Load supporting prefabricated wall reinforced by a frame

This load supporting prefabricated wall consists of a thin plate reinforced along its boundaries by a frame. With the loads acting on the frame, the plate has its boundary conditions defined neither by forces nor by displacements. On the basis of satisfying the biharmonic equation of the stress function for the plate, we make the total strain energy to be minimum to ensure the compatibility of displacements for the two elastic bodies. Thus we get a set of infinite simultaneous equations. The results obtained indicate the method of solution is effective.     

The hole-pressure problem

There is a need to unify present hypotheses of the nature and role of the hole-pressure,p _e , and thus provide consolidation on which to base future research and understanding. This paper is intended to meet this need. Attention is directed towards the calculation ofp _e from the velocity and stress fields for viscoelastic fluids flowingacross rectangular holes. The constitutive models used are the Newtonian, Second-order and Maxwell models, for values of Reynolds number up to 10 and Weissenberg number up to 0.1.The numerical complications involved are studied through an investigation of the constituent parts ofp _e . Verification of present theory is then sought, from which justification may be derived for the estimation of elasticity fromp _e measurements. Attention is directed towards the predictions of Higashitani and Pritchard and the extension to the Tanner and Pipkin theory for Second-order fluids. The effects of variation of geometric dimensions and flow type uponp _e are also discussed.     

An approach to determine the stable interval of the constant term of a characteristic equation

In this paper, an approach is introduced to determine the stable interval of the constant term of a characteristic equation by using the theory of extended graphical representation of polynomials. Because the constant a_n itself is not taken into account and because this method is to get a stable interval of a_n, not merely to make a stability test for a set of known coefficients, this method of stability criteria has some advantages over the others. The interval of a_n can be obtained from the calculation of some algebraical expressions when n10, where n is the degree of the characteristic equation. It is very convenient to calculate for the cases n=5 and n=6. When n11, this interval can be found only by the method of numerical solutions.     

New development in Poincaré's problem of irregular integrals

In connection with non-Fuchsian equations Poincaré has made an important conclusion: It is impossible to obtain explicit expressions of irregular integrals .To elucidate the essence of Poincaré's problem, we establish correspondence theorem. Irregular integrals are analytic functions of new kind, possessing tree structure; part of which can be represented by conventional recursive series, while its remaining part is expressed by the so-called tree series, not subjecting to any recursive relation at all.In contrast to the numerical solution calculated by infinite determinant of classical theory (Hill-Poincaré-von Koch), our method yields naturally exact analytic solution in explicit form. The method proposed may be used to construct a unifying theory for general equations with variable coefficients, having various kinds of singularities as singular lines.The significance of Poincaré conjecture is discussed, the tree series obtained belong to higher automorphic functions.     

Die freie Oberfläche einer Flüssigkeit über einer rotierenden Scheibe

Zusammenfassung Es wird eine modifizierte Form des Weissenberg-Effekts untersucht, wobei sich die viskoelastische Flüssigkeit in einem kreiszylindrischen Gefäß befindet, an dessen Boden eine Scheibe rotiert. Normalspannungsdifferenzen rufen in der Flüssigkeit eine Strömung hervor, die auf der Drehachse von unten nach oben gerichtet ist, und die freie Oberfläche wölbt sich nahe der Achse nach außen. Unter der Voraussetzung hinreichend langsamer Strömung wird eine Theorie zweiter Ordnung entwickelt. Sie führt auf elliptische Randwertaufgaben zweiter bzw. vierter Ordnung für das Geschwindigkeitsfeld der Primärströmung in Umfangsrichtung und für die Stromfunktion der Sekundärströmung in der Meridianebene. Ihnen werden äquivalente Variationsaufgaben zugeordnet und mit der Methode der Finiten Elemente numerisch gelöst. Die Gestalt der freien Oberfläche setzt sich bei geeigneter Normierung aus drei universellen Formfunktionen zusammen, die für verschiedene Füllhöhen berechnet werden. Im experimentellen Teil wird nachgewiesen, daß durch entsprechende Messungen der Auslenkung des Flüssigkeitsspiegels die unteren Grenzwerte der beiden Normalspannungskoeffizienten bestimmt werden können. Das Rheometer besitzt den Vorzug, daß die Oberflächenspannung der Flüssigkeit die Meßgröße nur unwesentlich beeinflußt.

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Some kind of Weissenberg effect is considered where the viscoelastic fluid, being within a cylindrical vessel, is set in motion by a rotating disc near the tank bottom. Because of normal-stress differences within the fluid a secondary flow arises which is directed upwards near the axis of symmetry, and thus the free surface is deformed. Under the assumption of sufficiently slow flow a second-order theory is developed. It leads to second-order and fourth-order elliptic boundary value problems for the velocity field in azimuthal direction and for the stream function of the secondary flow, respectively. Equivalent variational problems are formulated and solved by the method of finite elements. When normalized appropriately, the shape of the free surface consists of three shape functions, which are independent of any material constants. It is shown by corresponding experiments, that the zero-shear-rate normal-stress coefficients can be determined by measuring the displacement of the free surface. In this rheometer, the surface tension of the fluid causes only insignificant influence on the quantity to be measured.

