Analysis of multilayer orthotropic viscoelastic shells of revolution

We propose a technique for numerical solution of the problems of viscoelastic equilibrium of multilayer orthotropic shells of revolution in a refined formulation that is based on two step-by-step integration algorithms. The calculation of the integrals using the first algorithm is based on multiplication of two functions following the Vereshchagin rule, the integration using the second algorithm is based on quadratic approximation of the deformations. The boundary-value viscoelastic problem is solved by numerical integration using the Runge-Kutta method with orthogonalization of the solution vectors following Godunov. The results obtained using the two proposed algorithms are compared with the results found by the Schapery method. We show the influence of creep of the load-carrying layers and of the filler with and without account for the transverse shear deformations.Translated from Problemy Prochnosti, No. 12, pp. 71–77, December, 1993.     

An adaptive interface‐enriched generalized FEM for the treatment of problems with curved interfaces

An adaptive refinement scheme is presented to reduce the geometry discretization error and provide higher‐order enrichment functions for the interface‐enriched generalized FEM. The proposed method relies on the h‐adaptive and p‐adaptive refinement techniques to reduce the discrepancy between the exact and discretized geometries of curved material interfaces. A thorough discussion is provided on identifying the appropriate level of the refinement for curved interfaces based on the size of the elements of the background mesh. Varied techniques are then studied for selecting the quasi‐optimal location of interface nodes to obtain a more accurate approximation of the interface geometry. We also discuss different approaches for creating the integration sub‐elements and evaluating the corresponding enrichment functions together with their impact on the performance and computational cost of higher‐order enrichments. Several examples are presented to demonstrate the application of the adaptive interface‐enriched generalized FEM for modeling thermo‐mechanical problems with intricate geometries. The accuracy and convergence rate of the method are also studied in these example problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Extended stochastic FEM for diffusion problems with uncertain material interfaces

This paper is concerned with the prediction of heat transfer in composite materials with uncertain inclusion geometry. To numerically solve the governing equation, which is defined on a random domain, an approach based on the combination of the Extended finite element method (X-FEM) and the spectral stochastic finite element method is studied. Two challenges of the extended stochastic finite element method (X-SFEM) are choosing an enrichment function and numerical integration over the probability domain. An enrichment function, which is based on knowledge of the interface location, captures the C ⁰-continuous solution in the spatial and probability domains without a conforming mesh. Standard enrichment functions and enrichment functions tailored to X-SFEM are analyzed and compared, and the basic elements of a successful enrichment function are identified. We introduce a partition approach for accurate integration over the probability domain. The X-FEM solution is studied as a function of the parameters describing the inclusion geometry and the different enrichment functions. The efficiency and accuracy of a spectral polynomial chaos expansion and a finite element approximation in the probability domain are compared. Numerical examples of a two-dimensional heat conduction problem with a random inclusion show the spectral PC approximation with a suitable choice of enrichment function is as accurate and more efficient than the finite element approach. Though focused on heat transfer in composite materials, the techniques and observations in this paper are also applicable to other types of problems with uncertain geometry.     

A posteriori error estimator and an adaptive technique in meshless finite points method

In this work, an adaptive technique for application of meshless methods in one- and two-dimensional boundary value problems is described. The proposed method is based on the use of implicit functions for the geometry definition, fixed weighted least squares approximation and an error estimation by means of simple formulas and a robust strategy of refinement based on the own nature of the approximation sub-domains utilised. With all these aspects, the proposed method becomes an attractive alternative for the adaptive solutions to partial differential equations in all scopes of engineering. Numerical results obtained from the computational implementation show the efficiency of the present method.     

