BOUNDARY ELEMENT ANALYSIS OF CONTACT PROBLEMS USING ARTIFICIAL BOUNDARY NODE APPROACH

An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.

RECONSTRUCTION STABILITY OF NEARFIELD ACOUSTIC HOLOGRAPHY

The distributed source boundary point method （DSBPM） is used as the spatial transform algorithm for realizing nearfield acoustic holography （NAH）, the sensitivity of the reconstructed solution to the measurement errors is analyzed, and the regularization method is proposed to stabilize the reconstruction process, control the influence of the measurement errors and get a better approximate solution. An oscillating sphere is investigated as a numerical example, the influence of the measurement errors on the reconstruction solution is demonstrated, and the feasibility and validity of the regularization method are validated. Key words： Acoustic holography Boundary point method Inverse problem Regularization

Efficient 2D Analysis of Interfacial Thermoelastic Stresses in Multiply Bonded Anisotropic Composites with Thin Adhesives

In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.

Sequence boundaries and regularities in the oil-gas distribution of the low swelling slope belt in the continental rift basin

Where are the zones more enriched in sand deposits in the down slope and deep depression of the low swelling slope belt? Are there any screening conditions for oil and gas there? These are the chief geological problems to be solved during exploration of a region. Taking the Paleogene system developed along the east slope belt of Chengdao as an example the concepts of sequence stratigraphy and sedimentary sequenc are applied. A new research method likened to a way ''to get a melon by following the vine'' is proposed to determine the direction for exploring within un-drilled or less-drilled areas. This is the process: ''the characteristics of the sequence boundary ? the forming mechanism of the stratigraphic sequence ? the conditions of oil and gas accumulation ? the distribution zones of oil and gas''. The relationship between the dynamic mechanism of stratigraphic sequence and the forming conditions for oil and gas accumulation establishes that the tectonic disturbance of the slope belt has significant responses as denudation and deposition. Above the stratigraphic sequence boundary there are large scale sand bodies of the low stand system tract (LST) that have developed in the low swelling slope belt and its deep depression. Below the sequence boundary there are the remaining sand bodies of the high stand system tract (HST). On the slope there is a convergence of mudstone layers of the extended system tract (EST) with the mudstone of the underlying strata, which constitutes the screening conditions for the reservoir of the down slope and deep depression. The distribution regularities in preferred sand bodies on the surface of the sequence boundary, and in the system tract, indicate the ordering of oil-gas deposits. From the higher stand down to the depth of the slope there are, in order, areas where exploration was unfavorable, major areas of stratigraphic overlap of oil-gas reservoirs, unconformity screened oil-gas reservoirs, and, finally, sandstone lens oil-gas reservoirs. The low swelling slope belt of Chengdao was tectonically active, which is typical for a continental rift basin. The methodology and results of the present paper are significant for the theory and practice of predicting subtle reservoir and selecting strategic areas for exploration.

Existence theory for Rosseland equation and its homogenized equation

The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.

The Method of A-Harmonic Approximation and Boundary Regularity for Nonlinear Elliptic Systems under the Natural Growth Condition

We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.

Boundary Regularity for Minimal Graphs of Higher Codimensions

In this paper,the authors derive H¨older gradient estimates for graphic functions of minimal graphs of arbitrary codimensions over bounded open sets of Euclidean space under some suitable conditions.

Boundary Lipschitz Regularity of Solutions for Semilinear Elliptic Equations in Divergence Form

In this paper,we consider the pointwise boundary Lipschitz regularity of solutions for the semilinear elliptic equations in divergence form mainly under some weaker assumptions on nonhomogeneous term and the boundary.If the domain satisfies C1,Dinicondition at a boundary point,and the nonhomogeneous term satisfies Dini continuity condition and Lipschitz Newtonian potential condition,then the solution is Lipschitz continuous at this point.Furthermore,we generalize this result to Reifenberg C1,Dinidomains.

The Birth–death Processes with Regular Boundary: Stationarity and Quasi-stationarity

For the birth–death Q-matrix with regular boundary,its minimal process and its maximal process are closely related.In this paper,we obtain the uniform decay rate and the quasi-stationary distribution for the minimal process.And via the construction theory,we mainly derive the eigentime identity and the distribution of the fastest strong stationary time(FSST)for the maximal process.

