Axisymmetric static nets

A class of nets is studied which are statically indeterminate and may possess a unique configuration despite their high degree of kinematic indeterminacy. The intricately interrelated statical and geometric properties of such nets are revealed and investigated on the basis of closed-form solutions obtained for several main types of axisymmetric nets. A special emphasis is placed on the important case of torque-free nets. Together with a previously published paper [8] this study constitutes a compendium of results for axisymmetric static nets.     

考虑恒载效应的拱形梁静力近似解

应用虚功原理,推导了考虑恒载效应影响时拱形梁在活载作用下的非线性微分方程,得到了方程的近似闭合解。根据方程的解,讨论了恒载大小及结构自身刚度(矢高、跨度、惯性矩及惯性半径等)不同因素在考虑恒载效应时对拱形梁静力特性的影响。通过与Takabatake得到的直梁解析解结果及作者在其他文献提出的有限元方法对拱形梁分析结果的比较,验证了本文非线性微分方程及其求解公式。结果表明,本文给出的非线性微分方程对于拱形梁和直线梁具有通用性,初始恒载的存在减小了拱形梁在活载作用下的静力反应,这种影响与恒载的大小及结构自身的刚度有关,对轻型结构的设计提出了一些建议。     

Constitutive equation for friction with transition from static to kinetic friction and recovery of static friction

A high friction coefficient is first observed as a sliding between bodies commences, which is called the static friction. Then, the friction coefficient decreases approaching the lowest stationary value, which is called the kinetic friction. Thereafter, if the sliding stops for a while and then it starts again, the friction coefficient recovers and a similar behavior as that in the first sliding is reproduced. In this article the subloading-friction model with a smooth elastic–plastic sliding transition [Hashiguchi, K., Ozaki, S., Okayasu, T., 2005. Unconventional friction theory based on the subloading surface concept. Int. J. Solids Struct. 42, 1705–1727] is extended so as to describe the reduction from the static to kinetic friction and the recovery of the static friction. The reduction is formulated as the plastic softening due to the separations of the adhesions of surface asperities induced by the sliding and the recovery is formulated as the viscoplastic (creep) hardening due to the reconstructions of the adhesions of surface asperities during the elapse of time under a quite high actual contact pressure between edges of asperities.     

Measuring static strains at high temperatures

A recently introduced strain gage is described. It depends on the variation in electrical capacitance brought about by the deflection of an arched strip when the separation of its feet is altered. The gage has a wide range (1-percent strain) and good stability even in the 1100–1200°F range. With the design adopted, the output when a gage is heated but not stressed can be controlled and reduced. Using the techniques described, problems of connections for field work are not severe and remote readings can be made of the small capacitances involved, which are about 0.5 pF. Several trials are in progress. In one installation, automatic logging from scores of gages has proved successful. The gage has particular attractions for monitoring the formation of cracks in structures working at high temperatures.     

Propagation of discontinuities against a static background

The solution of the ideal gasdynamic equations describing propagation of a shock wave initiated, for example, by the motion of a piston against an inhomogeneous static background is considered. The solution is constructed in the form of Taylor series in a special time variable which is equal to zero on the shock wave. In the case of weak shock waves divergence of the series serves as the constraint for such an approach. Then the solution is constructed by linearizing the equations about the solution with a weak discontinuity. In the case of a given background the last solution can be always found exactly by solving successively a set of transport equations, all these equations are reduced to linear ordinary differential equations. The presentation begins from the one-dimensional solutions with plane waves and ends by discussion of spatial problems.     

Analytical prediction of ROPS static elastic-plastic behavior

This paper outlines a method for accurately predicting the elastic-plastic force-vs.-deflection curve for a rolover protective structure (ROPS). A knowledge of the plastic behavior of structural members is combined with a finite-element beam model to produce a piecewise linear analysis. Experimental and analytical results are compared. Intermediate results are used to update the model at various stages in the process. The paper does not discuss the computer program—only its use.     

