On a counterexample to a conjecture of Saint Venant

The elliptic boundary value problem % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqGHsi% slcqGHuoarcaWG1bGaeyypa0dccaGae8hiaaIaaGymaiab-bcaGiab% -bcaGiab-bcaGiaabMgacaqGUbGaaeiiaiabfM6axjaabYcaaeaaae% aacaWG1bGaeyypa0JaaGimaiab-bcaGiab-bcaGiab-bcaGiaab+ga% caqGUbGaaeiiaiabgkGi2kabfM6axjaabYcaaaaa!4E11!\[\begin{gathered}- \Delta u = 1 {\text{in }}\Omega {\text{,}} \hfill \\\hfill \\u = 0 {\text{on }}\partial \Omega {\text{,}} \hfill \\\end{gathered}\]is considered. The Saint Venant's conjecture for convex plane domains , having symmetry about two orthogonal axes, is that the maximum of |u| occurs only at the points on which are nearest to the origin. G. Sweers constructed one such domain and claimed that either the conjecture fails for or for ={(x, y);u(x, y) >}, which again is convex. We give a totally different proof of this claim. Our proof brings out clearly the reason for the failure of the conjecture and also allows us to construct many more such domains.     

A proposed method of measuring the complex modulus of a thick viscoelastic layer

A simple, non-destructive method of measuring the complex modulus of a layer of viscoelastic material is proposed. The method relies upon an analysis of the frictionless contact of a rigid smooth indentor and the layer. The contact is maintained by means of a fluctuating normal load. The total load (or the indentation) is required to vary in a simple sinusoidal way. The complex modulus may then be determined from the results of observations made when the contact area is maximum (or minimum).     

On the validity of the method of Knudsen iretation

The Knudsen iteration is shown to be valid to predict the near free molecular corrections to drag, heat flux, etc., for non-linear rarefied gas flow problems.     

力矩析微

力矩是力学教学中最重要的基础概念之一,但教材中一般会同时给出力对点之矩和力对轴之矩两种定义,这在概念上容易引起学习者的困惑,尤其是空间问题中的力对点之矩,从物理意义的角度讲更是不易理解.本文在利用杠杆原理阐述力矩定义起源的基础上明确指出:力矩本质上即力对轴之矩,是力使刚体绕特定轴转动效应的一种度量,是滑动矢量;而力对点之矩是力对轴之矩的一种抽象的等价表述,是定位矢量,是力矩概念在复杂应用中的进一步发展.这种解释理清了力对点之矩与力对轴之矩两种定义之间的关系,物理意义明确直观,更有利于教学和实践中对力矩概念的清晰理解和准确应用.     

Image decomposition method for the analysis of a mixed dislocation in a general multilayer

The elastic solutions for a mixed dislocation in a general multilayer with N dissimilar anisotropic layers are obtained via a generalized image decomposition method. The original problem is decomposed into N homogeneous subproblems with strategically placed continuously distributed image (virtual) dislocations which satisfy the consistency conditions for degenerate N − M (M < N) layer problems. The image dislocations are used to satisfy the interface or free surface conditions, and represent the unknowns of the problem. The resulting singular Cauchy integral equations are transformed into non-singular Fredholm integral equations of the second kind using certain H- and I-integral transforms. The Fredholm integral equations are then solved via the classical Nyström method. The general decomposition and the elimination of all singular integrals yield an exact formulation of the problem; the approximation arises only in the Nyström method. The dislocation mixity and the number of layers dissimilar in thickness and elastic anisotropy can be handled without difficulty, constrained only by the number of linear algebraic equations in the Nyström method for large N. For the numerical study, image forces on a dislocation in two- and three-layer systems are calculated. The accuracy of the results is verified by checking the boundary conditions and by comparison with previous results. The dependence of the image force on the dislocation position and mixity, and on the layer thicknesses and elastic anisotropies, is also illustrated via numerical investigations.     

A proposed through-flow inverse method for the design of mixed-flow pumps

A through-flow (hub-to-shroud) truly inverse method is proposed and described in this paper. It uses as a initial design specification, an imposition of mean swirl, i.e. radius times mean tangential velocity, given throughout the meridional section of the turbomachine. In the present implementation, it is assumed that the fluid is invsicid, incompressible and irrotational at inlet and the blades are supposed to have zero thickness. Only blade rows that impart to the fluid a constant work along the span will be considered. An application of this procedure to design the rotor of a mixed-flow pump will be described in detail. The strategy used to find a suitable mean swirl distribution and the other design inputs is also described. The final blade shape and pressure distributions on the blade surface are presented, showing that it is possible to obtain feasible designs using this technique. Another advantage of this technique is the fact that it does not require large amounts of CPU time.     

