A hybrid flux model for heat conduction problems

A hybrid method of solution for the linear problem of heat conduction in a body is presented. The variational support is a two‐field functional whose arguments are heat flux, which meets a priori inner thermal equilibrium, and temperature on the boundary of the body. The stationary conditions of the functional are the Fourier's law and the prescribed boundary conditions. This variational framework allows to develop a finite element model that exhibits good accuracy, especially in the presence of geometry irregularities in a mesh. Copyright © 2000 John Wiley & Sons, Ltd.     

A discontinuous Galerkin method for a hyperbolic model for convection–diffusion problems in CFD

This paper proposes a hyperbolic model for convection–diffusion transport problems in computational fluid dynamics (CFD). The hyperbolic model is based on the so‐called Cattaneo's law. This is a time‐dependent generalization of Fick's and Fourier's laws that was originally proposed to solve pure‐diffusive heat transfer problems. We show that the proposed model avoids the infinite speed paradox that is inherent in the standard parabolic model. A high‐order upwind discontinuous Galerkin (DG) method is developed and applied to classic convection‐dominated test problems. The quality of the numerical results is remarkable, since the discontinuities are very well captured without the appearance of spurious oscillations. These results are compared with those obtained by using the standard parabolic model and the local DG (LDG) method and with those given by the parabolic model and the Bassi–Rebay scheme. Finally, the applicability of the proposed methodology is demonstrated by solving a practical case in engineering. We simulate the evolution of pollutant being spilled in the harbour of A Coruña (northwest of Spain, EU). Copyright © 2007 John Wiley & Sons, Ltd.     

Three-dimensional solution of low-velocity impact on sandwich panels with hybrid nanocomposite face sheets

In this article, a three-dimensional solution based on Fourier's series and the generalized differential quadrature method is presented to model the low-velocity impact on sandwich panels with hybrid nanocomposite face sheets. Navier's equations are derived and displacements are substituted by their corresponding Fourier's series. The contact force is considered as a Fourier's series of impactor displacement and deflection of contact point. To verify the theoretical model, experiments are performed on a polyurethane foam-cored sandwich panel with epoxy/woven-fiberglass/nanosilica hybrid nanocomposite face sheets. Contact force and lateral displacement of contact point histories are compared with the theoretical model.     

Hamilton's law of variable mass system and time finite element formulations for time‐varying structures based on the law

Traditional principles of mechanics are primarily conceived for constant mass systems, which are only valid if mass is gained or lost at null velocity with respect to an inertial reference frame for variable mass systems, thus the numerical algorithms for time‐varying structures based on these principles are only suitable for this special case. In this paper, Hamilton's law of variable mass system is derived based on Meshchersky's fundamental equation, and two classes of novel time finite element formulations for linear systems with arbitrary continuous time‐varying parameters are developed based on the previous law. The formulations are verified extensively through numerical examples in which the convergence and effectiveness of algorithms are evaluated. Numerical examples demonstrate that compared with the algorithms for time‐varying structures that developed based on traditional principles of mechanics, the proposed algorithms provide extended capabilities in both time‐varying mass problems that mass is gained or lost at any velocity (such as rocket problem) and moving‐mass problems (such as vehicle‐bridge interaction problem) besides the time‐varying stiffness and damping problems, the proposed algorithms have a wider range of application. In particular, Hamilton's law of variable mass system provides a solid theoretical foundation for further research on the algorithm design for time‐varying structures. Copyright © 2014 John Wiley & Sons, Ltd.     

Extending RSA cryptosystems to proxy multi‐signature scheme allowing parallel individual signing operation

Abstract

Even though there have been many research studies on proxy signature schemes, only Shao's proxy multi‐signature scheme is based on the factoring problem (FAC). Unfortunately, Shao's scheme requires sequential signing operations and strict order of the modulus. It is not practical and not efficient. We, therefore, based on RSA cryptosystems, propose new proxy‐protected mono‐signature and proxy‐protected multi‐signature schemes. In contrast to their counterparts, our scheme allows parallel signing operations and also improves the signers’ computational performance.     

