A 3D shell-like approach using element-free Galerkin method for analysis of thin and thick plate structures

A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares （MLS） approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only dis- placement degrees of freedom （d.o.f.s）, is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.

ANALYSIS OF 2-D THIN STRUCTURES BY THE MESHLESS REGULAR HYBRID BOUNDARY NODE METHOD

Thin structures are generally solved by the Finite Element Method(FEM), using plate or shell finite elements which have manylimitations in applications, such as numerical locking, edge effects,length scaling and the cnvergence problem. Recently, by proposing anew approach to tranting the nearly- singular integrals, Liu et al.developed a BEM to successfully solve thin structures with thethickness-to- length ratios in the micro-or nano-scales. On the otherhand, the meshless Regular Hybrid Boundary Node Method (RHBNM), whichis proposed by the current authors and based on a modified functionaland the Moving Least-Square (MLS) approximation, has very promisingapplications for engineering problems owing To its meshless natureand dimension-reduction advantage, and not involving any singular ornearly-singular Integrals. Test examples show that the RHBNM can alsobe applied readily to thin structures with high accu- Racy withoutany modification.

AN IMPROVED HYBRID BOUNDARY NODE METHOD IN TWO-DIMENSIONAL SOLIDS

The hybrid boundary node method （HBNM） is a promising method for solving boundary value problems with the hybrid displacement variational formulation and shape functions from the moving least squares（MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the latter. Following its application in solving potential problems, it is further developed and numerically implemented for 2D solids in this paper. The rigid movement method is employed to solve the hyper-singular integrations. Numerical examples for some 2D solids have been given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method are studied through numerical examples.

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

We first give a stabilized improved moving least squares （IMLS） approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis.

MESHLESS ANALYSIS FOR THREE-DIMENSIONAL ELASTICITY WITH SINGULAR HYBRID BOUNDARY NODE METHOD

The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares （MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ＇boundary layer effect＇, which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method （RHBNM） can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.

Numerical Simulation and Performance Analysis on Windmill Starting Process of Small Turbojet Engine

A new simulation strategy is proposed for the starting process of missile turbojet engine windmill. The starting process of windmill before ignition is simulated using a radial basis function neural network (RBFNN) , and the acceleration process after ignition which model is a set of nonlinear equations is solved using a particle swarm optimization (PSO) algorithm. The introduction of PSO helped to tackle the problem of divergence caused by traditional iteration methods. The calculated result is in a great agreement with test data, which shows that the presented model has a high accuracy. The starting processes are simulated at different ignition times, and the results are analyzed synthetically. The analysis shows how the ignition time affects the starting performance of engine windmill. The method offers a useful tool for ignition time optimization as well as engine starting performance analysis.

Online quantitative analysis of soluble solids content in navel oranges using visible-nearinfrared spectroscopy and variable selection methods

Variable selection is applied widely for visible-near infrared(Vis-NIR)spectroscopy analysis of internal quality in fruits.Different spectral variable selection methods were compared for online quantitative analysis of soluble solids content(SSC)in navel oranges.Moving window partial least squares(MW-PLS),Monte Carlo uninformative variables elimination(MC-UVE)and wavelet transform(WT)combined with the MC-UVE method were used to select the spectral variables and develop the calibration models of online analysis of SSC in navel oranges.The performances of these methods were compared for modeling the Vis NIR data sets of navel orange samples.Results show that the WT-MC-UVE methods gave better calibration models with the higher correlation cofficient(r)of 0.89 and lower root mean square error of prediction(RMSEP)of 0.54 at 5 fruits per second.It concluded that Vis NIR spectroscopy coupled with WT-MC-UVE may be a fast and efective tool for online quantitative analysis of SSC in navel oranges.

AO-MW-PLS method applied to rapid quantification of teicoplanin with near-infrared spectroscopy