HARMONIC COMPONENT EXTRACTION FROM A CHAOTIC SIGNAL BASED ON EMPIRICAL MODE DECOMPOSITION METHOD

A novel approach of signal extraction of a harmonic component from a chaotic signal generated by a Duffing oscillator was proposed. Based on empirical mode decomposition (EMD) and concept that any signal is composed of a series of the simple intrinsic modes, the harmonic components were extracted from the chaotic signals. Simulation results show the approach is satisfactory.     

基于区域分解的环肋圆柱壳-圆锥壳组合结构振动分析

提出了一种区域分解法来分析不同边界条件下环肋骨圆柱壳-圆锥壳组合结构的振动特性.首先把组合壳体分解为自由的圆柱壳、圆锥壳段;视环肋骨为离散元件,根据肋骨与圆柱壳段之间的变形协调条件,将肋骨的动能和应变能附加于圆柱壳段能量泛函中.然后基于分区广义变分和最小二乘加权残值法将所有分区界面的位移协调方程引入到组合壳体的能量泛函中.圆柱壳段、圆锥壳段位移变量的周向和轴向分量分别采用Fourier级数和Chebyshev多项式展开.以自由-自由、自由-固支和固支-固支边界条件的环肋骨组合壳体为例,采用区域分解法分析了其自由振动及在不同激励下的振动响应.通过与有限元软件ANSYS结果进行对比,发现两种方法计算结果非常吻合,验证了区域分解方法的计算精度和高效性.     

基于层次分解方法的桁架结构形状优化

对于桁架结构形状优化,应用层次分解优化方法,将设计变量分成杆件截面积和节点位置两类变量。求解时分为两层,第一层在给定节点位置下对杆件截面进行优化,同时考虑了应力、局部稳定约束和位移约束的重量最轻;第二层假定截面层的有效位移约束作用不变,求解一个使桁架刚度增强的二次规划问题,获得既不违反约束,又使目标函数不上升的新的节点位置,再返回第一层。两层交替进行直至收敛。     

Validation of the GeoWATCH soil moisture model and proposed bias correction method

The US Army is required to be a good steward of the land per US Army regulation AR 200-1. Based on this regulation, Army installations need to manage lands, to reduce potential damage and impacts to water quality and habitat that may occur from training. Maneuver training does impact the vegetation and soil and this damage is directly related to soil moisture. Soil moisture is an important factor for understanding the potential for soil surface disturbance due to vehicle impacts and predicting soil resilience to vehicle traffic, however, producing accurate estimates of the spatial and temporal variation of soil moisture has historically been elusive. GeoWATCH, which stands for Geospatial Weather-Affected Terrain Conditions and Hazards (formerly DASSP), simulates soil moisture world-wide, at relatively small spatial and temporal scales. GeoWATCH uses a physics-based downscaling approach that uses weather-scale land surface model estimates of soil moisture and land surface water and energy fluxes, with high resolution geospatial data. GeoWATCH soil moisture outputs coupled with vehicle impact models, are anticipated to be useful for near-real-time estimation of ground disturbance, but will require ground validation. To validate GeoWATCH soil moisture estimates, we utilized Soil Climate Analysis Network (SCAN) gauge network soil moisture data from 127 sites across 34 states. Statistical analysis of the raw GeoWATCH output indicated the model performs statistically better in certain soil textures. Model bias is largest for sandy soils, whereas clayey soils were least biased. As a result, bias correction models were applied to the raw GeoWATCH simulated values using linear regression to predict correction factor (CF) values based on physical site characteristics. The bias correction models significantly improved the performance of the GeoWATCH soil moisture model in terms of average performance statistics and number of statistically cally unbiased sites. This process could easily be incorporated into GeoWATCH, allowing for a capability to rapidly estimate vehicle impacts and determine rehabilitation requirements by installation land managers.     