A Hermite reproducing kernel approximation for thin‐plate analysis with sub‐domain stabilized conforming integration

A Hermite reproducing kernel (RK) approximation and a sub‐domain stabilized conforming integration (SSCI) are proposed for solving thin‐plate problems in which second‐order differentiation is involved in the weak form. Although the standard RK approximation can be constructed with an arbitrary order of continuity, the proposed approximation based on both deflection and rotation variables is shown to be more effective in solving plate problems. By imposing the Kirchhoff mode reproducing conditions on deflectional and rotational degrees of freedom simultaneously, it is demonstrated that the minimum normalized support size (coverage) of kernel functions can be significantly reduced. With this proposed approximation, the Galerkin meshfree framework for thin plates is then formulated and the integration constraint for bending exactness is also derived. Subsequently, an SSCI method is developed to achieve the exact pure bending solution as well as to maintain spatial stability. Numerical examples demonstrate that the proposed formulation offers superior convergence rates, accuracy and efficiency, compared with those based on higher‐order Gauss quadrature rule. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimization of mechanical systems: On strategy of non-linear first-order approximation

The paper presents an extended approach to non-linear first-order approximation of non-linear programming problems and it explains how to transform an approximate problem into a strictly convex one. The essence of the proposed approximation technique is to rewrite each given function h_j as a composite g_j ^o Ψ^j. The function Ψ^j has to be chosen—the paper explains how to do this—while g_j is linear approximated with g_j. The approximation of h_j is then obtained as g_j ^o Ψ^j. This approach enables one to obtain approximate functions with variable conservativeness, which implies an adjustable approximate problem. A solution procedure, which replaces the original problem with a sequence of approximate problems, can therefore adjust each succeeding approximate problem to improve the convergence properties. The theory is illustrated with a three parameters controlled approximation. This technique represents, together with an optimality criteria based solution procedure, a powerful and economic tool for solving nonlinear programming problems. The three parameters, which influence to a great extent the conservativeness of the approximate functions, are under full control of the optimizer. They are varied automatically during the process of optimization to speed-up the convergence or to prevent oscillations. The benefits gained from the proposed approach are demonstrated on several numerical examples involving structures and a dynamic multibody system.     

Structural-Damage Detection by Distributed Piezoelectric Transducers and Tuned Electric Circuits

ABSTRACT

A novel technique for damage detection of structures is introduced and discussed. It is based on purely electric measurements of the state variables of an electric network coupled to the main structure through a distributed set of piezoelectric patches. The constitutive parameters of this auxiliary network are optimized to increase the sensitivity of global measurements—as the frequency, response functions relative to selected electric degrees of freedom—with respect to a given class of variations in the structural–mechanical properties. Because the proposed method is based on purely electric input and output measurements, it allows for accurate results in the identification and localization of damages. Use of the electric frequency-response function to identify the mechanical damage leads to nonconvex optimization problems; therefore the proposed sensitivity-enhanced identification procedure becomes computationally efficient if an a priori knowledge about the damage is available.     

Porous Media Analysis by Modified MLPG Formulations

This work proposes a modified procedure, based on analytical integrations, to analyse poroelastic models discretized by time-domain Meshless Local Petrov-Galerkin formulations. In this context, Taylor series expansions of the incognita fields are considered, and the related integrals of the meshless formulations are solved analytically, rendering a so called modified methodology. The work is based on the u-p formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the interstitial fluid pore pressures. Independent spatial discretization is considered for each phase of the model, rendering a more flexible and efficient methodology. The Moving Least Squares approximation is employed for the spatial variation of the displacement and pore-pressure fields and two variants of the meshless local Petrov-Galerkin formulation are discussed here, which are based on the use of Heaviside or Gaussian weight test functions. Modified expressions to properly compute the shape function derivatives are also considered. At the end of the paper, numerical examples illustrate the performance and potentialities of the proposed techniques.     

Mesh independent modelling of cracks by using higher order shape functions

A mesh independent crack modelling approach based on displacement approximation with higher order shape functions is proposed. The Heaviside step function based local enrichment method, known as eXtended Finite Element Method, is modified by replacing the step function with a higher order shape functions approximation. Polynomial B‐spline approximation functions are used in the present paper. An advantage of the proposed method is that its implementation only involves integration of the products of original shape functions and their derivatives and does not require modification of the integration domains. A volume integral based expression is proposed to calculate the effective surface area of the crack modelled by using an approximate step function. It is shown to give the actual crack surface area in the limit of the approximate step function approaching the Heaviside function. The convergence and accuracy of the method is illustrated in examples of transverse and oblique (with respect to loading direction) crack problems in rectangular plates. Uniaxial tension of a unidirectional composite with an open hole is considered. Hoop stress relaxation due to longitudinal splitting is successfully modelled by the method proposed and compared to direct modelling by using ANSYS software. Published in 2002 by John Wiley & Sons, Ltd.     