关于精确结构静力重分析法的注记

结构重分析是与结构优化设计紧密相关的分析环节。位移约束条件、载荷与单元刚度矩阵可修改的精确结构静力重分析是较新的一种方法，文献[1,2]提出其结构静力重分析的列式，这一重分析方法被多篇综述文章引用。本文从另一角度推导结构修改的基本方程，并给出广义柔度矩阵的简便可行算法，推导过程简单明了，力学意义明显。     

Higher order sensitivities in structural static design

I.IntroductionStructuraldesignplaysoneofthemostimportantrolesinthefieldofaeronauticsandastronautics.Itsessenceisaninversealgebraiceigenvalueproblem.Whenwe'resolvingthiskindofproblems,sensitivity(theeigenvaluesandeigenvectorsderivativeswithrespecttodesignp…     

Convex analysis and unilateral static problems

Summary In this paper by the use of convex analysis the general nonlinear unilateral static problem of structural mechanics is formulated. By means of the subdifferentiability concept the unilateral nonlinear boundary conditions and the unilateral nonlinear constitutive laws are formulated as subdifferential relations, permitting the derivation of the variational inequalities of virtual and complementary virtual work. Thus the minimum potential and complementary energy theorems are proved. These minimum theorems are used to formulate the analysis as a nonlinear programming problem. Numerical examples on structures with nonlinear unilateral constitutive laws and nonlinear unilateral boundary conditions illustrate the theory.

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Übersicht In diesem Aufsatz wird mit Hilfe der konvexen Analyse das allgemeine nichtlineare, einseitige statische Problem der Mechanik formuliert. Durch den Begriff der Subdifferentiabilität werden einseitige, nichtlineare Randbedingungen und einseitige nichtlineare Stoffgesetze als subdifferentielle Relatiouen formuliert. Diese Relationen ermöglichen es, die variationellen Ungleichungen der virtuellen und komplementären Arbeit und auch die Minimum-Theoreme der potentiellen und der komplementären Energie herzuleiten. Durch die Minimum-Theoreme wird das Problem numerisch mit Hilfe der Algorithmen der nichtlinearen Optimierung behandelt. Die Theorie wird durch numerische Beispiele von Konstruktionen mit einseitigen nichtlinearen Stoffgesetzen und einseitigen nichtlinearen Randbedingungen erläutert.

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The author would like to extend his grateful thanks to Prof. G. Fichera for invaluable advice and to the Alexander von Humboldt Stiftung for the financial support.     

一种精确结构静力重分析法

本文提出了一种结构静力重分析方法。通过引入结构刚体位移特征向量，可以导出结构广义柔度矩阵，原阶数较高的刚度方程被转化成一阶数较小的线性系统，位移一般解可以在边界条件尚未引入结构刚度矩阵之前导出，对于有局部变化的结构，新的结构广义柔度矩阵可以迅速进行修改。这种静力重分析可以用在载荷条件、边界条件、结构单元同时或分别改变时的静力分析之中，文中提供了两个算例，以证明此方法的有效性     

On a moment static problem in stresses

Recently one has often been speaking of problems with couple stresses. The theory in which such problems are considered is sometimes called micropolar, or the theory of Cosserat continuum [1]. In the case of elastic medium, such a theory is considered in [2].     

On the elastic stability of static non-holonomic systems

This paper presents a new formulation for the elastic stability of static non-holonomic structural systems. The theory is developed within the tradition of discrete (or discretized) systems written in terms of a set of generalized coordinates and control parameters. The non-holonomic conditions are written as constraint functions. The formulation employs a Lagrangian functional in terms of the total potential energy, the constraint functions and multipliers. Critical states are identified and the solution is next expanded by regular perturbations. This allows to establish a classification of critical states and identify the initial postcritical behavior. This solution is valid provided that there is no change in the active constraints of the system. The paper presents a mathematical analysis of the critical condition, and concludes with simple examples of two degree-of-freedom systems previously investigated by other authors.     

Response of static pressure probes in turbulent streams

A theory of the effect of turbulence on the response of static pressure probes is given. To apply it to a given probe, the response in a laminar stream must be known as a function of orientation. Results are reported for Prandtl probes. For these the effect of turbulence is negligible at the levels encountered in pipe flows, but is highly significant at those prevailing in jets and other strongly turbulent systems. Experimental verification is given and the effect of turbulence length scale is demonstrated.     

固定接触界面法向静弹性刚度

基于Hertz接触理论推导了两个微凸体之间互相作用的法向接触静弹性刚度.根据修正后的一个微接触点的平截面积尺寸分布,给出了界面的总法向接触静弹性条件刚度、总条件载荷的解析解.将法向静弹性刚度的解析解嵌入到有限元软件中,获得整机的理论模态.通过实验对解析解进行了定量验证.以机床结合部为研究对象,在理论振型与实验振型一致的...     

Crack detection in elastic beams by static measurements

This paper deals with the identification of a single crack in a beam based on the knowledge of the damage-induced variations in the static deflection of the beam. The crack is simulated by an equivalent linear spring connecting the two adjacent segments of the beam. Sufficient conditions on static measurements which allow for the unique identification of the crack are presented and discussed. The inverse analysis provides exact closed-form expressions of position and severity of the crack as functions of deflection measurements for different boundary conditions. The theoretical results are confirmed by a comparison with static measurements on steel beams with a crack. Extension of the presented analysis to multiple cracks is briefly discussed.     