A Representative volume model for a CNT composite material

The concept of a ‘Representative Volume Model’ is used in combination with ‘Equivalent Mechanical Strain’ or Aboudi's ‘Average Strain’ theorem to illustrate how a carbon nanotube reinforced composite material constitutive law for a nano‐composite material can be implemented into a finite element program for modeling structural applications. Current methods of modeling each individual composite layer to build up an element composed of carbon nanotube reinforced composite material may not be the best approach for modeling structural applications of this composite. The approach presented here is based upon presentations given at the National Science Foundation‐Civil and Mechanical Systems division workshop at John Hopkins University in 2004, which is referred to in this paper as the Williams‐Baxter approach. This approach is also used to demonstrate that damage modeling can be included as was suggested in this workshop. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal condition based maintenance with imperfect information and the proportional hazards model

Condition based maintenance (CBM) is based on collecting observations over time, in order to assess equipment's state, to prevent its failure and to determine the optimal maintenance strategies. In this paper, we derive an optimal CBM replacement policy when the state of equipment is unknown but can be estimated based on observed condition. We use a proportional hazards model (PHM) to represent the system's degradation. Since equipment's state is unknown, the optimization of the optimal maintenance policy is formulated as a partially observed Markov decision process (POMDP), and the problem is solved using dynamic programming. Practical advantages of combining the PHM with the POMDP are shown.     

Hessian‐based model reduction for large‐scale systems with initial‐condition inputs

Reduced‐order models that are able to approximate output quantities of interest of high‐fidelity computational models over a wide range of input parameters play an important role in making tractable large‐scale optimal design, optimal control, and inverse problem applications. We consider the problem of determining a reduced model of an initial value problem that spans all important initial conditions, and pose the task of determining appropriate training sets for reduced‐basis construction as a sequence of optimization problems. We show that, under certain assumptions, these optimization problems have an explicit solution in the form of an eigenvalue problem, yielding an efficient model reduction algorithm that scales well to systems with states of high dimension. Furthermore, tight upper bounds are given for the error in the outputs of the reduced models. The reduction methodology is demonstrated for a large‐scale contaminant transport problem. Copyright © 2007 John Wiley & Sons, Ltd.     

A specific device for enhanced measurement of mechanical dissipation in specimens subjected to long‐term tensile tests in fatigue

This paper presents a calorimetric approach to the measurement of mechanical dissipation in specimens subjected to cyclic tensile tests. Mechanical dissipation, that is, the heat power produced by the material due to mechanical irreversibility, can potentially be deduced from the temperature changes captured on the specimen surface by infrared thermography. However, a difficulty arises for long‐term cyclic tests: Results are easily skewed by any change in the specimen's environment. The problem is amplified by the fact that mechanical dissipation is in general small compared to the heat sources associated with thermomechanical couplings, making its estimation difficult. The paper proposes a simple procedure to extract a well‐resolved estimation of mechanical dissipation by solving two key points specific to long‐term cyclic tests: (a) the reduction of the parasitic effects associated with changes in the specimen's environment by using a specific device based on two references samples and (b) the choice of relevant thermal data acquisition parameters. A test is performed on a copper‐based shape‐memory alloy whose calorific response comprises three origins of heat sources: thermoelastic coupling, phase transformation, and mechanical irreversibility. The results obtained demonstrate the relevancy of the approach in extracting mechanical dissipation from the thermal response of the specimen subjected to long‐term tensile tests in fatigue.     

Fabrication and Optical Properties of Periodic Ag Nano‐Pore and Nano‐Particle Arrays with Controlled Shape and Size over Macroscopic Length Scales

A facile and economical route to preparation of highly ordered sliver pore or particle arrays with controlled pore‐shape and size extended over cm² areas is described. The substrates are prepared at planar and curved surfaces via sphere‐imprinted polymer (PDMS) templating using polystyrene spheres with diameters of 820, 600, or 430 nm. Nano‐pore arrays are created by sputtering 80 nm of Ag directly onto the templates and nano‐particle arrays are prepared by electrode‐less deposition of Ag from Tollen's reagent. The shape of the nano‐pore or particles in the array conformed to that of the imprint of the sphere on the template. Stretching the flexible template enable creation of cuboid shaped nano‐voids and nano‐particles following Ag deposition. Diffuse reflectance from the spherical Ag nano‐cavity arrays showed absorbance maxima at wavelengths comparable similar to the diameter of the templating sphere, whereas reflectance from the cuboid arrays, showed little correlation with the sphere diameter. The cuboid nano‐particle arrays showed the most intense visible absorption which is red‐shifted compared to the spherical arrays. White light diffraction from the arrays, observed by rotating 1 cm² substrates relative to a fixed light source, reflected exactly the symmetry axes of the periodic nano‐features in the arrays demonstrating the remarkable macroscopic order of the periodic structures. Raman spectra of 1‐benzenethiol adsorbed at the arrays indicated SERS enhancements from the substrates are attributed mainly to surface nano‐roughness with only moderate contributions from the periodically corrugated structures. Despite excitation at the major resonance dip in the reflectance spectrum, a weak, localized rim dipole mode is found to elicit a small increase in the SERS enhancement factor for the 430 nm diameter spherical arrays. FDTD studies of nano‐void arrays provided insights into v arious factors affecting the SERS experiment and confirmed the array's plasmonic spectra are dominated by propagating plasmon modes under microscope excitation/collection angles.     

