Flood Routing Models in Confluent and Dividing Channels

By introducing a water depth connecting formula, the hydraulic equations in the dividing channel system were coupled and the relation of discharge distribution between the branches of the dividing channels can be yielded. In this manner, a numerical model for the confluent channels was established to study the variation of backwater effects with the parameters in the channel junction. The meeting of flood peaks in the mainstream and tributary can be analyzed with this model. The flood peak meeting is found to be a major factor for the extremely high water level in the mainstream during the 1998 Yangtze River flood. Subsequently the variations of discharge distribution and water level with channel parameters between each branch in this system were studied as well. As a result, flood evolution caused by Jingjiang River shortcut and sediment deposition in the entrance of dividing channels of the Yangtze River may be qualitatively elucidated. It is suggested to be an effective measure for flood mitigation to enhance regulation capability of reservoirs available upstream of the tributaries and harness branch entrance channels.

Practical matching of principal stress field geometries in composite components

A simple composite design methodology has been developed from the basic principles of composite component failure. This design approach applies the principles of stress field matching to develop suitable reinforcement patterns around three-dimensional details such as lugs in mechanical components. The resulting patterns are essentially curvilinear orthogonal meshes, adjusted to meet the restrictions imposed by geometric restraints and the intended manufacturing process. Whilst the principles behind the design methodology can be applied to components produced by differing manufacturing processes, the results found from looking at simple generic example problems suggest a realistic and practical generic manufacturing approach. The underlying principles of the design methodology are described and simple analyses are used to help illustrate both the methodology and how such components behave. These analyses suggest it is possible to replace high-strength steel lugs with composite components whose strength-to-weight ratio is some 4-5 times better. © 1998 Elsevier Science Ltd. All rights reserved.

Topics in bifurcation theory

I. Existence and Structure of Bifurcation Branches

The problem of bifurcation is formulated as an operator equation in a Banach space, depending on relevant control parameters, say of the form G(u,λ) = 0. If dimN(G_u(u_O,λ_O)) = m the method of Lyapunov-Schmidt reduces the problem to the solution of m algebraic equations. The possible structure of these equations and the various types of solution behaviour are discussed. The equations are normally derived under the assumption that G^O_λεR(G^O_u). It is shown, however, that if G^O_λεR(G^O_u) then bifurcation still may occur and the local structure of such branches is determined. A new and compact proof of the existence of multiple bifurcation is derived. The linearized stability near simple bifurcation and "normal" limit points is then indicated.

II. Constructive Techniques for the Generation of Solution Branches

A method is described in which the dependence of the solution arc on a naturally occurring parameter is replaced by the dependence on a form of pseudo-arclength. This results in continuation procedures through regular and "normal" limit points. In the neighborhood of bifurcation points, however, the associated linear operator is nearly singular causing difficulty in the convergence of continuation methods. A study of the approach to singularity of this operator yields convergence proofs for an iterative method for determining the solution arc in the neighborhood of a simple bifurcation point. As a result of these considerations, a new constructive proof of bifurcation is determined.