The finite point method for the <Emphasis Type="Italic">p</Emphasis>-Laplace equation

In this paper, the finite point method (FPM) is presented for solving the 2D, nonlinear, elliptic p-Laplace or p-harmonic equation. The FPM is a truly meshfree technique based on the combination of the moving least squares approximation on a cloud of points with the point collocation method to discretize the governing equation. The lack of dependence on a mesh or integration procedure is an important feature, which makes the FPM simple, efficient and applicable to solve nonlinear problems. Applications are demonstrated through illustrative examples.     

Image recoloring using specular decomposition and in-painting

ABSTRACT

Image recoloring using wavelet transform, in-painting and dichromatic reflection model is proposed. Detailed wavelet bands are passed through a sharpening filter whereas the approximation band is passed through dichromatic reflection model to extract body and specular coefficients. In-painting and white illumination minimization using erosion and Gaussian blur further enhance the image quality. The proposed technique produces better results, both qualitatively and quantitatively, in terms of edge preservation and minimization of noise, artefacts in contrast to state-of-art existing techniques.     

A Kriging‐based error‐reproducing and interpolating kernel method for improved mesh‐free approximations

An error‐reproducing and interpolating kernel method (ERIKM), which is a novel and improved form of the error‐reproducing kernel method (ERKM) with the nodal interpolation property, is proposed. The ERKM is a non‐uniform rational B‐splines (NURBS)‐based mesh‐free approximation scheme recently proposed by Shaw and Roy (Comput. Mech. 2007; 40 (1):127–148). The ERKM is based on an initial approximation of the target function and its derivatives by NURBS basis functions. The errors in the NURBS approximation and its derivatives are then reproduced via a family of non‐NURBS basis functions. The non‐NURBS basis functions are constructed using a polynomial reproduction condition and added to the NURBS approximation obtained in the first step. In the ERKM, the interpolating property at the boundary is achieved by repeating the knot (open knot vector). However, for most problems of practical interest, employing NURBS with open knots is not possible because of the complex geometry of the domain, and consequently ERKM shape functions turn out to be non‐interpolating. In ERIKM, the error functions are obtained through localized Kriging based on a minimization of the squared variance of the estimate with the reproduction property as a constraint. Interpolating error functions so obtained are then added to the NURBS approximant. While enriching the ERKM with the interpolation property, the ERIKM naturally possesses all the desirable features of the ERKM, such as insensitivity to the support size and ability to reproduce sharp layers. The proposed ERIKM is finally applied to obtain strong and weak solutions for a class of linear and non‐linear boundary value problems of engineering interest. These illustrations help to bring out the relative numerical advantages and accuracy of the new method to some extent. Copyright © 2007 John Wiley & Sons, Ltd.     

Direct meshless local Petrov–Galerkin method for elastodynamic analysis

This article describes a new and fast meshfree method based on a generalized moving least squares (GMLS) approximation and the local weak forms for vibration analysis in solids. In contrast to the meshless local Petrov–Galerkin method, GMLS directly approximates the local weak forms from meshless nodal values, which shifts the local integrations over the low-degree polynomial basis functions rather than over the complicated MLS shape functions. Besides, if the method is set up properly, all local integrals have the same value if all local subdomains have the same shape. These features reduce the computational costs, remarkably. The new technique is called direct meshless local Petrov–Galerkin (DMLPG) method. In DMLPG, the stiff and mass matrices are constructed by integration against polynomials. This overcomes the main drawback of meshfree methods in comparison with the finite element methods (FEM). The Newmark scheme is adapted as a time integration method, and numerical results are presented for various dynamic problems. The results are compared with the exact solutions, if available, and the FEM solutions.     