Axisymmetric static and dynamic buckling of hollow microspheres

Syntactic foams are particulate composites that are obtained by dispersing thin hollow inclusions in a matrix material. The wide spectrum of applications of these composites in naval and aerospace structures has fostered a multitude of theoretical, numerical, and experimental studies on the mechanical behavior of syntactic foams and their constituents. In this work, we study static and dynamic axisymmetric buckling of single hollow spherical particles modeled as non-linear thin shells. Specifically, we compare theoretical predictions obtained by using Donnell, Sanders–Koiter, and Teng–Hong non-linear shell theories. The equations of motion of the particle are obtained from Hamilton׳s principle, and the Galerkin method is used to formulate a tractable non-linear system of coupled ordinary differential equations. An iterative solution procedure based on the modified Newton–Raphson method is developed to estimate the critical static load of the microballoon, and alternative methodologies of reduced complexity are further discussed. For dynamic buckling analysis, a Newmark-type integration scheme is integrated with the modified Newton–Raphson method to evaluate the transient response of the shell. Results are specialized to glass particles, and a parametric study is conducted to investigate the effect of microballoon wall thickness on the predictions of the selected non-linear shell theories. Comparison with finite element predictions demonstrates that Sanders–Koiter theory provides accurate estimates of the static critical load for a wide set of particle wall thicknesses. On the other hand, Donnell and Teng–Hong theories should be considered valid only for very thin particles, with the latter theory generally providing better agreement with finite element findings due to its more complete kinematics. In this context, we also demonstrate that a full non-linear analysis is required when considering thicker shells, while simplified treatment can be utilized for thin particles. For dynamic buckling, we confirm the accuracy of Sanders–Koiter theory for all the considered particle thicknesses and of Teng–Hong and Donnell theories for very thin particles.     

The static drag on bodies in Bingham plastics

Summary A good indication of the static drag force experienced by a body immersed in a Bingham plastic can be obtained by summing the static yield stress over the cross-sectional area of the body normal to the direction of movement of the plastic and multiplying the result by 16.7. The actual drag may be slightly higher in the case of a disc or a sphere than for a cylinder or a rectangular plate, and an additional factor may be required if the length of the body parallel to the flow exceeds its width. The mechanism of transmission of the force from the Bingham plastic to the immersed body is not understood at present.

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Zusammenfassung Einen guten Hinweis auf den Fließwiderstand eines in einer fließenden Bingham-Substanz eingetauchten Körpers erhält man, indem man die statische Fließspannung über die Querschnittsfläche des Körpers senkrecht zur Bewegungsrichtung der Bingham-Substanz summiert und das Ergebnis mit 16,7 multipliziert. Der tatsächliche Fließwiderstand mag im Falle einer Scheibe oder einer Kugel etwas höher sein als für einen Zylinder oder eine rechteckige Platte, und möglicherweise ist ein zusätzlicher Faktor erforderlich, wenn die Länge des Körpers parallel zur Strömung größer ist als seine Breite. Der Mechanismus der Kräfteübertragung von der Bingham-Substanz auf den eingetauchten Körper ist zur Zeit noch nicht erkannt.

     

The theory of static decay in computational mechanics

In this paper,a new mathematical form,matrix,continued fraction(MCF)isintroduced to describe the decay of effects of an equilibrant system of forces acting on asphere of an elastic body.By this way,the famous Saint-Venant’s principle is proved oftenbut not always valid in computational mechanics.     

A machine for static and dynamic triaxial testing

A machine has been developed for studying the static and dynamic triaxial constitutive behavior of large specimens of geologic and construction materials. Test specimens can also contain a cylindrical tunnel cavity to permit study of tunnel-reinforcement structures and rock-structure interaction. The specimens are 0.3 m in diameter and 0.3 to 0.45 m high; the model tunnels can be up to 50 mm in diameter. Static and dynamic triaxial loads can be applied with maximum pressures of 200 MPa in static tests and 100 MPa in dynamic tests. Dynamic loading can also be superimposed on a static preload as large as 20 MPa. To facilitate study of tunnel reinforcement, the tunnel is maintained at ambient pressure, with access at both ends for instrumentation and photography. Example results show the influence on tunnel deformation of loading rate as well as the presence of joints and their orientation. For a given allowable tunnel closure, substantially greater pressures can be sustained under dynamic loading than under static loading, and substantially greater pressures can be sustained by an intact specimen than by a jointed specimen.