On a generalized taylor theorem: A rational proof of the validity of the homotopy analysis method

IntroductionIn 1 7thcenturyIsaacNewton[1]gavesuchabinomialexpressionforfractionalandnegativeexponents(1 +t) α,i.e.,(1 +t) α =1 + +∞k=1α(α-1 ) (α-2 )… (α -k+ 1 )k !tk　　 (α≠ 0 ,1 ,2 ,… ) ,(1 )whoseconvergenceradiusisone.Furthermore ,theclassicalTaylorseries (seeRef.[2 ] )limm→+∞ mk=0f(k) (z0 )k !(z-z0 ) k (2 )ofacomplexfunctionf(z)atz=z0 isvalidmostlyinarestrictedconvergenceregion｜z-z0 ｜相似文献   

PERTURBATION METHOD FOR REANALYSIS OF THE MATRIX SINGULAR VALUE DECOMPOSITION

The perturbation method for the reanalysis of the singular value decomposition(SVD)of general real matrices is presented in this paper.This is a simple but efficientreanalysis technique for the SVD,which is of great worth to enhance computationalefficiency of the iterative analysis problems that require matrix singular valuedecomposition repeatedly.The asymptotic estimate formulas for the singular values and thecorresponding left and right singular vectors up to second-order perturbation componentsare derived.At the end of the paper the way to extend the perturbation method to the case ofgeneral complex matrices is advanced.     

Efficient solution algorithms for thermomechanical contact problems based on a domain/boundary decomposition method

An efficient domain/boundary decomposition method is presented for fully coupled thermomechanical problems with contact boundaries. The whole domain is regarded as a union of subdomains, an interface, and contact interfaces. Penalized variational formulations are performed to connect the interface or contact interfaces with the neighboring subdomains that satisfy continuity constraints on the displacement and temperature fields. As a result, non-linear finite element computations due to the contact boundaries can be localized within a few subdomains or contact interfaces. Therefore, the computational efficiency can be enhanced considerably by devising suitable solution algorithms. A variety of numerical examples were tested to confirm the important features of the new algorithms presented.     

Ensemble-Empirical-Mode-Decomposition method for instantaneous spatial-multi-scale decomposition of wall-pressure fluctuations under a turbulent flow

This work illustrates the possibilities of the Ensemble-Empirical-Mode-Decomposition (E-EMD) technique for a detailed analysis of the time and space characteristics of the wall-pressure fluctuations under a turbulent flow. Pressure fluctuations are measured with a linear microphone array, for the cases of a turbulent boundary layer and for a diffuse airborne acoustic field. The E-EMD technique is shown to be an efficient tool for representing the spatial scales of the turbulent fluctuations at each instant. In particular, this representation is obtained without any particular assumption or a priori information on the data (e.g. temporal or spatial stationarity of the wall pressure data is not required), and acts, when applied to wide-band turbulent signals, as a wavenumber filter. Finally, it is shown how, to some extent, the E-EMD technique can separate at each instant the acoustic (propagative) from the hydrodynamic (convective) energy.     

复合材料失效判据有效性验证方法研究

为系统地验证复合材料失效判据计算精度和有效性范围,给出了4种材料体系、6种铺层形式的层合板在单轴、双轴载荷下的失效试验数据,用以评估复合材料失效判据在单向层合板失效包线、多向层合板初始失效包线、多向层合板最终失效包线、层合板变形及层合板的破坏特性等五个方面的预测能力。并根据验证方法和有效性评估策略对失效判据计算精度进行量化考核,给出了失效判据在五个层面上的计算精度。     

Adomian修正分解法的后处理方法比较

Adomian修正分解法在求解非线性微分方程中得到广泛应用。Adomian修正分解法的主要特点在于计算简单快速,并且不需要进行线性化或离散化。但是Adomian修正分解法的计算精度取决于其收敛域。为了扩大Adomian修正分解法的收敛域,需要对所得解进行后处理,目前常见的后处理方法包括Padé近似、LaplacePadé近似和多步迭代方法。本文首先简要回顾了Adomian修正分解法,然后讨论了这三种后处理方法,最后通过Duffing振子为例对这些后处理方法的优缺点进行讨论和分析。数值计算结果表明,多步迭代方法能够加速Adomian修正分解法解的收敛,并扩大其收敛域。     

Modal identification of multi-degree-of-freedom structures based on intrinsic chirp component decomposition method

Modal parameter identification is a mature technology. However, there are some challenges in its practical applications such as the identification of vibration systems involving closely spaced modes and intensive noise contamination. This paper proposes a new time-frequency method based on intrinsic chirp component decomposition(ICCD)to address these issues. In this method, a redundant Fourier model is used to ameliorate border distortions and improve the accuracy of signal reconstruction. The effectiveness and accuracy of the proposed method are illustrated using three examples: a cantilever beam structure with intensive noise contamination or environmental interference, a fourdegree-of-freedom structure with two closely spaced modes, and an impact test on a cantilever rectangular plate. By comparison with the identification method based on the empirical wavelet transform(EWT), it is shown that the presented method is effective,even in a high-noise environment, and the dynamic characteristics of closely spaced modes are accurately determined.