Non‐linear spatial Timoshenko beam element with curvature interpolation

The paper presents a spatial Timoshenko beam element with a total Lagrangian formulation. The element is based on curvature interpolation that is independent of the rigid‐body motion of the beam element and simplifies the formulation. The section response is derived from plane section kinematics. A two‐node beam element with constant curvature is relatively simple to formulate and exhibits excellent numerical convergence. The formulation is extended to N‐node elements with polynomial curvature interpolation. Models with moderate discretization yield results of sufficient accuracy with a small number of iterations at each load step. Generalized second‐order stress resultants are identified and the section response takes into account non‐linear material behaviour. Green–Lagrange strains are expressed in terms of section curvature and shear distortion, whose first and second variations are functions of node displacements and rotations. A symmetric tangent stiffness matrix is derived by consistent linearization and an iterative acceleration method is used to improve numerical convergence for hyperelastic materials. The comparison of analytical results with numerical simulations in the literature demonstrates the consistency, accuracy and superior numerical performance of the proposed element. Copyright © 2001 John Wiley & Sons, Ltd.     

A comparison of wave‐based discontinuous Galerkin,ultra‐weak and least‐square methods for wave problems

Several numerical methods using non‐polynomial interpolation have been proposed for wave propagation problems at high frequencies. The common feature of these methods is that in each element, the solution is approximated by a set of local solutions. They can provide very accurate solutions with a much smaller number of degrees of freedom compared to polynomial interpolation. There are however significant differences in the way the matching conditions enforcing the continuity of the solution between elements can be formulated. The similarities and discrepancies between several non‐polynomial numerical methods are discussed in the context of the Helmholtz equation. The present comparison is concerned with the ultra‐weak variational formulation (UWVF), the least‐squares method (LSM) and the discontinuous Galerkin method with numerical flux (DGM). An analysis in terms of Trefftz methods provides an interesting insight into the properties of these methods. Second, the UWVF and the LSM are reformulated in a similar fashion to that of the DGM. This offers a unified framework to understand the properties of several non‐polynomial methods. Numerical results are also presented to put in perspective the relative accuracy of the methods. The numerical accuracies of the methods are compared with the interpolation errors of the wave bases. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Non‐linear model reduction for uncertainty quantification in large‐scale inverse problems

We present a model reduction approach to the solution of large‐scale statistical inverse problems in a Bayesian inference setting. A key to the model reduction is an efficient representation of the non‐linear terms in the reduced model. To achieve this, we present a formulation that employs masked projection of the discrete equations; that is, we compute an approximation of the non‐linear term using a select subset of interpolation points. Further, through this formulation we show similarities among the existing techniques of gappy proper orthogonal decomposition, missing point estimation, and empirical interpolation via coefficient‐function approximation. The resulting model reduction methodology is applied to a highly non‐linear combustion problem governed by an advection–diffusion‐reaction partial differential equation (PDE). Our reduced model is used as a surrogate for a finite element discretization of the non‐linear PDE within the Markov chain Monte Carlo sampling employed by the Bayesian inference approach. In two spatial dimensions, we show that this approach yields accurate results while reducing the computational cost by several orders of magnitude. For the full three‐dimensional problem, a forward solve using a reduced model that has high fidelity over the input parameter space is more than two million times faster than the full‐order finite element model, making tractable the solution of the statistical inverse problem that would otherwise require many years of CPU time. Copyright © 2009 John Wiley & Sons, Ltd.     

Precorrected FFT accelerated BEM for large‐scale transient elastodynamic analysis using frequency‐domain approach

A precorrected fast Fourier transform (pFFT) accelerated boundary element method (BEM) for large‐scale transient elastodynamic analysis is developed and described in this paper. The frequency‐domain approach is used. To overcome the ‘wrap‐around’ problem associated with the discrete Fourier transform, the exponential window method (EWM) is employed and incorporated in the frequency‐domain BEM. An improved implementation scheme of the pFFT method based on polynomial interpolation technique is developed and applied to accelerate the elastodynamic BEM. This new scheme reduces the memory required to save the convolution matrix by a factor of 8. To further improve the efficiency of the code, a newly developed linear system solver based on the induced dimension reduction method is employed. Its performance is investigated and compared with that of the well‐known GMRES. The accuracy and computational efficiency of the method are evaluated and demonstrated by three examples: a classical benchmark, a plate subject to an impact loading and a porous cube with nearly half million DOFs subject to a step traction loading. Both analytical and experimental results are employed to validate the method. It has been found that the EWM can effectively resolve the wrap‐around problem and accurate time responses for an arbitrarily chosen time period can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