Teicoplanin(TCP)is an important lipoglycopeptide antibiotic produced by fermenting Acti-noplanes teichomyceticus.The change in TCP concentration is important to measure in the fermentation process.In this study,a reagent-free and rapid quantification method for TCP in the TCP-Tris-HCl mixture samples was developed using near infrared(NIR)spectroscopy by focusing our attention on the fermentation process for TCP.The absorbance optimization(AO)partial least squares(PLS)was proposed and integrated with the moving window(MW)PLS,which is called AO-MW-PLS method,to select appropriate wavebands.Amodel set that includes various wavebands that were equivalent to the optimal AO-MW-PLS waveband was,proposed based on statistical considerations.The public region of all equivalent wavebands was just one of the equivalent wavebands.The obtained public regions were 1540-1868 nm for TCP and 1114-1310 nm for Tris.The root-mean-square error and correlation coeficient for leave-one-out cross validation were 0.046 mg mL^(-1)and 0.9998 mg mL^(-1)for TCP,and 0.235 mg mL^(-1)and 0.9986 mg mL^(-1)for Tris,respectively.All the models achieved highly accurate prediction effects,and the selected wavebands provided valuable references for designing specialized spectrometers.This study provided a valuable reference for further application of the proposed methods to TCP fermentation broth and to other spectroscopic analysis fields.

Selection of stable equivalent wavebands for near-infrared spectroscopic analysis of total nitrogen in soil

The selection of stable wavebands for the near-infrared(NIR)spectroscopic analysis of total nitrogen(TN)in soil was accomplished by using an improved moving window partial leastsquares(MWPLS)method.A new modeling approach was performed based on randomness,similarity and stability,which produced an objective,stable and practical model.Based on the MWPLS method,a search was in the overali scanning region from 400 to 2498 nm,and the optimal waveband was identified to be 1424 to 282 nm.A model space that includes 41 wave-bands that are equivalent to the optimal waveband was then proposed.The public range of the 41equivalent optimal wavebands was 1590 to 1870 nm,which contained suficient TN information.The wavebands of 1424 to 2282 nm,1590 to 1870nm,and the long NIR region 1100 to 2498 nmall achieved satisfactory validation ffects.However,the public waveband of 1590 to 1870 nm hadonly a minimum number of wavelengths,which significantly reduced the method complexity.Various equivalent wavebands serve as guidelines for designing spect roscopic instruments.Thesewavebands could address the restrictions of position and the number of wavelengths in instru-ment design.

Multi-Level Partition of Unity Algebraic Point Set Surfaces

We present a multi-level partition of unity algebraic set surfaces （MPU-APSS） for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface （APSS） defines a smooth surface from a set of unorganized points using local moving least-squares （MLS） fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.

Weakly-Singular Traction and Displacement Boundary Integral Equations and Their Meshless Local Petrov-Galerkin Approaches

The general meshless local Petrov-Galerkin (MLPG) weak forms of the displacement and trac- tion boundary integral equations (BIEs) are presented for solids undergoing small deformations. Using the directly derived non-hyper-singular integral equations for displacement gradients, simple and straight- forward derivations of weakly singular traction BIEs for solids undergoing small deformations are also pre- sented. As a framework for meshless approaches, the MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs. By employing the various types of test functions, several types of MLPG/BIEs are formulated. Numerical examples show that the pre- sent methods are very promising, especially for solving the elastic problems in which the singularities in dis- placements, strains, and stresses are of primary concern.

Singular and Regular Implementations of the Hybrid Boundary Node Method

The hybrid boundary node method （HdBNM） combines a modified function with the moving least squares approximation to form a boundary-only truly meshless method. This paper describes two implementations of the HdBNM, the singular hybrid boundary node method （ShBNM） and the regular hybrid boundary node method （RhBNM）. The ShBNM and RhBNM were compared with each other, and the parameters that influence their performance were studied in detail. The convergence rates and their applicability to thin structures were also investigated. The ShBNM and RhBNM are found to be very easy to implement and to efficiently obtain numerical solutions to computational mechanics problems.

An improve d smoothe d particle hydrodynamics approach using new inverse kernel function

The main limitation of Smoothed Particle Hydrodynamics(SPH)method that resists the method’s poten-tial is its lack of providing stability and accuracy to the numerical technique.We improve the accuracy of the standard SPH technique,by formulating a new inverse logarithmic kernel function.This new kernel function is derived based on the underlying properties of kernel functions.The approximation technique used here is based on the Moving Least Squares based technique.The adequacy of the proposed ker-nel function is tested by simulation of 2D shock wave propagation and 3D dam-break free surface flow against a cuboidal obstacle.The method was validated against experimental data by Kleefsman et al.,[1].The numerical results reveal that our new SPH approach using inverse logarithmic kernel function outper-forms existing ones in particle restoration,zero error,better accuracy and enhanced efficiency in kernel approximation.This new kernel function showed some improvement over existing kernels by showing very less error approximation value of 0.035h 2.The results showed some improvements over standard technique by being capable of handling problems with large deformations accurately and precisely.