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Symbole C _H [—] Verhältnis der FormfunktionenF ₂/F₁ - f [—] die Sekundärströmung treibende radiale Volumenkraft, dimensionslos - F ₀, F₁, F₂ [—] universelle Formfunktionen - Fr [—] Froude-Zahl - g [m s^–2] Erdbeschleunigung - h [—] Auslenkung der Oberfläche, aufr ₀ bezogen - H [—] dimensionslose Füllhöhe - K [—] Kennzahl der Kapillarität - r,z [m] Zylinderkoordinaten - r, z [—] dimensionslose Koordinaten - r ₀ [m] Radius des Meßbehälters - Re [—] Reynolds-Zahl - v _r, v, v_z [m s^–1] Geschwindigkeitskomponenten - We ₁, We₂ [—] Weissenberg-Zahlen - [Pa s] Nullviskosität der Flüssigkeit - [°C] Temperatur - [m] Kapillarlänge - v ₁, v₂ [Pa s²] untere Grenzwerte der Normalspannungskoeffizienten - [kg m^–3] Dichte der Flüssigkeit - [N m^–1] Oberflächenspannung - [—] Zylinderkoordinate - [—] Dissipationsfunktion der Sekundärströmung, dimensionslos - [—] Stromfunktion, dimensionslos - [—] örtliche Winkelgeschwindigkeit, dimensionslos - [s^–1] Winkelgeschwindigkeit der Scheibe     

计算V形切口应力集中的奇应变单元

提出了计算 V 形切口断裂问题的含有两种奇异性的奇应变三角形单元。当 V 形切口闭合成裂缝时,该单元就自动演变成前人提出的计算裂纹的奇应变三角形单元。故本文提出的 V 形切口奇应变三角形单元是裂纹奇应变三角形单元的推广,可用来计算一般切口的应力强度因子,以进行断裂控制计算。     

A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

This paper considers the one-dimensional dissipative cubic nonlinear Schrödinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.     

Numerical study of the directed polymer in a 1 + 3 dimensional random medium

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length L, the high temperature phase is characterized by a diffusive behavior for the end-point displacement R² ∼L and by free-energy fluctuations of order ΔF(L) ∼O(1). The low-temperature phase is characterized by an anomalous wandering exponent R²/L ∼L^ω and by free-energy fluctuations of order ΔF(L) ∼L^ω where ω∼0.18. In this paper, we first study the scaling behavior of various properties to localize the critical temperature T_c. Our results concerning R²/L and ΔF(L) point towards 0.76 < T_c ≤T₂=0.79, so our conclusion is that T_c is equal or very close to the upper bound T₂ derived by Derrida and coworkers (T₂ corresponds to the temperature above which the ratio remains finite as L ↦ ∞). We then present histograms for the free-energy, energy and entropy over disorder samples. For T ≫T_c, the free-energy distribution is found to be Gaussian. For T ≪T_c, the free-energy distribution coincides with the ground state energy distribution, in agreement with the zero-temperature fixed point picture. Moreover the entropy fluctuations are of order ΔS ∼L^1/2 and follow a Gaussian distribution, in agreement with the droplet predictions, where the free-energy term ΔF ∼L^ω is a near cancellation of energy and entropy contributions of order L^1/2.     

Self-organized Criticality in an Earthquake Model on Random Network

A simplified Olami-Feder-Christensen model on a random network has been studied. We propose a new toppling rule — when there is an unstable site toppling, the energy of the site is redistributed to its nearest neighbors randomly not averagely. The simulation results indicate that the model displays self-organized criticality when the system is conservative, and the avalanche size probability distribution of the system obeys finite size scaling. When the system is nonconservative, the model does not display scaling behavior. Simulation results of our model with different nearest neighbors q is also compared, which indicates that the spatial topology does not alter the critical behavior of the system.     

Effect of ballistic electrons on ultrafast thermomechanical responses of a thin metal film

The ultrafast thermomechanical coupling problem in a thin gold film irradiated by ultrashort laser pulses with different electron ballistic depths is investigated via the ultrafast thermoelasticity model. The solution of the problem is obtained by solving finite element governing equations. The comparison between the results of ultrafast thermomechanical coupling responses with different electron ballistic depths is made to show the ballistic electron effect. It is found that the ballistic electrons have a significant influence on the ultrafast thermomechanical coupling behaviors of the gold thin film and the best laser micromachining results can be achieved by choosing the specific laser technology(large or small ballistic range).In addition, the influence of simplification of the ultrashort laser pulse source on the results is studied, and it is found that the simplification has a great influence on the thermomechanical responses, which implies that care should be taken when the simplified form of the laser source term is applied as the Gaussian heat source.