The diffuse Nitsche method: Dirichlet constraints on phase‐field boundaries

We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase‐field approximations of sharp domains. Leveraging the properties of the phase‐field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase‐field solutions of the Allen‐Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase‐field in the diffuse boundary region and a uniform mesh for the representation of the physics‐based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty‐type methods. In the context of imaging‐based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with sharp surfaces, if the inherent length scales, ie, the interface width of the phase‐field, the voxel spacing, and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human vertebral body.     

Hierarchical multiscale structure–property relationships of the red-bellied woodpecker (Melanerpes carolinus) beak

We experimentally studied beaks of the red-bellied woodpecker to elucidate the hierarchical multiscale structure–property relationships. At the macroscale, the beak comprises three structural layers: an outer rhamphotheca layer (keratin sheath), a middle foam layer and an inner bony layer. The area fraction of each layer changes along the length of the beak giving rise to a varying constitutive behaviour similar to functionally graded materials. At the microscale, the rhamphotheca comprises keratin scales that are placed in an overlapping pattern; the middle foam layer has a porous structure; and the bony layer has a big centre cavity. At the nanoscale, a wavy gap between the keratin scales similar to a suture line was evidenced in the rhamphotheca; the middle foam layer joins two dissimilar materials; and mineralized collagen fibres were revealed in the inner bony layer. The nano- and micro-indentation tests revealed that the hardness (associated with the strength, modulus and stiffness) of the rhamphotheca layer (approx. 470 MPa for nano and approx. 320 MPa for micro) was two to three times less than that of the bony layer (approx. 1200 MPa for nano and approx. 630 MPa for micro). When compared to other birds (chicken, finch and toucan), the woodpecker''s beak has more elongated keratin scales that can slide over each other thus admitting dissipation via shearing; has much less porosity in the bony layer thus strengthening the beak and focusing the stress wave; and has a wavy suture that admits local shearing at the nanoscale. The analysis of the woodpeckers'' beaks provides some understanding of biological structural materials'' mechanisms for energy absorption.     

A semi‐implicit time‐stepping model for frictional compliant contact problems

In this paper, we formulate a semi‐implicit time‐stepping model for multibody mechanical systems with frictional, distributed compliant contacts. Employing a polyhedral pyramid model for the friction law and a distributed, linear, viscoelastic model for the contact, we obtain mixed linear complementarity formulations for the discrete‐time, compliant contact problem. We establish the existence and finite multiplicity of solutions, demonstrating that such solutions can be computed by Lemke's algorithm. In addition, we obtain limiting results of the model as the contact stiffness tends to infinity. The limit analysis elucidates the convergence of the dynamic models with compliance to the corresponding dynamic models with rigid contacts within the computational time‐stepping framework. Finally, we report numerical simulation results with an example of a planar mechanical system with a frictional contact that is modelled using a distributed, linear viscoelastic model and Coulomb's frictional law, verifying empirically that the solution trajectories converge to those obtained by the more traditional rigid‐body dynamic model. Copyright © 2004 John Wiley Sons, Ltd.     

