What to Learn,What to Learn

Experimental Techniques -     

An Introduction to the Adjoint Approach to Design

Optimal design methods involving the solution of an adjoint system of equations are an active area of research in computational fluid dynamics, particularly for aeronautical applications. This paper presents an introduction to the subject, emphasising the simplicity of the ideas when viewed in the context of linear algebra. Detailed discussions also include the extension to p.d.e.'s, the construction of the adjoint p.d.e. and its boundary conditions, and the physical significance of the adjoint solution. The paper concludes with examples of the use of adjoint methods for optimising the design of business jets. This revised version was published online in July 2006 with corrections to the Cover Date.     

An Introduction to Differential Geometry with Applications to Elasticity

Journal of Elasticity -     

Global and local approaches to fracture normal to interfaces

The problem of a crack perpendicularly approaching a bimaterial interface is examined using both global and localapproaches to fracture. The global approach is based on the J-integral with a second parameter, Q, which scales the stress triaxiality ahead of the crack. The local approach is based on either brittle fracture(Beremin model ) or ductile fracture (Rice and Tracey model ). In the first case, the Weibull stress over the plasticzone is calculated. In the second case, the void growth rate is calculated at the tip of the crack over a representativevolume (generally associated with a characteristic length of the material ). After a brief summary of each approach,the results for a crack near an elastically homogeneous, plastically mismatched interface are presented. Thebehaviour of the bimaterial is expressed in relation to the behavior of the homogeneous material. It is shown thatthere is an effect on the crack behavior which depends on the direction of crack propagation, i.e. from the hardermaterial to the softer material or vice versa. This effect is examined as a function of change in yield strength ratioand hardening exponent, n. For the case of brittle fracture, the effect of changing the Weibull modulus, m, is also examined. The models based on the local approach show that both stress- and strain-controlledfracture mechanisms must be accounted for. This implies the necessity of using the two parameters J and Q in the global approach. This is due to the fact that the stress–strain fields ahead of the crack tip areaffected by the nature of the second material.     

Relationship between paddy soil adhesion to steel and to rubber

Forty-three pairs of samples concerning adhesion of paddy soil to steel and to rubber are used to identify the relationship between these two groups of variables. Results show that there is no significant difference between them, implying that they are roughly equal to each other in engineering practice.     

Methodology to assess integrity with application to collector copper lamellas

The performance of engineering components and structures is strongly influenced by the interaction between design, manufacture and materials. A methodology to assess the integrity of a circular collector is presented by investigating the failure of copper lamellas. The investigated circular collector, having 315 copper lamellas, is one of the main parts of an electric motor. The fracture of the copper lamellas was observed in normal operation. This unexpected fracture required an investigation of the fracture origin, in order to improve the initial design. The numerical results of the finite element analysis on the stress field in the copper lamellas for the operating regimes, and the stress concentration effects are shown. Failure assessment diagram, based on notch stress intensity factor, was considered in order to estimate if crack initiation can occur. Finally a study of crack propagation will present comparatively the numerical obtained crack path against the one observed in-service.     

Extension to three dimensions of a holographic-moiré technique to separate patterns corresponding to components of displacement

The holographic-moiré technique to obtain separate patterns for the Cartesian components of the displacement vector is extended to curved surfaces. An initial pattern which is often required for the observation of the displacement fringes is analyzed for this case. Criteria are established for the localization of this initial pattern to follow close to the contour of the object surface. A PVC pipe subjected to torsion demonstrates the proposed technique and, when analytical arguments are checked experimentally, a close correlation is observed.     

约束力学系统引入待定乘子的两种方式

讨论约束力学系统中引入待定乘子两种不同的途径及其对应的物理意义.一种方式引入待定乘子是处理非独立坐标变更,乘子与约束反力相关;另一种方式是变分原理条件极值要求,乘子与系统的拉格朗日函数相关.对完整系统由两种途径导出的带乘子运动方程是相同的,但是对非完整系统则分别导出两种不同的运动方程:罗斯方程和维科(Vacco)方程.     

Back to basics

Experimental Techniques -     

Back to basics

Experimental Techniques -     

Back to basics

Experimental Techniques -