On the pressure and stress singularities induced by steady flows of incompressible viscous fluids

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier-Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence-divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.

A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses

Based on the elementary solutions and new integral equations,a new analytical-numerical method is proposed to calculate the interacting stresses of multiple circular holes in an infinite elastic plate under both remote stresses and arbitrarily distributed stresses applied to the circular boundaries.The validity of this new analytical-numerical method is verified by the analytical solution of the bi-harmonic stress function method,the numerical solution of the finite element method,and the analytical-numerical solutions of the series expansion and Laurent series methods.Some numerical examples are presented to investigate the effects of the hole geometry parameters(radii and relative positions)and loading conditions(remote stresses and surface stresses)on the interacting tangential stresses and interacting stress concentration factors(SCFs).The results show that whether the interference effect is shielding(k<1)or amplifying(k>1)depends on the relative orientation of holes(α)and remote stresses(σ^∞x,σ^∞y).When the maximum principal stress is aligned with the connecting line of two-hole centers andσ^∞y<0.5σ^∞x,the plate containing two circular holes has greater stability than that containing one circular hole,and the smaller circular hole has greater stability than the bigger one.This new method not only has a simple formulation and high accuracy,but also has an advantage of wide applications over common analytical methods and analytical-numerical methods in calculating the interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses.

The wind-saltation interaction in a saltation boundary layer with a downwind air pressure gradient

Studies of interactions between wind and saltating particles （i.e., the wind-saltation interaction） are usually conducted without consideration of the downwind air pressure gradient. However, in a wind tunnel with limited size, this gradient is required to maintain the movement of the saltation cloud. Attempts are made to investigate the effects of the downwind air pressure gradient on the wind-saltation interaction in a saltation boundary layer based on the experimental results from a wind tunnel with a relatively small cross-sectional area. The wind-saltation interaction is characterized by airborne stress, grain-borne stress, and the force exerted on the wind by the saltation cloud. Basic equations were developed for wind-saltation interactions without and with a downwind air pressure gradient. The results reveal that unacceptable values of negative grain-borne stress and negative force exerted on the wind by the saltation cloud are obtained if the downwind air pressure gradient is ignored. When this air pressure gradient is defined using the measured wind velocity profiles in the presence of saltation and the downwind air pressure gradient is taken into account, reasonable values for grain-borne stress and the force exerted on the wind by the saltation cloud are obtained. These results suggest that attention must be paid to the effects of downwind air pressure gradients when studying the wind-saltation interaction in a wind tunnel. Consideration of the downwind air pressure gradient, inertial forces, and other unidentified variables will provide a more thorough understanding of the interactions within a saltation boundary layer.

Modal interactions in primary and subharmonic resonant dynamics of imperfect microplates with geometric nonlinearities

This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory,the equations of motion for the in-plane and out-of-plane motions are obtained employing the von Kármán plate theory as well as Kirchhoff＇s hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct timeintegration method. The system parameters are tuned to the values associated with modal interactions, and then nonlinear resonant responses and energy transfer are analysed.Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histories, phase-plane portraits, and fast Fourier transforms.

Diagnostic calculation of the upper-layer circulation in the South China Sea during the winter of 1998

On the basis of hydrographic data obtained in November 28 to December 27, 1998 cruise, the calculation of the circulation in the South China Sea (SCS) is made by using the P-vector method, in combination with SSH data from TOPEX/ERS-2 analysis. For study of the dynamical mechanism, which causes the pattern of winter circulation in the SCS, the diagnostic model (Yuan et al., 1982; Yuan and Su, 1992) is used to simulate numerically the winter circulation in the SCS. The following results have been obtained. (1) The main characteristics of the circulation systems in the central SCS are as follows: A coastal southward jet in winter is present at the western boundary near the coast of Vietnam; there is a stronger cyclonic circulation with a larger horizontal scale east of this coastal southward jet and west of 114°E; there is a weaker anti-cyclonic circulation in the central part of eastern SCS; there is a stronger and northeastward flow opposing the northeasterly monsoon between above a stronger cyclonic circulation and a weaker anti-cyclonic circulation. (2) The circulation systems in the northern SCS are as follows: 1) There is a cyclonic circulation system northwest of Luzon, and it has three centers of the cold water; 2) There is an anti-cyclonic eddy. Its center is located near(20°N, 116°40' E); 3)There is a warm and anti-cyclonic circulation south of Hainan Island; 4) There is a northeastward flow, the South China Sea Warm Current, in winter off Guangdong coast in the northern SCS. (3) In the southern SCS there is an anti-cyclonic circulation, and also there is a smaller scale cold water and cyclonic eddy. (4) The above pattern of winter circulation in the SCS agrees qualitatively with the horizontal distribution of temperature at 200 m level. (5) The dynamical mechanism which produces the above basic pattern of winter circulation is because of the following two causes: 1) The joint effect of the baroclinity and relief (JEBAR) is an essential dynamical cause; 2) The interaction between the wind stress and bottom topographic (IBWT) under the strong northeasterly monsoon is the next important dynamical mechanism. (6) Comparing the hydrographic structure and the horizontal distribution of velocity with the SSH data from TOPEX/ERS-2 analysis in the SCS during December of 1998, it is found that they agree qualitatively.