Boundary Holder Estimates for a Class of Degenerate Elliptic Equations in Piecewise Smooth Domains

In this paper, the authors will apply De Giorgi-Nash-Moser iteration to establish boundary H?lder estimates for a class of degenerate elliptic equations in piecewise C^(2)-smooth domains.

Regularity of Solutions to the Navier-Stokes Equations with a Nonstandard Boundary Condition

In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result similar to L q-theory for the one with Dirichlet boundary condition is obtained. Using the result, for the steady Navier-Stokes equations we obtain regularity as the case of Dirichlet boundary conditions. Furthermore,for the time-dependent 2-D Navier-Stokes equations we prove uniqueness and existence of regular solutions,which is similar to J.M.Bernard＇s results[6]for the time-dependent 2-D Stokes equations.

Building segmentation and modeling from airborne LiDAR data

Due to the high accuracy and fast acquisition speed offered by airborne Light Detection and Ranging(LiDAR)technology,airborne LiDAR point clouds have been widely used in three-dimensional building model reconstruction.This paper presents a novel approach to segment building roofs from point clouds using a Gaussian mixture model in which buildings are represented by a mixture of Gaussians(MoG).The Expectation-Maximization(EM)algorithm with the minimum description length(MDL)principle is employed to obtain the optimal parameters of the MoG model for separating building roofs.To separate complete planar building roofs,coplanar Gaussian components are merged according to their distances to the corresponding planes.In addition,shape analysis is utilized to remove nonplanar objects caused by trees and irregular artifacts.Building models are obtained by combining segmented planar roofs,topological relationships,and regularized building boundaries.Roof intersection segments and points are derived by the segmentation results,and a rasterbased regularization method is employed to obtain geometrically correct and regular building models.Experimental results suggest that the segmentation method is able to separate building roofs with high accuracy while maintaining correct topological relationships among roofs.

On the Regularity of Shear Thickening Viscous Fluids

The aim of this note is to improve the regularity results obtained by H. Beirao da Veiga in 2008 for a class of p-fluid flows in a cubic domain. The key idea is exploiting the better regularity of solutions in the tangential directions with respect to the normal one, by appealing to anisotropic Sobolev embeddings.

Continuity of Almost Harmonic Maps with the Perturbation Term in a Critical Space

The authors study the continuity estimate of the solutions of almost harmonic maps with the perturbation term f in a critical integrability class(Zygmund class)L^(n/2)log^(q) L,n is the dimension with n≥3.They prove that when q>n/2 the solution must be continuous and they can get continuity modulus estimates.As a byproduct of their method,they also study boundary continuity for the almost harmonic maps in high dimension.

Refined Scattering and Hermitian Spectral Theory for Linear Higher-Order Schrōdinger Equations

The Cauchy problem for a linear 2mth-order Schrōdinger equation ut=-i（-△）^mu, in R^N×R＋,u｜t=0=u0;m≥1 is an integer,is studied, for initial data uo in the weighted space L^2ρ（R^N）,withρ^＊（x）=e｜x｜^a and a=2m/2m-1∈（1,2].The following five problems are studied： （I） A sharp asymptotic behaviour of solutions as t → ＋∞ is governed by a discrete spectrum and a countable set Ф of the eigenfunctions of the linear rescaled operator B=-i（-△）^m＋1/2my·↓△＋N/2mI,with the spectrum σ（B）={λβ=-｜β｜≥0}. （Ⅱ） Finite-time blow-up local structures of nodal sets of solutions as t → 0^- and a formation of ＂multiple zeros＂ are described by the eigenfunctions, being generalized Hermite polynomials, of the ＂adjoint＂ operator B=-i（-△）^m-1/2my·↓△,with the same spectrum σ（B^＊）=σ（B）.Applications of these spectral results also include： （Ⅲ） a unique continuation theorem, and （IV） boundary characteristic point regularity issues. Some applications are discussed for more general linear PDEs and for the nonlinear Schr6dinger equations in the focusing （＂＋＂） and defocusing （＂-＂） cases ut=-（-△）^mu±i｜u｜^p-1u,in R^N×R＋,where P〉1,as well as for： （V） the quasilinear Schr6dinger equation of a ＂porous medium type＂ ut=-（-△）^m（｜u｜^nu）,in R^N×R＋,where n〉0.For the latter one, the main idea towards countable families of nonlinear eigenfunctions is to perform a homotopic path n → 0^＋ and to use spectral theory of the pair {B,B^＊}.