Hat interpolation wavelet‐based multi‐scale Galerkin method for thin‐walled box beam analysis

The objective of the present work is to propose a new adaptive wavelet‐Galerkin method based on the lowest‐order hat interpolation wavelets. The specific application of the present method is made on the one‐dimensional analysis of thin‐walled box beam problems exhibiting rapidly varying local end effects. Higher‐order interpolation wavelets have been used in the wavelet‐collocation setting, but the lowest‐order hat interpolation is applied here first and a hat interpolation wavelet‐based Galerkin method is newly formulated. Unlike existing orthogonal or biorthogonal wavelet‐based Galerkin methods, the present method does not require special treatment in dealing with general boundary conditions. Furthermore, the present method directly works with nodal values and does not require special formula for the evaluation of system matrices. Though interpolation wavelets do not have any vanishing moment, an adaptive scheme based on multi‐resolution approximations is possible and a preconditioned conjugate gradient method can be used to enhance numerical efficiency. Copyright © 2001 John Wiley & Sons, Ltd.     

A linearly conforming point interpolation method (LC‐PIM) for three‐dimensional elasticity problems

Linearly conforming point interpolation method (LC‐PIM) is formulated for three‐dimensional elasticity problems. In this method, shape functions are generated using point interpolation method by adopting polynomial basis functions and local supporting nodes are selected based on the background cells. The shape functions so constructed have the Kronecker delta functions property and it allows straightforward imposition of point essential boundary conditions. Galerkin weak form is used for creating discretized system equations, and a nodal integration scheme with strain‐smoothing operation is used to perform the numerical integration. The present LC‐PIM can guarantee linear exactness and monotonic convergence for the numerical results. Numerical examples are used to examine the present method in terms of accuracy, convergence, and efficiency. Compared with the finite element method using linear elements, the LC‐PIM can achieve better efficiency, and higher accuracy especially for stresses. Copyright © 2007 John Wiley & Sons, Ltd.     

Distortion‐immune nine‐node displacement‐based quadrilateral thick plate finite elements that satisfy constant‐bending patch test

We employ the linked interpolation concept to develop two higher‐order nine‐node quadrilateral plate finite elements with curved sides that pass the constant bending patch test for arbitrary node positions. The linked interpolation for the plate displacements is expanded with three bubble parameters to get polynomial completeness necessary to satisfy the patch test. In contrast to some other techniques, the elements developed in this way retain a symmetric stiffness matrix at a marginal computational expense at the element level. The new elements generated using this concept are tested on several examples with curved sides or some other kind of geometric distortion. Copyright © 2014 John Wiley & Sons, Ltd.     

A high‐order accurate particle‐in‐cell method

We propose the use of high‐order weighted essentially non‐oscillatory interpolation and moving‐least‐squares approximation schemes alongside high‐order time integration to enable high‐order accurate particle‐in‐cell methods. The key insight is to view the unstructured set of particles as the underlying representation of the continuous fields; the grid used to evaluate integro–differential coupling terms is purely auxiliary. We also include a novel regularization term to avoid the accumulation of noise in the particle samples without harming the convergence rate. We include numerical examples for several model problems: advection–diffusion, shallow water, and incompressible Navier–Stokes in vorticity formulation. The implementation demonstrates fourth‐order convergence, shows very low numerical dissipation, and is competitive with high‐order Eulerian schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Truly Concomitant and Independently Expressed Short‐ and Long‐Term Plasticity in a Bi2O2Se‐Based Three‐Terminal Memristor

Concomitance of diverse synaptic plasticity across different timescales produces complex cognitive processes. To achieve comparable cognitive complexity in memristive neuromorphic systems, devices that are capable of emulating short‐term (STP) and long‐term plasticity (LTP) concomitantly are essential. In existing memristors, however, STP and LTP can only be induced selectively because of the inability to be decoupled using different loci and mechanisms. In this work, the first demonstration of truly concomitant STP and LTP is reported in a three‐terminal memristor that uses independent physical phenomena to represent each form of plasticity. The emerging layered material Bi₂O₂Se is used for memristors for the first time, opening up the prospects for ultrathin, high‐speed, and low‐power neuromorphic devices. The concerted action of STP and LTP allows full‐range modulation of the transient synaptic efficacy, from depression to facilitation, by stimulus frequency or intensity, providing a versatile device platform for neuromorphic function implementation. A heuristic recurrent neural circuitry model is developed to simulate the intricate “sleep–wake cycle autoregulation” process, in which the concomitance of STP and LTP is posited as a key factor in enabling this neural homeostasis. This work sheds new light on the development of generic memristor platforms for highly dynamic neuromorphic computing.     

