On the modelling of smooth contact surfaces using cubic splines

In this paper, a new strategy for the smooth representation of 2D contact surfaces is developed and implemented. The contact surfaces are modelled using cubic splines which interpolate the finite element nodes. These splines provide a unique surface normal vector and do not require prior knowledge of surface tangents and normals. C²‐continuous cubic splines are suitable for representing rigid contact surfaces, while C¹‐continuous Overhauser splines are shown to be most suitable for representing flexible contact surfaces. A consistent linearization of the kinematic contact constraints, based on the spline interpolation, is derived. The new spline‐based contact surface interpolation scheme does not influence the element calculations. Consequently, it can be easily implemented in standard FE codes. Several numerical examples are used to illustrate the advantages of the proposed smooth representation of contact surfaces. The results show a significantimprovement in accuracy compared to traditional piecewise element‐based surface interpolation. The predicted contact stresses are also less sensitive to the mismatch in the meshes of the different contacting bodies. This property is useful for problems where the contact area is unknown a priori and when there is significant tangential slip. Copyright © 2001 John Wiley & Sons, Ltd.     

Large deformation analysis of contact in degenerate shell elements

A new formulation is presented for the analysis of contact in degenerate shell elements. This formulation accounts for the transverse stress and strain through the shell thickness and can accommodate double-sided shell contact. The kinematic contact conditions are expressed accurately in terms of the physical shell contacting surfaces, and the problem is formulated in terms of Variational Inequalities (VI). Large deformations and rotations are accounted for by invoking the appropriate stress and strain measures. The solution of the variational inequality is obtained using Lagrange multipliers. This guarantees that the kinematic contact constraints are accurately satisfied and that the solution is free from user-defined parameters. Two examples involving three beams in contact and ring compression are simulated to establish the validity of the developed formulations and the solution technique. © 1998 John Wiley & Sons, Ltd.     

Pitting susceptibility of UNS NO. 8904 stainless steel in bromide-sulphide solution

The effect of sulphide ion on the pitting corrosion behaviour of UNS* no. 8904 (904L) stainless steel (SS) in 0.6 M NaBr at 25 °C has been investigated by using potentiodynamic anodic polarization and electrochemical impedance spectroscopy techniques. The pitting potential, E _pit, in 0.6 M NaBr + 10^–2 M Na₂S was more negative than that obtained in 0.6 M NaBr, and decreased with increasing temperature in the range 25–60 °C. Scanning electron microscopy observation showed that elemental sulphur formed on the steel surface before E _pit was reached in 0.6 M NaBr + 10^–2 M Na₂S at 60°C. E _pit of 904L SS pH independent in the pH range from 3–10 of 0.6 M NaBr + 10^–2 M Na₂S at 25 °C, while at high pH values the pitting was suppressed. The impedance measurements showed that the charge transfer resistance, R _t, decreased with time, when the controlled potential became higher than E _pit.     

Optimal shape control of functionally graded smart plates using genetic algorithms

This paper deals with optimal shape control of functionally graded smart plate containing patches of piezoelectric sensors and actuators. The genetic algorithm (GA) is designed to search for optimal actuator voltage and displacement control gains for the shape control of the functionally graded material (FGM) plates. The work extends the earlier finite element formulations of the two leading authors, so that it can be readily treated using genetic algorithms. Numerical results have been obtained to study the effect of the shape control of the FGM plates under a temperature gradient by optimising (i) the voltage distribution for the open loop control, and (ii) the displacement control gain values for the closed loop feedback control. The effect of the constituent volume fractions of zirconia, through varying the volume fraction exponent n, on the optimal voltages and gain values has also been examined.     

Elasto-plastic behaviour of cantilever beams containing varied stress concentration cut out features

International Journal of Mechanics and Materials in Design - In machine component design, it is necessary to introduce openings or cut outs to carry out specific service functions such as...     

