A theory of thin shells with finite displacements and deformations based on a modified Kirchhoff–Love model

A refined classical Kirchhoff–Love theory of thin shells with finite displacements and deformations is given that takes account of deformation in a transverse direction by introducing an additional unknown function to describe it. It is shown that the last of the three equilibrium equations for the moments obtained from the variational equation of the principle of virtual displacements serves to determine it. Constitutive relations are constructed for the internal forces and moments introduced into the treatment based on the introduction of the true Novoshilov stresses and strains into the discussion. The solution of problem of the static stability of a cylindrical shell made of a rubber-like incompressible material inflated by an internal pressure is given using the equations constructed. Chernykh's constitutive relations are used in its formulation.     

Boundary stabilization of structural acoustic interactions with interface on a Reissner–Mindlin plate

Boundary stabilization of a structural acoustic model comprised of a wave and a Reissner–Mindlin plate is addressed. Both the components of the dynamics are subject to localized nonlinear boundary damping: the acoustic dissipative feedback is restricted to the flexible boundary and only a portion of the rigid wall; the plate is damped only on a segment of its edge.Derivation of stabilization/observability inequalities for a coupled system requires weighted energy multipliers dependent on the geometry of the domain, and special microlocal trace estimates for the Reissner–Mindlin plate. The behavior of the energy at infinity can be quantified by a solution to an explicitly constructed nonlinear ODE. The nonlinearities in the feedbacks may include sub- and superlinear growth at infinity, in which case the decay scheme presents a trade-off between the regularity of trajectories and attainable uniform dissipation rates of the finite energy.     

A Jacobi–Davidson like method for nonlinear eigenvalue problems based on singularity theory

We present a Jacobi–Davidson like correction formula for left and right eigenvector approximations for non-Hermitian nonlinear eigenvalue problems. It exploits techniques from singularity theory for characterizing singular points of nonlinear equations. Unlike standard nonlinear Jacobi-Davidson, the correction formula does not contain derivative information and works with orthogonal projectors only. Moreover, the basic method is modified in that the new eigenvalue approximation is taken as a nonlinear Rayleigh functional obtained as root of a certain scalar nonlinear equation the existence of which – as well as a first order perturbation expansion – is shown. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A polynomial algorithm for a two parameter extension of Wythoff NIM based on the Perron–Frobenius theory

For any positive integer parameters a and b, Gurvich recently introduced a generalization mex _b of the standard minimum excludant mex = mex₁, along with a game NIM(a, b) that extends further Fraenkel’s NIM = NIM(a, 1), which in its turn is a generalization of the classical Wythoff NIM = NIM(1, 1). It was shown that P-positions (the kernel) of NIM(a, b) are given by the following recursion: $$x_n = {\rm mex}_b(\{x_i, y_i \;|\; 0 \leq i < n\}), \;\; y_n = x_n + an; \;\; n \geq 0,$$ and conjectured that for all a, b the limits ?(a, b) = x _n (a, b)/n exist and are irrational algebraic numbers. In this paper we prove that showing that ${\ell(a,b) = \frac{a}{r-1}}$ , where r > 1 is the Perron root of the polynomial $$P(z) = z^{b+1} - z - 1 - \sum_{i=1}^{a-1} z^{\lceil ib/a \rceil},$$ whenever a and b are coprime; furthermore, it is known that ?(ka, kb) = k?(a, b). In particular, ${\ell(a, 1) = \alpha_a = \frac{1}{2} (2 - a + \sqrt{a^2 + 4})}$ . In 1982, Fraenkel introduced the game NIM(a) = NIM(a, 1), obtained the above recursion and solved it explicitly getting ${x_n = \lfloor \alpha_a n \rfloor, \; y_n = x_n + an = \lfloor (\alpha_a + a) n \rfloor}$ . Here we provide a polynomial time algorithm based on the Perron–Frobenius theory solving game NIM(a, b), although we have no explicit formula for its kernel.     

Concept and prototype of a web tool for public–private project contracting based on a system dynamics model

Central European Journal of Operations Research - Contracting has a significant impact on the efficiency of acquisition processes, especially in the context of so-called public–private...     

