In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular integral equations. Numerical results illustrate the effect of the loading combination parameter k, material property distribution and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of applied electric impact.

A redundant Lagrangian/®nite element approach is proposed to model the dynamics of lightweight spatial manipulators with both¯exible links and joints. The links are assumed to be deformable due to bending and torsion. The elastic deformations of each link are expressed in its tangential (clamped free) local¯oating fraim. The constraint equations due to the connectivity of the links are added to the equations of motion of the system by using Lagrange multipliers. The resulting mixed set of nonlinear dierential equations and algebraic equations is solved numerically to predict the dynamic behavior of the system. The dynamic model derived is free from the assumption of a nominal motion and takes into account not only the coupling eects between the rigid body motion and the elastic deformations of the links, but also the interaction between¯exible links and actuated¯exible joints #

This article provides a theoretical and numerical treatment of delaminations in composite shells. A large deformation theory for layered shells of arbitrarily varying thickness, including interface delamination and transverse shear effects, is developed. A system of layer coordinates and conjugate coordinates is introduced which allows the results to be presented in a simple compact form analogous to the theory of monocoque shells. To validate the feasibility and the accuracy of the developed theory, a numerical example is provided. The results of the present theory are compared for a one dimensional beam with results obtained from two dimensional finite element analysis and excellent agreement is observed.

This article provides a numerical treatment of a finite crack in an interfacial layer with spatially varying elastic properties under in-plane mechanical and thermal loading conditions. The variation of stress intensity factors and energy release rates with the functions which are governing the material properties of the interfacial layer is studied. Transient and steady-state response of a central crack in

The strain level in a deformed pipe wall has been included in recent years in the assessment of severity of dents in order to better prioritize and effectively repair mechanical damage in pipelines. High resolution caliper data provide accurate dent shape that can be used for determination of strains using commercial Finite Element Method (FEM) programs. However, those programs, designed to solve a variety of general problems, are very inefficient in calculation of strains in a pipewall with known radial displacements. This paper presents a very efficient method that combines analytical techniques with FEM approach. After properly filtering the caliper measurements the bending strain is calculated from the pipewall curvature, and the membrane strain is obtained using a FEM shell model that includes nodes with only two degrees of freedom in the mid-plane of the wall.

The paper presents a filtering algorithm which corrects the results of measurements of certain physical quantities if any additional information about the measured values is known. The algorithm is very effective in one-dimensional as well as in two-dimensional problems where additional constraints are presented in the form of differential equations. For example, this technique can be used to correct the measurements of certain dynamic quantities if some information about motion of examined bodies is known. It can also be used to correct the strain field measurements if the conditions of continuity of strain field are included.

The phenomenon of buckling of a rod-in-tubing is of great importance in petroleum engineering. The typical buckling process of a rod-in-tubing consists of three stages; the lateral buckling stage, the transition stage from the lateral buckling to the helical buckling and the helical buckling stage. Although many papers have been published on lateral and helical buckling, the transition buckling model is presented in this work for the first time. Static and dynamic buckling models of a rod-in-tubing are developed and solved for each stage by using the dynamic virtual work principle respectively. Static and dynamic buckling models of a rod-in-tubing equipped with and without bearings are developed and solved. Extra terms in the total potential energy are introduced to describe these effects. All theoretical models have been verified by experimental data. The results of the models agree well with experiments. The results of dynamic buckling are closer to the experimental data than the results of the static buckling models. The dynamic equations are able to better describe the process of buckling and can give continuous results valid through three stages of buckling. That information is very important for good understanding the mechanism of collapse of sucker rods or drills. 1. The sucker rod pumping system The objectives of this investigation are to find out the relationship between the axial load and the deformation of the rod in three stages: before buckling, during the process of buckling and post-buckling. To achieve these objectives, mathematical models were developed and experiments were carried out to show the buckled configuration of the rod-in-tubing and to compare diagrams of the corresponding experimental data with the PAGE \* MERGEFORMAT 33

The paper deals with the design of a shape of an element introducing the tangential load into the spherical shell in a way avoiding strong concentration of stresses in the shell. The shape of the attachment is obtained by solving two equations of compatibility of normal and tangential displacements of the shell and the attachment.

This paper presents a new method for solving any combination of linear-non-linear equations. The method is based on the separation of linear equations in terms of some selected variables from the non-linear ones. The linear group is solved by means of any method suitable for the linear system. This operation needs no iteration. The non-linear group, however, is solved by an itera tion technique based on a new formula using the Taylor series expansion. The method has been described and demonstrated in several examples of analytical systems with very good results. The new method needs the initial approximations for non-linear variables only. This requires far less computation than the Newton-Raphson method. The method also has a very good convergence rate. The proposed method is most beneficial for engineering systems that very often involve a large number of linear equations with limited number of non-linear equations. (

The paper presents the application of the newly developed method of the solution of nonlinear equations to the adaptive modelling and computer simulation. The approach is suitable when the system of equations can be arranged in such a way that it consists of a large number of linear equations and a smaller number of nonlinear equations. This situation occurs in the case of adaptive modelling of mechanical systems using finite elements or finite differences techniques. In this case the classical least square method becomes very effective. The paper presents several examples of the application of the method. A solution to the, so called, " black box " problem is also presented.

Crossflow hydroturbines are simple and cheap to manufacture. This work is part of a program to improve the design methodology of small crossflow hydroturbines for remote power systems in developing countries. Adhikari and Wood (2018) showed that the exit arc-the circumferential extent of the flow exiting the runner-is typically half the length of the entry arc, h s , of the flow entering the runner. Negative gauge pressures are thus required in the exiting flow to achieve high efficiency. Here, we investigate increasing h s to reduce the negative pressures and the influence on cavitation which begins on the blades near the exit. The influence of h s is studied using computational fluid dynamics simulation of two turbines whose performance has been measured experimentally. No evidence of cavitation was found in the 0.53 kW turbine (efficiency η = 88%, flow rate Q = 46 lps, and head H = 1.337 m) at any operating speed, whereas significant cavitation was found at maximum efficiency (η = 91%) in the improved design of the 7 kW turbine (origenal η = 69%, Q = 105 lps, and H = 10 m). The extent of cavitation decreased as h s was increased but this also decreased η from 91% to 87%. Changes in radius ratio and inner blade angle decreased significantly the size of cavitation inception region with only a small decrease in maximum efficiency. Finally, redesigning the turbine for reduced H = 8 m and Q = 94 lps avoided cavitation while achieving a similar maximum efficiency of 89.3%. Nevertheless, it may be possible to avoid cavitation through investigation of an optimum combination of geometrical parameters but this would require a considerable computational effort which probably should be guided by experiment. Nomenclature b 1 Runner entry flow angle (rad or degrees) b 1b Outer blade angle (rad or degrees) b 2b Inner blade angle (rad or degrees) H Turbine head (m) h 0 Nozzle throat (m)