Crack propagation in structures subjected to periodic excitation

In the present paper, a simple mechanical model is developed to predict the dynamic response of a cracked structure subjected to periodic excitation, which has been used to identify the physical mechanisms in leading the growth or arrest of cracking. The structure under consideration consists of a beam with a crack along the axis, and thus, the crack may open in Mode I and in the axial direction propagate when the beam vibrates. In this paper, the system is modeled as a cantilever beam lying on a partial elastic foundation, where the portion of the beam on the foundation represents the intact portion of the beam. Modal analysis is employed to obtain a closed form solution for the structural response. Crack propagation is studied by allowing the elastic foundation to shorten (mimicking crack growth) if a displacement criterion, based on the material toughness, is met. As the crack propagates, the structural model is updated using the new foundation length and the response continues. From this work, two mechanisms for crack arrest are identified. It is also shown that the crack propagation is strongly influenced by the transient response of the structure.

Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated.

Numerical analyses for the material bifurcation in plane sheet under tension

The various patterns (shear banding, surface wrinkling and necking) of material bifurcation in plane sheet under tension are investigated in this paper by means of a numerical method. It is found that numerical analysis can provide better ground for searching for the lowest critical loads. The inhomogeneity caused by void damage and the nonuniformity in the stress distribution across sheet thickness are proved to have detrimental effects on the material bifurcation. Nevertheless, material stability can be promoted by any means of depressing void damage or alleviating stress, even locally across the thickness. Besides, the peculiar behaviour of material bifurcation under slight biaxiality state is demonstrated. Copyright (C) 1996 Elsevier Science Ltd

Notch sensitivity of circular rings subjected to impact loading

'Notch-sensitive regions' have been observed during a series of experimental investigations into the dynamic plastic behaviour and failure of thin-walled metallic radially notched circular rings with are-shaped supports subjected to concentrated impact loads. The experimental results show that the exterior notches at some regions have no effect on the deformation of the rings, but do have effect at the remaining regions. The notch-sensitive region is theoretically determined by using the equivalent structures technique; fairly good agreement has been reached between the simple theory and the experimental results. Both dimensional and theoretical analyses prove that whether a plastic hinge formed or not at the notched section does not depend on the mean radius of the ring and the input kinetic energy. It depends on the weak coefficient of the notched section and the angle of the support. Generally speaking, there are mainly three failure modes for a notched circular ring with are-shaped support under impact loading: Mode I, large inelastic deformation when the notch is outside the sensitive region, in this case the ring deforms as a normal one; Mode II, large inelastic deformation only at some part of the ring and tearing occurred at the notched sections; Mode III, large inelastic deformation and total rupture occurred at the notched sections. It is believed that the present study could assist the understanding of the dynamic behaviour and failure of other kinds of nonstraight components with macroscopic imperfections under impulsive loading.

Elastodynamic stress-intensity factors for a semiinfinite crack under 3-d combined mode loading

The dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body are analyzed. The crack is subjected to a traction distribution consisting of two pairs of suddenly-applied shear point loads, at a distance L away from the crack tip. The exact expression for the combined mode stress intensity factors as the function of time and position along the crack edge is obtained. The method of solution is based on the direct application of integral transforms together with the Wiener-Hopf technique and the Cagniard-de Hoop method, which were previously believed to be inappropriate. Some features of solutions are discussed and the results are displayed in several figures.

Stress-distribution at the rigid circular-arc inclusion end

The elastic plane problem of a rigid co-circular arc inclusion under arbitrary loads is dealt with. Applying Schwarz's reflection principle integrated with the analysis of the singularity of complex stress functions, the general solution of the problem is found and several closed-form solutions to some problems of practical importance are given. Finally, the stress distribution at the arc inclusion end is examined and a comparison is made with that of the rigid line inclusion end to show the effect of curvature.

Analysis of flexural vibration of viscoelastically damped sandwich plates

The simplified governing equations and corresponding boundary conditions of flexural vibration of viscoelastically damped unsymmetrical sandwich plates are given. The asymptotic solution of the equations is then discussed. If only the first terms of the asymptotic solution of all variables are taken as an approximate solution, the result is identical with that obtained from the Modal Strain Energy (MSE) Method. As more terms of the asymptotic solution are taken, the successive calculations show improved accuracy. With the natural frequencies and the modal loss factors of a damped sandwich plate known, one can calculate the response of the plate to various loads providing a reliable basis for engineering design.

Application of the strain energy density criterion to ductile fracture

The strain energy density criterion due to Sih is used to predict fracture loads of two thin plates subjected to large elastic-plastic deformation. The prediction is achieved with a finite element analysis which is based on Hill's variational principle for incremental deformations capable of solving gross yielding problems involving arbitrary amounts of deformation. The computed results are in excellent agreement with those obtained in Sih's earlier analysis and with an experimental observation.

Ductile crack propagation with the strain-energy density criterion

The strain energy density criterion is used to characterize subcritical crack growth in a thin aluminum alloy sheet undergoing general yielding. A finite element analysis which incorporates both material and geometrical nonlinear behaviors of the cracked sheets is developed to predict fracture loads at varying crack growth increments. The predicted results are in excellent agreement with those measured experimentally, thus confirming the validity of the strain energy density criterion for characterizing ductile crack propagation.

粉质粘土中的刚性桩在横向载荷作用下失稳的模型试验研究

为解释横向载荷作用下刚性桩的失稳机理,针对桩头自由的刚性桩做了一系列横向加载试验.基础土为粉质粘土,含水量介于9.85%～13.85%之间.由载荷-位移全过程曲线发现,刚性桩在横向载荷达到一定值时会失稳;由试验录像及土体剖面发现,由于土体的软化破坏,在桩后土体内会出现贯穿的局部破坏并形成一楔体,同时在土面伴随一不完全的椭圆形鼓包及一条平行于加载方向的拉伸裂缝,而在桩前土中,由于桩的挤压会形成一条侵彻沟.分析认为,对大位移刚性桩桩后土体的破坏是桩失稳的根本原因.

