A spectral‐element method for modelling cavitation in transient fluid–structure interaction

In an underwater‐shock environment, cavitation (boiling) occurs as a result of reflection of the shock wave from the free surface and/or wetted structure causing the pressure in the water to fall below its vapour pressure. If the explosion is sufficiently distant from the structure, the motion of the fluid surrounding the structure may be assumed small, which allows linearization of the governing fluid equations. In 1984, Felippa and DeRuntz developed the cavitating acoustic finite‐element (CAFE) method for modelling this phenomenon. While their approach is robust, it is too expensive for realistic 3D simulations. In the work reported here, the efficiency and flexibility of the CAFE approach has been substantially improved by: (i) separating the total field into equilibrium, incident, and scattered components, (ii) replacing the bilinear CAFE basis functions with high‐order Legendre‐polynomial basis functions, which produces a cavitating acoustic spectral element (CASE) formulation, (iii) employing a simple, non‐conformal coupling method for the structure and fluid finite‐element models, and (iv) introducing structure–fluid time‐step subcycling. Field separation provides flexibility, as it admits non‐acoustic incident fields that propagate without numerical dispersion. The use of CASE affords a significant reduction in the number of fluid degrees of freedom required to reach a given level of accuracy. The combined use of subcycling and non‐conformal coupling affords order‐of‐magnitude savings in computational effort. These benefits are illustrated with 1D and 3D canonical underwatershock problems. Copyright © 2004 John Wiley & Sons, Ltd.     

A finite element formulation to identify damage fields: the equilibrium gap method

It is proposed to determine damage parameters in two dimensions (surface of a material) or three dimensions (in the bulk of a solid) by using full‐field displacement measurements. A finite‐element approach is developed to evaluate piece‐wise constant elastic parameters modeled by an isotropic damage variable. Two sets of examples are discussed. The first series deals with mechanical fields obtained by finite element simulations to assess the performance of the approach. The second series is concerned with displacement measurements performed during a biaxial test on a composite material. Copyright © 2004 John Wiley & Sons, Ltd.     

Exact static element stiffness matrices of non‐symmetric thin‐walled curved beams

An evaluation procedure of exact static stiffness matrices for curved beams with non‐symmetric thin‐walled cross section are rigorously presented for the static analysis. Higher‐order differential equations for a uniform curved beam element are first transformed into a set of the first‐order simultaneous ordinary differential equations by introducing 14 displacement parameters where displacement modes corresponding to zero eigenvalues are suitably taken into account. This numerical technique is then accomplished via a generalized linear eigenvalue problem with non‐symmetric matrices. Next, the displacement functions of displacement parameters are exactly calculated by determining general solutions of simultaneous non‐homogeneous differential equations. Finally an exact stiffness matrix is evaluated using force–deformation relationships. In order to demonstrate the validity and effectiveness of this method, displacements and normal stresses of cantilever thin‐walled curved beams subjected to tip loads are evaluated and compared with those by thin‐walled curved beam elements as well as shell elements. Copyright © 2004 John Wiley & Sons, Ltd.     

Algorithms for the analysis of 3D finite strain contact problems

From the constraint imposition aspects in 3D to friction regularization, various ideas are exposed in this paper. A variation of the Rockafellar Lagrangian is proposed which results in continuous second‐order derivatives if Lagrange multiplier estimates are greater or equal than one. This fact allows the adoption of a full second‐order (i.e. Lagrange–Newton) method avoiding sequential unconstrained minimization techniques. An algorithm for global and local contact detection is presented which is developed for dealing with large step sizes typical of implicit methods. A modified constraint definition to deal with non‐smooth situations is presented. Aspects of friction implementation, including a regularization scheme which ensures stepwise objectivity, are detailed. Finally, several illustrative examples are carried out with success. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical solution of second‐order,two‐point boundary value problems using continuous genetic algorithms

Second‐order, two‐point boundary‐value problems are encountered in many engineering applications including the study of beam deflections, heat flow, and various dynamic systems. Two classical numerical techniques are widely used in the engineering community for the solution of such problems; the shooting method and finite difference method. These methods are suited for linear problems. However, when solving the non‐linear problems, these methods require some major modifications that include the use of some root‐finding technique. Furthermore, they require the use of other basic numerical techniques in order to obtain the solution. In this paper, the author introduces a novel method based on continuous genetic algorithms for numerically approximating a solution to this problem. The new method has the following characteristics; first, it does not require any modification while switching from the linear to the non‐linear case; as a result, it is of versatile nature. Second, this approach does not resort to more advanced mathematical tools and is thus easily accepted in the engineering application field. Third, the proposed methodology has an implicit parallel nature which points to its implementation on parallel machines. However, being a variant of the finite difference scheme with truncation error of the order O(h²), the method provides solutions with moderate accuracy. Numerical examples presented in the paper illustrate the applicability and generality of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.     

