governing differential equations in the circumferential direction and then solving the weakened equations analytically in the radial direction. Therefore, the SBNM permits an accurate representation of the singularities in the radial direction when the scaling center is located at the crack tip. Numerical examples using the SBNM for computing the SIFs are presented. Good agreements with available results in the literature are obtained.

Dynamic interaction numerical models in the time domain based on the high performance scaled boundary finite element method

Consideration of structure-foundation-soil dynamic interaction is a basic requirement in the evaluation of the seismic safety of nuclear power facilities. An efficient and accurate dynamic interaction numerical model in the time domain has become an important topic of current research. In this study, the scaled boundary finite element method （SBFEM） is improved for use as an effective numerical approach with good application prospects. This method has several advantages, including dimensionality reduction, accuracy of the radial analytical solution, and unlike other boundary element methods, it does not require a fundamental solution. This study focuses on establishing a high performance scaled boundary finite element interaction analysis model in the time domain based on the acceleration unit-impulse response matrix, in which several new solution techniques, such as a dimensionless method to solve the interaction force, are applied to improve the numerical stability of the actual soil parameters and reduce the amount of calculation. Finally, the feasibility of the time domain methods are illustrated by the response of the nuclear power structure and the accuracy of the algorithms are dynamically verified by comparison with the refinement of a large-scale viscoelastic soil model.

Determination of the natural frequencies of axially moving beams by the method of multiple scales

The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

Dynamic Crack Propagation Analysis Using Scaled Boundary Finite Element Method

The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.

A LIMITED MEMORY QUASI-NEWTON METHOD FOR LARGE SCALE PROBLEM

We study how to use the SR1 update to realize minimization methods for problems where the storage is critical. We give an update formula which generates matrices using information from the last m iterations. The numerical tests show that the method is efficent.

Research on Analytical Method of Fatigue Characteristics of Soft Yoke Mooring System Based on Full-Scale Measurement

By focusing on the vulnerability of the structure of marine equipments, together with considering the randomness of meta-ocean load in statistics, a kind of analytical method of fatigue characteristics of marine structure based on full- scale and actual measurement of prototype is proposed. On the basis of short-term field measurement results of structural response, research is carried out on the fatigue analysis of hinge joints at the upper part of the Soft Yoke single point Mooring System （SYMS） by simultaneously monitoring the environmental load and considering the design criteria of offshore structure. Through analysis of finite element modeling, the time-histories of typical stress response are obtained, and then the assessment of fatigue damage at key hinge joints is conducted. The simulation results indicate that the proposed method can accurately analyze the fatigue damage of offshore engineering structure caused by the effect of wave load. The present analytical method of fatigue characteristics can be extended on other offshore engineering structures subjected to meta-ocean load.

Free vibration of vibrating device coupling two pendulums using multiple time scales method

A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis. Based on energy analysis, dynamic equations with cubic nonlinearities were established using Lagrange's equation. In order to obtain approximate solution, multiple time scales method, one of perturbation technique, was applied. Cases of non-resonant and 1:1:2:2 internal resonant were discussed. In the non-resonant case, the validity of multiple time scales method is confirmed, comparing numerical results derived from fourth order Runge-Kutta method with analytical results derived from first order approximate expression. In the 1:1:2:2 internal resonant case, modal amplitudes of Aa1 and Ab2 increase, respectively, from 0.38 to 0.63 and from 0.19 to 0.32, while the corresponding frequencies have an increase of almost 1.6 times with changes of initial conditions, indicating the existence of typical nonlinear phenomenon. In addition, the chaotic motion is found under this condition.

Scaled radar cross section measurement method for lossy targets via dynamically matching reflection coefficients in THz band

In the terahertz band,the dispersive characteristic of dielectric material is one of the major problems in the scaled radar cross section(RCS)measurement,which is inconsistent with the electrodynamics similitude deducted according to the Maxwell’s equations.Based on the high-frequency estimation method of physical optics(PO),a scaled RCS measurement method for lossy objects is proposed through dynamically matching the reflection coefficients according to the distribution of the object facets.Simulations of the model of SLICY are conducted,and the inversed RCS of the lossy prototype is obtained using the proposed method.Comparing the inversed RCS with the calculated results,the validity of the proposed method is demonstrated.The proposed method provides an effective solution to the scaled RCS measurement for lossy objects in the THz band.

High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

Nonlinear vibrations of nano-beams accounting for nonlocal effect using a multiple scale method

The nonlinear free transverse vibrations of a nano-beam on simple supports are investigated based on nonlocal elasticity theory. The governing equation is proposed by considering geometric nonlinearity due to finite stretching of the beam. The method of multiple scales is applied to the governing equa- tion to evaluate the nonlinear natural frequencies. Numerical examples are presented to demonstrate the analytical results and highlight the contributions of the nonlinear term and nonlocal effect.

Increment-Dimensional Scaled Boundary Finite Element Method for Solving Transient Heat Conduction Problem

An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.

Fabrication of micro-scale gratings for moiré method with a femtosecond laser

Fabrication of micro gratings using a femtosecond laser exposure system is experimentally investigated for the electron moire method. Micro holes and lines are firstly etched for parameter study. Grating profile is theoretically optimized to form high quality moire patterns. For a demonstration, a parallel grating is fabricated on a specimen of quartz glass. The minimum line width and the distance between two adjacent lines are both set to be 1 μm, and the frequency of grating is 500 lines/ram. The experimental results indicate that the quality of gratings is good and the relative error of the gratings pitch is about 1.5%. Based on molte method, scanning electron microscope （SEM） moire patterns are observed clearly, which manifests that gratings fabricated with the femtosecond laser exposure is suitable for micro scale deformation measurement.