Quality optimization (multi‐characteristics) through Taguchi's technique and utility concept

The work of Taguchi for determining the optimal settings of controllable factors through off‐line experiments focuses on products with a single quality characteristic or response. However, most products have several quality characteristics or responses of interest. Taguchi's technique in itself optimizes a single response or performance characteristic yielding a set of process parameters. This particular setting may not give desired results for other characteristics of the product. In such cases, a need arises to obtain a single setting (optimal setting) of the process parameters, which can be used to produce the products with optimum or near optimum quality characteristics as a whole. Multi‐characteristic response optimization may be the solution of the above problem. In the present paper a case study on V‐processed castings of Al–7%Si alloy, utilizing a simplified multi‐criterion methodology based on Taguchi's approach and utility concept, is discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

Inverse geometry heat transfer problem based on a radial basis functions geometry representation

We present a methodology for solving a non‐linear inverse geometry heat transfer problem where the observations are temperature measurements at points inside the object and the unknown is the geometry of the volume where the problem is defined. The representation of the geometry is based on radial basis functions (RBFs) and the non‐linear inverse problem is solved using the iteratively regularized Gauss–Newton method. In our work, we consider not only the problem with no geometry restrictions but also the bound‐constrained problem. The methodology is used for the industrial application of estimating the location of the 1150°C isotherm in a blast furnace hearth, based on measurements of the thermocouples located inside it. We validate the solution of the algorithm against simulated measurements with different levels of noise and study its behaviour on different regularization matrices. Finally, we analyse the error behaviour of the solution. Copyright © 2005 John Wiley & Sons, Ltd.     

Simultaneous determination for a space-dependent heat source and the initial data by the MFS

In this paper we propose a numerical algorithm based on the method of fundamental solutions for recovering a space-dependent heat source and the initial data simultaneously in an inverse heat conduction problem. The problem is transformed into a homogeneous backward-type inverse heat conduction problem and a Dirichlet boundary value problem for Poisson's equation. We use an improved method of fundamental solutions to solve the backward-type inverse heat conduction problem and apply the finite element method for solving the well-posed direct problem. The Tikhonov regularization method combined with the generalized cross validation rule for selecting a suitable regularization parameter is applied to obtain a stable regularized solution for the backward-type inverse heat conduction problem. Numerical experiments for four examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed algorithm.     

Two improvements in formulation of nine‐node element MITC9

The paper concerns a well‐known two‐dimensional nine‐node quadrilateral element MITC9, which is based on two‐level approximations of strains (assumed strain method). The element has good accuracy, but does not pass the patch test. As the first improvement, we propose a modification of the element's transformations, partly resolving the problem with the patch test. The source of the problem is the use of covariant components in a (local) natural co‐basis, different at each sampling point. As the second improvement, we use the corrected shape functions of Celia MA, Gray WG. An improved isoparametric transformation for finite element analysis. International Journal for Numerical Methods in Engineering 1984; 20 :1447–1459, extending their applicability to the nine‐node element for plane elasticity and the 3 × 3 integration. Originally, they are tested for an eight‐node element for the heat conduction equation and the 4 × 4 integration. The improved element, designated as MITC9i, is based on the Green strain and derived from the potential energy for the plane stress condition. It is subjected to a range of tests, to confirm that it passes the patch test for several types of mesh distortions, to prove its coarse mesh accuracy and the absence of locking as well as to establish its sensitivity to mesh distortions. The improved element MITC9i performs substantially better than the MITC9 element, QUAD9** element, and our previous 9‐AS element.Copyright © 2012 John Wiley & Sons, Ltd.     

Articulated mechanism design with a degree of freedom constraint

This paper deals with design of articulated mechanism using a truss‐based ground‐structure representation. The proposed method can accommodate extremely large displacement by considering geometric non‐linearity. In addition, it can also control the mechanical degrees of freedom (DOF) of the resultant mechanism by using a DOF equation based on Maxwell's rule. The optimization is based on a relaxed formulation of an original integer problem and also involves developments directed at handling the redundancy inherent in the ground‐structure representation. One planar test example is selected as the basis for the developments so as to compare the proposed method with other alternative approaches including a graph‐theoretical enumeration approach which guarantees the identification of the globally optimal solution. Also, an inverter problem is treated where a continuation method is required in order to direct the optimization algorithm towards an integer solution. Copyright © 2004 John Wiley & Sons, Ltd.     

Cumulative fatigue damage evaluations on spot‐welded joints using 590 MPa‐class automobile steel

This study focused on local strain behaviour near the slit edge of spot‐welded joints, where the fatigue crack initiated, and investigated methods of evaluating cumulative fatigue damage. A method of evaluating local strain amplitude by following modified Goodman's law gave almost the same result as an evaluation approach based on the external force and provided reasonable result on general strength design. An approach based on Smith–Watson–Topper's equation was easy to evaluate cumulative fatigue damage compared with the method based on modified Goodman's law and gave a good agreement with a criterion of the modified Miner's rule.