Approximation of fluctuating pressure cross-spectra of dome-like roofs under turbulent flow

ABSTRACT

Large span roof structures have been widely adopted for their good performance in multiple functionalities and innovative designs. However, because of their light weight, wind-resistant design is more urgent than earthquake-resistant design. And further, their long span geometry often results in a weak spatial correlation in pressure distributions and hence makes the estimation of wind loads a difficult task. Spectrum characteristics of wind pressures have been mentioned in several publications; however, there is still little discussion of cross-spectrum characteristics. In this paper, cross-spectra of fluctuating wind pressures on various dome-like roofs are investigated under a suburban terrain flow. By examining separately the root-coherence function and the phase function, approximation models of both functions are proposed in terms of the rise/span ratio based on certain simple but efficient assumptions. Once the two functions are simulated in good agreement with experimental results, the cross-spectra, or the co-coherence function, can be simulated by simply combining the root-coherence function and the phase function.     

RDS-NSGA-II: a memetic algorithm for reference point based multi-objective optimization

Reference point based optimization offers tools for the effective treatment of preference based multi-objective optimization problems, e.g. when the decision-maker has a rough idea about the target objective values. For the numerical solution of such problems, specialized evolutionary strategies have become popular, despite their possible slow convergence rates. Hybridizing such evolutionary algorithms with local search techniques have been shown to produce faster and more reliable algorithms. In this article, the directed search (DS) method is adapted to the context of reference point optimization problems, making this variant, called RDS, a well-suited option for integration into evolutionary algorithms. Numerical results on academic test problems with up to five objectives demonstrate the benefit of the novel hybrid (i.e. the same approximation quality can be obtained more efficiently by the new algorithm), using the state-of-the-art algorithm R-NSGA-II for this coupling. This represents an advantage when treating costly-to-evaluate real-world engineering design problems.     

The Extended-focus,Auto-focus and Surface-profiling Techniques of Confocal Microscopy

Abstract

The extended focus and auto-focus techniques of confocal microscopy, which can be used to give greatly increased depth of field, are compared. These methods rely on the use of high numerical apertures, so that the paraxial approximation is found to give inaccurate theoretical image predictions. An improved approximation is discussed and compared with exact high-angle calculations. The confocal surface-profiling technique, which allows non-invasive investigation surface topography is also considered.     

A new query expansion method for document retrieval based on the inference of fuzzy rules

Abstract

Automatic query expansion based on user relevance feedback techniques can improve the performance of document retrieval systems. In this paper, we present a new query expansion method based on the inference of fuzzy rules and user relevance feedback techniques to deal with document retrieval. The proposed method uses membership functions and fuzzy rules to infer relevant degrees of expansion terms and puts the expansion terms with larger relevant degrees into the original user's query. Then, the system calculates the degree of similarity of each document with respect to the expanded user's query. The proposed method gets a higher average precision rate and a higher average recall rate than the existing methods for document retrieval.     

An approach to the implementation and verification of abstract data

Abstract

The concept of abstraction can be used to simplify and formalize the design of software. However, most of the existing techniques based on abstraction only consider the control structure but not the data structures in the software. The transformation of a data abstraction, i.e., an abstract data type, to a physical data structure is a complicated process. It is composed of three major parts: a specification technique for describing a data abstraction; a deriving process for deriving the representation of the abstraction based on the specification; and a verification method for verifying the correctness of the specification and the representation of the abstraction. In this paper, we will concentrate on the last two problems, and it is assumed that the algebraic specification technique is used for describing abstract data types. Also, we will use examples to illustrate the use of the proposed approach.     

A Hermite reproducing kernel Galerkin meshfree approach for buckling analysis of thin plates

A Hermite reproducing kernel Galerkin meshfree approach is proposed for buckling analysis of thin plates. This approach employs the Hermite reproducing kernel meshfree approximation that incorporates both the deflectional and rotational nodal variables into the approximation of the plate deflection and the C ¹ continuous approximation requirement for the Galerkin analysis of thin plates can be easily achieved herein. The strain smoothing operation is consistently introduced to construct the smoothed rotation and curvature fields which appear in the weak form governing the thin plate buckling. The domain integration of the weak form is carried out by the method of sub-domain stabilized conforming integration with the smoothed measures of rotation and curvature, as leads to an efficient discrete meshfree formulation for the eigenvalue problem of thin plate buckling. A series of benchmark buckling problems are presented to assess the proposed algorithm and the results uniformly demonstrate the present approach is very effective and it performs superiorly compared to the conventional Galerkin meshfree formulations whose domain integration are performed by Gauss quadrature rules.