Calculation of circulation in the South China Sea during summer of 2000 by the modified inverse method

On the basis of hydrographic data obtained in August 2000 cruise, the circulation in the South China Sea (SCS) is computed by the modified inverse method in combination with SSH data from TOPEX/ERS-2 analysis. For study of the dynamical mechanism, which causes the pattern of summer circulation in the SCS, the diagnostic model (Yuan et al. 1982. Acta Oceanologica Sinica,4(1):1-11; Yuan and Su. 1992. Numerical Computation of Physical Oceanography.474-542) is used to simulate numerically the summer circulation in the SCS. The following results have been obtained. (1) The central and southwestern SCSs are dominated mainly by anticy-clonic circulation systems. They are mainly as follows. 1) There is strong anticyclonic eddy southeast of Vietnam (W1). Its horizontal scale is about 300 km, and it extends vertically from the surface to the about 1 000 m level. 2) There are a warm eddy W2 southeast of Zhongsha Islands and the anticyclonic circulation system W3 west off the Luzon Island. 3) There is a stronger cyclonic eddy C1 between the anticyclonic eddies W1 and W2.4) A strong northward coastal jet is present near the coast of Vietnam, and separates from the coast of Vietnam at about 12° N to the northeast.(2)The northern SCS is dominated mainly by a cyclonic circulation system. There is a cyclonic circulation system near and north of Section N2. (3) The southeastern SCS is dominated mainly by the cyclonic circulation system. (4) Comparing the results of circulation in the SCS during the summer of 2000 with those during the summer of 1998, it is found that they agree qualitatively, but there is the some difference between them in quantity.This shows that the circulation in the SCS has obviously seasonal feature. (5) The dynamical mechanism which products the basic pattern of summer circulation is because the following two reasons: 1) the joint effect of the baroclinity and relief (JEBAR) is essential dynamical cause; and 2) it is next important dynamical cause that the interaction between the wind stress and bottom topography under the southerly monsoon. (6) Comparing the hydrographic structure and distribution of stream functions with the SSH data from TOPEX/ERS-2 analysis in the SCS during August of 2000, they agree qualitatively.

A size-gradient hypothesis for alpine treeline ecotones

Research on the stress gradient hypothesis recognizes that positive(i.e. facilitative) and negative(i.e. competitive) plant interactions change in intensity and effect relative to abiotic stress experienced on a gradient. Motivated by observations of alpine treeline ecotones, we suggest that this switch in interaction could operate along a gradient of relative size of individual plants. We propose that as neighbors increase in size relative to a focal plant they improve the environment for that plant up to a critical point. After this critical point is surpassed, however, increasing relative size of neighbors will degrade the environment such that the net interaction intensity becomes negative. We developed a conceptual(not site or species specific) individual based model to simulate a single species with recruitment, growth, and mortality dependent on the environment mediated by the relative size of neighbors. Growth and size form a feedback. Simulation results show that the size gradient model produces metrics similar to that of a stress gradient model. Visualizations reveal that the size gradient model produces spatial patterns that are similar to the complex ones observed at alpine treelines. Size-mediated interaction could be a mechanism of the stress gradient hypothesis or it could operate independent of abiotic stress.

Use of genotype-environment interactions to elucidate the pattern of maize root plasticity to nitrogen deficiency

Maize（Zea mays L.） root morphology exhibits a high degree of phenotypic plasticity to nitrogen（N） de ficiency,but the underlying genetic architecture remains to be investigated Using an advanced BC_4F_3 population,we investigated the root growth plasticity under two contrasted N levels and identi fied the quantitative trait loci（QTLs） with QTL-environment（Q×E）interaction effects. Principal components analysis（PCA） on changes of root traits to N de ficiency（D LN-HN） showed that root length and biomass contributed for 45.8% in the same magnitude and direction on the first PC,while root traits scattered highly on PC_2 and PC_3. Hierarchical cluster analysis on traits for D LN-HN further assigned the BC_4F_3 lines into six groups,in which the special phenotypic responses to N de ficiency was presented These results revealed the complicated root plasticity of maize in response to N de ficiency that can be caused by genotype environment（G×E） interactions. Furthermore,QTL mapping using a multi-environment analysis identi fied 35 QTLs for root traits. Nine of these QTLs exhibited signi ficant Q×E interaction effects. Taken together,our findings contribute to understanding the phenotypic and genotypic pattern of root plasticity to N de ficiency,which will be useful for developing maize tolerance cultivars to N de ficiency.