Electrically Pumped White‐Light‐Emitting Diodes Based on Histidine‐Doped MoS2 Quantum Dots

MoS₂ quantum dots (QDs)‐based white‐light‐emitting diodes (QD‐WLEDs) are designed, fabricated, and demonstrated. The highly luminescent, histidine‐doped MoS₂ QDs synthesized by microwave induced fragmentation of 2D MoS₂ nanoflakes possess a wide distribution of available electronic states as inferred from the pronounced excitation‐wavelength‐dependent emission properties. Notably, the histidine‐doped MoS₂ QDs show a very strong emission intensity, which exceeds seven times of magnitude larger than that of pristine MoS₂ QDs. The strongly enhanced emission is mainly attributed to nitrogen acceptor bound excitons and passivation of defects by histidine‐doping, which can enhance the radiative recombination drastically. The enabled electroluminescence (EL) spectra of the QD‐WLEDs with the main peak around 500 nm are found to be consistent with the photoluminescence spectra of the histidine‐doped MoS₂ QDs. The enhanced intensity of EL spectra with the current increase shows the stability of histidine‐doped MoS₂ based QD‐WLEDs. The typical EL spectrum of the novel QD‐WLEDs has a Commission Internationale de l'Eclairage chromaticity coordinate of (0.30, 0.36) exhibiting an intrinsic broadband white‐light emission. The unprecedented and low‐toxicity QD‐WLEDs based on a single light‐emitting material can serve as an excellent alternative for using transition metal dichalcogenides QDs as next generation optoelectronic devices.     

MLS‐based variable‐node elements compatible with quadratic interpolation. Part I: formulation and application for non‐matching meshes

Two‐dimensional variable‐node elements compatible with quadratic interpolation are developed using the moving least‐square (MLS) approximation. The mapping from the parental domain to the physical element domain is implicitly obtained from MLS approximation, with the shape functions and their derivatives calculated and saved only at the numerical integration points. It is shown that the present MLS‐based variable‐node elements meet the patch test if a sufficiently large number of integration points are employed for numerical integration. The cantilever problem with non‐matching meshes is chosen to check the feasibility of the present MLS‐based variable‐node elements, and the result is compared with that from the lower‐order case compatible with linear interpolation. Copyright © 2005 John Wiley & Sons, Ltd.     

Medical image fusion based on improved sum‐modified‐Laplacian

Sum‐modified‐Laplacian (SML) plays an important role in medical image fusion. However, fused rules based on larger SML always lead to fusion image distortion in transform domain image fusion or image information loss in spatial domain image fusion. Combined with average filter and median filter, a new medical image fusion method based on improved SML (ISML) is proposed. First, a basic fused image is gained by ISML, which is used for evaluation of the selection map of medical images. Second, difference images can be obtained by subtracting average image of all sources of medical images. Finally, basic fused image can be refined by difference images. The algorithm can both preserve the information of the source images well and suppress pixel distortion. Experimental results demonstrate that the proposed method outperforms the state‐of‐the‐art medical image fusion methods. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 206–212, 2015     

Acceleration of material‐dominated calculations via phase‐space simplicial subdivision and interpolation

We develop an acceleration method for material‐dominated calculations based on phase‐space simplicial interpolation of the relevant material‐response functions. This process of interpolation constitutes an approximation scheme by which an exact material‐response function is replaced by a sequence of approximating response functions. The terms in the sequence are increasingly accurate, thus ensuring the convergence of the overall solution. The acceleration ratio depends on the dimensionality, the complexity of the deformation, the time‐step size, and the fineness of the phase‐space interpolation. We ascertain these trade‐offs analytically and by recourse to selected numerical tests. The numerical examples with piecewise‐quadratic interpolation in phase space confirm the analytical estimates. Copyright © 2015 John Wiley & Sons, Ltd.     