A residual–based error estimator for BEM–discretizations of contact problems

Summary. We develop an a posteriori error estimate for boundary element solutions of static contact problems without friction. The presented result is based on an error estimate for linear pseudodifferential equations and on a certain commutator property for pseudodifferential operators. A heuristic extension of the obtained error estimate to frictional contact problems is presented, too. Numerical examples indicate a good performance of the error estimator for both the frictionless and the frictional problem. Mathematics Subject Classification (1991):35J85, 65N38, 73T05Dedicated to Hans Grabmüller on the occasion of his 60th birthday     

A multistage algorithm for best-subset model selection based on the Kullback–Leibler discrepancy

The selection of a best-subset regression model from a candidate family is a common problem that arises in many analyses. The Akaike information criterion (AIC) and the corrected AIC (\(\text {AIC}_c\)) are frequently used for this purpose. AIC and \(\text {AIC}_c\) are designed to estimate the expected Kullback–Leibler discrepancy. For best-subset selection, both AIC and \(\text {AIC}_c\) are negatively biased, and the use of either criterion will lead to the selection of overfitted models. To correct for this bias, we introduce an “improved” AIC variant, \(\text {AIC}_i\), which has a penalty term evaluated using Monte Carlo simulation. A multistage model selection procedure \(\text {AIC}_{\text {aps}}\), which utilizes \(\text {AIC}_i\), is proposed for best-subset selection. Simulation studies are compiled to compare the performances of the different model selection methods.     

A generalized probabilistic edge-based smoothed finite element method for elastostatic analysis of Reissner–Mindlin plates

Probabilistic analysis is becoming more important in mechanical science and real-world engineering applications. In this work, a novel generalized stochastic edge-based smoothed finite element method is proposed for Reissner–Mindlin plate problems. The edge-based smoothing technique is applied in the standard FEM to soften the over-stiff behavior of Reissner–Mindlin plate system, aiming to improve the accuracy of predictions for deterministic response. Then, the generalized nth order stochastic perturbation technique is incorporated with the edge-based S-FEM to formulate a generalized probabilistic ES-FEM framework (GP_ES-FEM). Based upon a general order Taylor expansion with random variables of input, it is able to determine higher order probabilistic moments and characteristics of the response of Reissner–Mindlin plates. The significant feature of the proposed approach is that it not only improves the numerical accuracy of deterministic output quantities with respect to a given random variable, but also overcomes the inherent drawbacks of conventional second-order perturbation approach, which is satisfactory only for small coefficients of variation of the stochastic input field. Two numerical examples for static analysis of Reissner–Mindlin plates are presented and verified by Monte Carlo simulations to demonstrate the effectiveness of the present method.     

Cattaneo–Christov heat flux model for three-dimensional flow of a viscoelastic fluid on an exponentially stretching surface

ABSTRACT

In this article, we explore the three-dimensional boundary-layer flow over an exponentially stretching surface in two parallel ways. Constitutive equations of a second-grade fluid are used. Instead of classical Fourier’s law, Cattaneo–Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. The resulting partial differential equations are reduced into ordinary differential equations by similarity transformations. Homotopy Analysis Method (HAM) is employed to solve the non-linear problem. Physical impact of emerging parameters on the momentum and thermal boundary-layer thickness are studied.     

Soliton perturbation theory for phi-four model and nonlinear Klein–Gordon equations

This paper obtains the adiabatic variation of the soliton velocity, in presence of perturbation terms, of the phi-four model and the nonlinear Klein–Gordon equations. There are three types of models of the nonlinear Klein–Gordon equation, with power law nonlinearity, that are studied in this paper. The soliton perturbation theory is utilized to carry out this investigation.     

A model of Cahn—Hilliard equation based on a microforce balance

We derive in this Note a model of Cahn—Hilliard equation that takes into account the effects of internal microforces. This model is based on constitutive equations developed by M. Gurtin in [4]. We then obtain the existence and uniqueness of solutions and the existence of global attractors.     

A note on a nonlocal nonlinear reaction–diffusion model

We give an application of the Crandall–Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.     

A skin detection approach based on the Dempster–Shafer theory of evidence

Skin detection is an important step for a wide range of research related to computer vision and image processing and several methods have already been proposed to solve this problem. However, most of these methods suffer from accuracy and reliability problems when they are applied to a variety of images obtained under different conditions. Performance degrades further when fewer training data are available. Besides these issues, some methods require long training times and a significant amount of parameter tuning. Furthermore, most state-of-the-art methods incorporate one or more thresholds, and it is difficult to determine accurate threshold settings to obtain desirable performance. These problems arise mostly because the available training data for skin detection are imprecise and incomplete, which leads to uncertainty in classification. This requires a robust fusion framework to combine available information sources with some degree of certainty. This paper addresses these issues by proposing a fusion-based method termed Dempster–Shafer-based Skin Detection (DSSD). This method uses six prominent skin detection criteria as sources of information (SoI), quantifies their reliabilities (confidences), and then combines their confidences based on the Dempster–Shafer Theory (DST) of evidence. We use the DST as it offers a powerful and flexible framework for representing and handling uncertainties in available information and thus helps to overcome the limitations of the current state-of-the-art methods. We have verified this method on a large dataset containing a variety of images, and achieved a 90.17% correct detection rate (CDR). We also demonstrate how DSSD can be used when very little training data are available, achieving a CDR as high as 87.47% while the best result achieved by a Bayesian classifier is only 68.81% on the same dataset. Finally, a generalized DSSD (GDSSD) is proposed achieving 91.12% CDR.     