A reined global-local approach for evaluation of singular stress ield based on scaled boundary inite element method

A reined global-local approach based on the scaled boundary inite element method（SBFEM） is proposed to improve the accuracy of predicted singular stress ield. The proposed approach is carried out in conjunction with two steps. First, the entire structure is analyzed by employing an arbitrary numerical method. Then, the interested region, which contains stress singularity, is re-solved using the SBFEM by placing the scaling center right at the singular stress point with the boundary conditions evaluated from the irst step imposed along the whole boundary including the side-faces. Beneiting from the semi-analytical nature of the SBFEM, the singular stress ield can be predicted accurately without highly reined meshes. It provides the FEM or other numerical methods with a rather simple and convenient way to improve the accuracy of stress analysis. Numerical examples validate the effectiveness of the proposed approach in dealing with various kinds of problems.

Interacting Stress Intensity Factors of Multiple Elliptical-Holes and Cracks Under Far-Field and Arbitrary Surface Stresses

Calculating interacting stress intensity factors(SIFs)of multiple ellipticalholes and cracks is very important for safety assessment,stop-hole optimization design and resource exploitation production in underground rock engineering,e.g.,buried tunnels,deep mining,geothermal and shale oil/gas exploitation by hydraulic fracturing technology,where both geo-stresses and surface stresses are applied on buried tunnels,horizontal wells and natural cracks.However,current literatures are focused mainly on study of interacting SIFs of multiple elliptical-holes(or circularholes)and cracks only under far-field stresses without consideration of arbitrary surface stresses.Recently,our group has proposed a new integral method to calculate interacting SIFs of multiple circular-holes and cracks subjected to far-filed and surface stresses.This new method will be developed to study the problem of multiple elliptical-hole and cracks subjected to both far-field and surface stresses.In this study,based on Cauchy integral theorem,the exact fundamental stress solutions of single elliptical-hole under arbitrarily concentrated surface normal and shear forces are derived to establish new integral equation formulations for calculating interacting SIFs of multiple elliptical-holes and cracks under both far-field and arbitrary surface stresses.The new method is proved to be valid by comparing our results of interacting SIFs with those obtained by Green’s function method,displacement discontinuity method,singular integral equation method,pseudo-dislocations method and finite element method.Computational examples of one elliptical-hole and one crack in an infinite elastic body are given to analyze influence of loads and geometries on interacting SIFs.Research results show that whenσ_(xx)^(∞)≥σ^(yy′)^(∞),there appears a neutral crack orientation angle b0(without elliptical-hole’s effect).Increasing s¥xx/s¥yy and b/a(close to circularhole)usually decreases b0 of KI and benefits to the layout of stop-holes.The surface compressive stresses applied onto elliptical-hole(n)and crack(p)have significant influence on interacting SIFs but almost no on b0.Increasing n and p usually results in increase of interacting SIFs and facilitates crack propagation and fracture networks.The elliptical-hole orientation angle(a)and holed-cracked distance(t)have great influence on the interacting SIFs while have little effect on b0.The present method is not only simple(without any singular parts),high-accurate(due to exact fundamental stress solutions)and wider applicable(under far-field stresses and arbitrarily distributed surface stress)than the common methods,but also has the potential for the anisotropic problem involving multiple holes and cracks.

The Effect of Particle Shape on the Structure and Rheological Properties of Carbon-based Particle Suspensions

The structure and rheological properties of carbon-based particle suspensions, i.e., carbon black（CB）, multi-wall carbon nanotube（MWNT）, graphene and hollow carbon sphere（HCS） suspended in polydimethylsiloxane（PDMS）, are investigated. In order to study the effect of particle shape on the structure and rheological properties of suspensions, the content of surface oxygen-containing functional groups of carbon-based particles is controlled to be similar. Original spherical-like CB（fractal filler）, rod-like MWNT and sheet-like graphene form large agglomerates in PDMS, while spherical HCS particles disperse relatively well in PDMS. The dispersion state of carbon-based particles affects the critical concentration of forming a rheological percolation network. Under weak shear, negative normal stress differences（ΔN） are observed in CB, MWNT and graphene suspensions, while ΔN is nearly zero for HCS suspensions. It is concluded that the vorticity alignment of CB, MWNT and graphene agglomerates under shear results in the negative ΔN. However, no obvious structural change is observed in HCS suspension under weak shear, and accordingly, the ΔN is almost zero.