Dispersion and isogeometric analyses of second‐order and fourth‐order implicit gradient‐enhanced plasticity models

Implicit gradient plasticity models incorporate higher‐order spatial gradients via an additional Helmholtz type equation for the plastic multiplier. So far, the enrichment has been limited to second‐order spatial gradients, resulting in a formulation that can be discretised using ‐continuous finite elements. Herein, an implicit gradient plasticity model is formulated that includes a fourth‐order gradient term as well. A comparison between the localisation properties of both the implicit gradient plasticity formulations and the explicit second‐order gradient plasticity model is made using a dispersion analysis. The higher‐order continuity requirement for the fourth‐order implicit gradient plasticity model has been met by exploiting the higher‐order continuity property of isogeometric analysis, which uses nonuniform rational B‐splines as shape functions instead of Lagrange polynomials. The discretised variables, displacements, and plastic multiplier may require different orders of interpolation, an issue that is also addressed. Numerical results show that both formulations can be used as a localisation limiter, but that quantitative differences occur, and a different evolution of the localisation band is obtained for 2‐dimensional problems.     

Extended isogeometric analysis based on PHT‐splines for crack propagation near inclusions

Adaptive local refinement is one of the main issues for isogeometric analysis (IGA). In this paper, an adaptive extended IGA (XIGA) approach based on polynomial splines over hierarchical T‐meshes (PHT‐splines) for modeling crack propagation is presented. The PHT‐splines overcome certain limitations of nonuniform rational B‐splines–based formulations; in particular, they make local refinements feasible. To drive the adaptive mesh refinement, we present a recovery‐based error estimator for the proposed method. The method is based on the XIGA method, in which discontinuous enrichment functions are added to the IGA approximation and this method does not require remeshing as the cracks grow. In addition, crack propagation is modeled by successive linear extensions that are determined by the stress intensity factors under linear elastic fracture mechanics. The proposed method has been used to analyze numerical examples, and the stress intensity factors results were compared with reference results. The findings demonstrate the accuracy and efficiency of the proposed method.     

A modified Newton‐type Koiter‐Newton method for tracing the geometrically nonlinear response of structures

The Koiter‐Newton (KN) method is a combination of local multimode polynomial approximations inspired by Koiter's initial postbuckling theory and global corrections using the standard Newton method. In the original formulation, the local polynomial approximation, called a reduced‐order model, is used to make significantly more accurate predictions compared to the standard linear prediction used in conjunction with Newton method. The correction to the exact equilibrium path relied exclusively on Newton‐Raphson method using the full model. In this paper, we proposed a modified Newton‐type KN method to trace the geometrically nonlinear response of structures. The developed predictor‐corrector strategy is applied to each predicted solution of the reduced‐order model. The reduced‐order model can be used also in the correction phase, and the exact full nonlinear model is applied only to calculate force residuals. Remainder terms in both the displacement expansion and the reduced‐order model are well considered and constantly updated during correction. The same augmented finite element model system is used for both the construction of the reduced‐order model and the iterations for correction. Hence, the developed method can be seen as a particular modified Newton method with a constant iteration matrix over the single KN step. This significantly reduces the computational cost of the method. As a side product, the method has better error control, leading to more robust step size adaptation strategies. Numerical results demonstrate the effectiveness of the method in treating nonlinear buckling problems.     

An Automatic Evaluation System for Contrast‐Detail Phantom Images in Digital Radiography

Currently, contrast‐detail phantom (CD phantom) images are widely used to assist medical experts for diagnosis, because these images can be used to study imaging quality and assess the radiation dose amount for digital X‐ray imaging systems. However, the quality of the CD phantom image varies from person to person, increasing the possibility of false diagnosis. In this article, we propose an automatic evaluation system to measure the quality of a phantom image an alternative to assessment by radiologists. The proposed method is based on bilinear pixel interpolation, geometric transformation, and region shifting to efficiently and objectively evaluate the quality of a phantom image. Moreover, misjudgment modification is also proposed to further improve the recognition accuracy. The experimental results show that the accuracy of the proposed method is very close to that of the radiologists observations. The results have also proven that the proposed method is a feasible way to evaluate the quality of a phantom image in an objective and automatic manner.     

Insight into the flow‐condition‐based interpolation finite element approach: solution of steady‐state advection–diffusion problems

The flow‐condition‐based interpolation (FCBI) finite element approach is studied in the solution of advection–diffusion problems. Two FCBI procedures are developed and tested with the original FCBI method: in the first scheme, a general solution of the advection–diffusion equation is embedded into the interpolation, and in the second scheme, the link‐cutting bubbles approach is used in the interpolation. In both procedures, as in the original FCBI method, no artificial parameters are included to reach stability for high Péclet number flows. The procedures have been implemented for two‐dimensional analysis and the results of some test problems are presented. These results indicate good stability and accuracy characteristics and the potential of the FCBI solution approach. Copyright © 2005 John Wiley & Sons, Ltd.