Two simple and efficient displacement‐based quadrilateral elements for the analysis of composite laminated plates

Two simple 4‐node 20‐DOF and 4‐node 24‐DOF displacement‐based quadrilateral elements named RDKQ‐L20 and RDKQ‐L24 are developed in this paper based on the first‐order shear deformation theory (FSDT) for linear analysis of thin to moderately thick laminates. The deflection and rotation functions of the element sides are obtained from Timoshenko's laminated composite beam functions. Linear displacement interpolation functions of the standard 4‐node quadrilateral isoparametric plane element and displacement functions of a quadrilateral plane element with drilling degrees of freedom are taken as in‐plane displacements of the proposed elements RDKQ‐L20 and RDKQ‐L24, respectively. Due to the application of Timoshenko's laminated composite beam functions, convergence can be ensured theoretically for very thin laminates. The elements are simple in formulation, and shear‐locking free for extremely thin laminates even with full integration. A hybrid‐enhanced procedure is employed to improve the accuracy of stress analysis, especially for transverse shear stresses. Numerical tests show that the new elements are convergent, not sensitive to mesh distortion, accurate and efficient for analysis of thin to moderately thick laminates. Copyright © 2004 John Wiley & Sons, Ltd.     

Higher‐order extensions of a discontinuous Galerkin method for mid‐frequency Helmholtz problems

Recently, a discontinuous Galerkin method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution of Helmholtz problems in the mid‐frequency regime. In this paper, this method is extended to higher‐order elements. Performance results obtained for various two‐dimensional problems highlight the advantages of these elements over classical higher‐order Galerkin elements such as Q₂ and Q₄ for the discretization of interior and exterior Helmholtz problems. Copyright © 2004 John Wiley & Sons, Ltd.     

A changing range genetic algorithm

During the last decade various methods have been proposed to handle linear and non‐linear constraints by using genetic algorithms to solve problems of numerical optimization. The key to success lies in focusing the search space towards a feasible region where a global optimum is located. This study investigates an approach that adaptively shifts and shrinks the size of the search space to the feasible region; it uses two strategies for estimating a point of attraction. Several test cases demonstrate the ability of this approach to reach effectively and accurately the global optimum with a low resolution of the binary representation scheme and without additional computational efforts. Copyright © 2004 John Wiley & Sons, Ltd.     

Development of a system for measurement of permeability of aroma compounds through multilayer polymer films by coupling dynamic vapour sorption with purge‐and‐trap/fast gas chromatography

A system for measurement of permeability of aroma compounds through laminated polymer films was constructed by combining dynamic vapour sorption (DVS) with purge‐and‐trap/fast gas chromatography (P&T–fGC). Data validation was achieved by measuring the permeability of limonene across an HDPE film (film C) and comparing the permeation data with the literature values. The general applicability of this system, as well as its potential for simultaneous measurement of permeability of multiple aroma compounds, was demonstrated by measuring the permeability of limonene and ethyl butyrate as single permeants or as co‐permeants under different environmental conditions (at 25°C, 30°C or 35°C and 0% or 75% RH) through three different multilayer polymer films (film A, HDPE/EVOH/HDPE/HDPE; film B, HDPE/nylon/HDPE/HDPE; film C, HDPE/HDPE). The results showed that the aroma barrier performance of plastic films was determined by the polymer composition and was affected by various factors, such as temperature and the presence of other co‐permeants. Simplicity, speed and accuracy were some of the attractive features of this system, which indicates its potential as a useful tool that could be applied in the food industry for screening or selection of appropriate packaging materials for specific applications. Copyright © 2004 John Wiley & Sons, Ltd.     

Assessment of oxygen levels in convenience‐style muscle‐based sous vide products through optical means and impact on shelf‐life stability

An optical oxygen analyser was used in two small‐scale industrial trials to non‐destructively assess the quality of packaged convenience foods and packaging process. Beef lasagne packed under 70% vacuum and cooked under standard sous vide conditions was monitored for residual oxygen, using disposable sensors incorporated in each pack and a benchtop optical oxygen analyser. High levels of residual oxygen close to ambient were determined in the majority of packs after packaging, as opposed to anticipated levels of 4–5%. Residual oxygen was monitored over product shelf‐life (4 weeks at +4–10°C) along with measurement of microbial growth and lipid oxidation in food by conventional destructive methods. Oxygen levels in packs went down to almost zero between weeks 2 and 3 indicating deterioration of packaged product. Correlation between oxygen profiles and the rate of microbial growth and lipid oxidation was established. The optical oxygen sensor system was shown to provide valuable information about performance of the packaging process, product storage conditions and food quality in a convenient and cost‐efficient fashion and non‐destructively. Copyright © 2004 John Wiley & Sons, Ltd.