Thermomechanical postbuckling analysis of functionally graded plates and shallow cylindrical shells

Summary. In this paper, an analytic solution is provided for the postbuckling behavior of plates and shallow cylindrical shells made of functionally graded materials under edge compressive loads and a temperature field. The material properties of the functionally graded shells are assumed to vary continuously through the thickness of the shell according to a power law distribution of the volume fraction of the constituents. The fundamental equations for thin rectangular shallow shells of FGM are obtained using the von Karman theory for large transverse deflection, and the solution is obtained in terms of mixed Fourier series. The effect of material properties, boundary conditions and thermomechanical loading on the buckling behavior and stress field are determined and discussed. The results reveal that thermomechanical coupling effects and the boundary conditions play a major role in dictating the response of the functionally graded plates and shells under the action of edge compressive loads.     

Bio-inspired wing morphing for unmanned aerial vehicles using intelligent materials

Biologically inspired engineering or Biomimicry is the practice of developing designs and technologies inspired by nature. This conscious use of examples from nature is a form of applied case-based reasoning thus treating nature itself as a database of solutions that have survived for millions of years-survival of the fittest. Inspired by nature, we have developed aircraft wings that imitate the amazing flight of birds. This bio-inspired effort, which is the result of a collaborative research program with Defence Science Organisation National Laboratories of Singapore, is concerned with the design and development of a novel wing prototype for unmanned aerial vehicles (UAVs) that morphs seamlessly without the use of complex hydraulics and/or servo motors. The novel design, selected from a number of designs, is characterised by a high degree of flight adaptability, enhanced manoeuvrability and improved performance with a limited added weight. These characteristics were attained through the use of shape memory alloys as actuators in an antagonistic fashion. Unlike compliant actuators that require continued input of thermal energy, antagonistic setup does not suffer from this difficulty. This is because they require the thermal energy to deform the wing but not to maintain its morphed shape. Structural analysis based upon safety factors specified by FAR23 standards and aerodynamic analysis using FLUENT were conducted on the novel designs to validate their suitability as viable wings for UAVs. In addition, conditioning of the shape memory actuators was conducted using a specially designed circuitry that imposes the appropriate heating and cooling cycles at set periodic times. The outcome of this study is manifest in the new designs that satisfy the missions of different UAVs.     

On the elastic solution of frictional contact problems using variational inequalities

This article is devoted to the development and implementation of a variational inequalities approach to treat the general frictional contact problem. Unlike earlier studies which adopt penalty methods for the solution of the corresponding variational inequalities, the current investigation uses quadratic programming and Lagrange's multipliers to solve the frictional contact problem and identify the candidate contact surface. The proposed method avoids the use of user-defined penalty parameters, which ultimately govern the convergence and accuracy of the solution. To establish the validity of the method, a number of test cases are examined and compared with existing solutions where penalty methods are employed.     

Modelling and analysis of the dynamic behaviour of piezoelectric materials containing interacting cracks

This study is concerned with the treatment of the dynamic behaviour of piezoelectric materials containing interacting cracks under antiplane mechanical and inplane electric loading. A general electrical boundary condition is used to enable the treatment of both permeable and impermeable conditions along the crack surfaces. The theoretical solution of the problem is formulated using integral transform techniques and an appropriate pseudo-incident wave method. The resulting singular integral equations are solved using Chebyshev polynomials to provide the dynamic stress and electric fields. Numerical examples are provided to show the effect of the geometry of the cracks, the piezoelectric constant of the material and the frequency of the incident wave upon the dynamic stress intensity factors. The results show the significant effect of electromechanical coupling upon local stress distribution.     

3D Effects of Surface Construction Over Existing Subway Tunnels

A 3D elasto‐plastic finite element model is used to examine the effect of construction over two existing tunnels. Tunnel deformation and the change in lining shape are compared with the field measurements of the York‐Mills Centre project constructed in 1989 over an existing Toronto subway tunnel. The criterion for potential damage to the tunnel liner is established based on the extreme fiber stresses of the lining. Typical 2D plane strain analyses were also conducted to investigate the importance of the 3D analysis in this case. Reasonable agreement is found between the observed field measurements and the predicted results using the 3D numerical simulation.