Fast calculation based on a spatial two-grid finite element algorithm for a nonlinear space–time fractional diffusion model

In this article, a spatial two-grid finite element (TGFE) algorithm is used to solve a two-dimensional nonlinear space–time fractional diffusion model and improve the computational efficiency. First, the second-order backward difference scheme is used to formulate the time approximation, where the time-fractional derivative is approximated by the weighted and shifted Grünwald difference operator. In order to reduce the computation time of the standard FE method, a TGFE algorithm is developed. The specific algorithm is to iteratively solve a nonlinear system on the coarse grid and then to solve a linear system on the fine grid. We prove the scheme stability of the TGFE algorithm and derive a priori error estimate with the convergence result O(Δt² + h^{r + 1 − η} + H^{2r + 2 − 2η}) . Finally, through a two-dimensional numerical calculation, we improve the computational efficiency and reduce the computation time by the TGFE algorithm.     

Adaptive extended isogeometric analysis based on PHT-splines for thin cracked plates and shells with Kirchhoff–Love theory

In this paper, a posteriori error estimation and mesh adaptation approach for thin plate and shell structures of through-the-thickness crack is presented. This method uses the extended isogeometric analysis (XIGA) based on PHT-splines (Polynomial splines over Hierarchical T-meshes), which is abbreviated as XIGA-PHT. In XIGA-PHT, the isogeometric displacement approximation is locally enriched with enrichment functions, which efficiently capture the displacement discontinuity across the crack face as well as the stress singularity in the vicinity of the crack tip. On the one hand, the rotational degrees of freedom (RDOFs) are not required in Kirchhoff–Love theory, which drastically reduces the complexity of enrichment mode and computational scale for crack analysis. On the other hand, the PHT-splines basis functions can automatically satisfy the requirement of C¹-continuity for the Kirchhoff–Love theory. Moreover, the PHT-splines facilitate the local refinement, which is the deficiency of NURBS-based isogeometric formulations. The local refinement is highly suitable for adaptive analysis. The stress recovery-based posteriori error estimator combined with the superconvergent patch recovery (SPR) technique is used to evaluate the approximate local discretization error. A new strategy for selecting enriched recovered functions in the enriched areas was proposed. Special functions extracted from the asymptotic stress solutions are applied to obtain the recovered stress field in the enriched area. The results of stress intensity factors or J-integral values obtained by the adaptive XIGA-PHT are compared with reference solutions. Several thin plate and shell illustrative examples demonstrate the effectiveness and accuracy of the proposed adaptive XIGA-PHT.     

Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes–Darcy model

Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes–Darcy model with Beavers–Joseph–Saffman interface condition in literatures, the numerical analysis only gets the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis.     

Synchronization analysis for complex networks with coupling delay based on T–S fuzzy theory

In this paper, synchronization problems for a general complex networks are investigated by Takagi–Sugeno (T–S) fuzzy theory. A novel concept named linear approximation method is firstly proposed to solve the synchronization problems for T–S fuzzy complex networks. This novel method can linearize the system into some time-delay subsystems, which can effectively simplify the complicated system and then be easy to acquire the synchronization results. Since the expression based on linear matrix inequality (LMI) is used, the synchronization criteria can be easily checked in practice. Numerical simulation examples are provided to verify the effectiveness and the applicability of the proposed method.     

Coupling of a one-dimensional river routing model and a three-dimensional ocean model to predict overbank flows in a complex river–ocean system

River–ocean coupled models were developed to calculate overbank flows in a complex river–coastal ocean system comprising the Wu River and the adjacent coastal ocean of central Taiwan. The hydrodynamic quantities were exchanged between one-dimensional and three-dimensional domains during runtime to resolve the real-time exchange and interaction between the coastal waters and the river system. The coupled model was calibrated and verified with the observed water levels using data from three typhoon events. The results indicate a reasonable agreement between the model simulations and the observed data. The model was then used to calculate hydrographs of the overbank flow caused by Typhoon Kalmaegi, which occurred in 2008. The simulated overbank flows quantitatively agreed with the reported information. We also demonstrated that most of the overbank flows occurred at the upper reaches of the tributaries of the Wu River system, except for the tributary in the Fazi River.