Optimal Minimum Wage in a Competitive Economy: an Alternative Modelling Approach

This paper analyzes whether a minimum wage can be an optimal redistribution policy when distorting taxes and lump-sum transfers are also available in a competitive economy. We build a static general equilibrium model with a Ramsey planner making decisions on taxes, transfers, and minimum wage levels. Workers are assumed to differ only in their productivity. We find that optimal redistribution may imply the use of a minimum wage. The key factor driving our results is the reaction of the demand for low skilled labor to the minimum wage law. Hence, an optimal minimum wage appears to be most likely when low skilled households are scarce, the complementarity between the two types of workers is large or the difference in productivity is small. The main contribution of the paper is a modelling approach that allows us to adopt analysis and solution techniques widely used in recent public finance research. Moreover, this modelling strategy is flexible enough to allow for potential extensions to include dynamics into the model.

Summary report on water quantity and quality studies of Vancouver Lake, Washington

Vancouver Lake, located adjacent to the Columbia River and just north of the Vancouver-Portland metropolitan area, is a "dying" lake. Although all lakes die naturally in geologic time through the process of eutrophication,* Vancouver Lake is dying more rapidly due to man's activities and due to the resultant increased accumulation of sediment, chemicals, and wastes. Natural eutrophication takes thousands of years, whereas man-made modifications can cause the death of a lake in decades. Vancouver Lake does, however, have the potential of becoming a valuable water resource asset for the area, due particularly to its location near the Columbia River which can be used as a source of "flushing" water to improve the quality of Vancouver Lake. (Document pdf contains 59 pages) Community interest in Vancouver Lake has waxed and waned. Prior to World War II, there were relatively few plans for discussions about the Lake and its surrounding land area. A plan to drain the Lake for farming was prohibited by the city council and county commissioners. Interest increased in 1945 when the federal government considered developing the Lake as a berthing harbor for deactivated ships at which time a preliminary proposal was prepared by the City. The only surface water connection between Vancouver Lake and the Columbia River, except during floods, is Lake River. The Lake now serves as a receiving body of water for Lake River tidal flow and surface flow from creeks and nearby land areas. Seasonally, these flows are heavily laden with sediment, septic tank drainage, fertilizers and drainage from cattle yards. Construction and gravel pit operations increase the sediment loads entering the Lake from Burnt Bridge Creek and Salmon Creek (via Lake River by tidal action). The tidal flats at the north end of Vancouver Lake are evidence of this accumulation. Since 1945, the buildup of sediment and nutrients created by man's activities has accelerated the growth of the large water plants and algae which contribute to the degeneration of the Lake. Flooding from the Columbia River, as in 1968, has added to the deposition in Vancouver Lake. The combined effect of these human and natural activities has changed Vancouver Lake into a relatively useless body of shallow water supporting some wildlife, rough fish, and shallow draft boats. It is still pleasant to view from the hills to the east. Because precipitation and streamflow are the lowest during the summer and early fall, water quantity and quality conditions are at their worst when the potential of the Lake for water-based recreation is the highest. Increased pollution of the Lake has caused a larger segment of the community to become concerned. Land use and planning studies were undertaken on the Columbia River lowlands and a wide variety of ideas were proposed for improving the quality of the water-land environment in order to enhance the usefulness of the area. In 1966, the College of Engineering Research Division at Washington State University (WSU0 in Pullman, Washington, was contacted by the Port of Vancouver to determine possible alternatives for restoring Vancouver Lake. Various proposals were prepared between 1966 and 1969. During the summer and fall of 1967, a study was made by WSU on the existing water quality in the Lake. In 1969, the current studies were funded to establish a data base for considering a broad range of alternative solutions for improving the quantity and quality of Vancouver Lake. Until these studies were undertaken, practically no data on a continuous nature were available on Vancouver Lake, Lake River, or their tributaries. (Document pdf contains 59 pages)

客运架空索道线路支架的极限承载力分析

给出了用来分析客运架空索道线路支架极限承载力的一种有效的有限元分析方法，重点讨论使用该方法的具体分析过程，同时给出了编程框图，最后通过实例作了进一步的说明。

A rational fraction polynomials model to study vertical dynamic wheel-rail interaction

This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel-rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel-rail contact passing over a welding defect at different speeds.

Reducing non-point DOC and nitrogen exports from rice fields: A pilot study and quantitative survey to determine the effects of different hydrologic management practices : Deliverable 15.3 Final Report

Rice cultivation at any level in the Sacramento–San Joaquin Delta (existing or expanded) compels the need to quantify surface and subsurface loads of dissolved organic carbon (DOC), disinfection byproduct precursors (DBPPs) and nitrogen. This information can be used to develop Best Management Practices (BMPs) to reduce export of these constituents in order to improve drinking water quality. Although rice cultivation in the Delta is relatively limited, several factors outside of this research could contribute to increased rice acreage in the Delta: • Recently developed rice varieties seem more suitable for the Delta climate than earlier varieties which required warmer conditions; • Previous economic analyses (Appendix A.10) suggest rice is more profitable than corn, a dominant land use in the Delta; • Recent studies on wetlands at Twitchell Island suggest rice production can help mitigate oxidative subsidence (Miller et al. 2000); • The different oxidative states that result from flooding in rice as compared to those found in crops that require drained soils may help control crop specific weeds and nematodes when rice is incorporated into a crop rotation; and • Providing flooded conditions during a greater part of the year than other crops may benefit water birds. ... (PDF contains 249 pages)