A computational method for quasi-static fracture

A direct method for solving quasi-static, mixed-mode fracture problems is presented. The element-free Galerkin method is used in order to allow for crack growth without remeshing. An expression for the normalized, critical traction is derived in terms of the fracture resistance (R-curve) and a crack-dependent function. Sample problems demonstrate the capability of this method to accurately compute the post-peak equilibrium paths for structures with growing cracks.     

An efficient approach to converting three-dimensional image data into highly accurate computational models

Image-based meshing is opening up exciting new possibilities for the application of computational continuum mechanics methods (finite-element and computational fluid dynamics) to a wide range of biomechanical and biomedical problems that were previously intractable owing to the difficulty in obtaining suitably realistic models. Innovative surface and volume mesh generation techniques have recently been developed, which convert three-dimensional imaging data, as obtained from magnetic resonance imaging, computed tomography, micro-CT and ultrasound, for example, directly into meshes suitable for use in physics-based simulations. These techniques have several key advantages, including the ability to robustly generate meshes for topologies of arbitrary complexity (such as bioscaffolds or composite micro-architectures) and with any number of constituent materials (multi-part modelling), providing meshes in which the geometric accuracy of mesh domains is only dependent on the image accuracy (image-based accuracy) and the ability for certain problems to model material inhomogeneity by assigning the properties based on image signal strength. Commonly used mesh generation techniques will be compared with the proposed enhanced volumetric marching cubes (EVoMaCs) approach and some issues specific to simulations based on three-dimensional image data will be discussed. A number of case studies will be presented to illustrate how these techniques can be used effectively across a wide range of problems from characterization of micro-scaffolds through to head impact modelling.     

A computational method for frictional contact problem using finite element method

Using the finite element method a numerical procedure is developed for the solution of the two-dimensional frictional contact problems with Coulomb's law of friction. The formulation for this procedure is reduced to a complementarity problem. The contact region is separated into stick and slip regions and the contact stress can be solved systematically by applying the solution technique of the complementarity problem. Several examples are given to demonstrate the validity of the present formulation.     

A computational method for inverse free boundary determination problem

Based on the method of fundamental solutions and discrepancy principle for the choice of location for source points, we extend in this paper the application of the computational method to determine an unknown free boundary of a Cauchy problem of parabolic‐type equation from measured Dirichlet and Neumann data with noises. The standard Tikhonov regularization technique with the L‐curve method for an optimal regularized parameter is adopted for solving the resultant highly ill‐conditioned system of linear equations. Both one‐dimensional and two‐dimensional numerical examples are given to verify the efficiency and accuracy of the proposed computational method. Copyright © 2007 John Wiley & Sons, Ltd.     

A simple background elimination method for Raman spectra

In this paper, we consider a new background elimination method for Raman spectra. The proposed method is based on peak detection, smoothing, and interpolation. Since the background is usually slowly varying with respect to wavelength, we could estimate the background by eliminating significant peaks. For this purpose, we seek the peaks by inspecting the smoothed derivative of a given spectrum. After clipping out the corresponding peak regions, we estimate the background by applying a modified linear interpolation. Then the background is eliminated from the measured Raman spectrum by simple subtraction. The experimental results showed that the proposed method gave satisfactory results for real Raman spectra as well as synthetic data. As the proposed method requires no prior knowledge of spectrum, we expect that the method could be applied to other spectral data as well.     

A simple method for linearizing nonlinear spectra for calibration

The development and acceptance of spectral calibration methods has been an important success story for the field of chemometrics. This paper contains a new study of a very old calibration method (K-matrix calibration, parallel calibration, or generalized inverse prediction) and partial least squares (PLS), the mainstay of modern chemometrics. We show that with some modest amount of modification, the old method of calibration is comparable, in terms of prediction, to PLS for spectroscopy involving nonlinear spectral responses.     

A computational method to differentiate normal individuals,osteoarthritis and rheumatoid arthritis patients using serum biomarkers

The objective of this study was to develop a method for categorizing normal individuals (normal, n = 100) as well as patients with osteoarthritis (OA, n = 100), and rheumatoid arthritis (RA, n = 100) based on a panel of inflammatory cytokines expressed in serum samples. Two panels of inflammatory proteins were used as training sets in the construction of two separate artificial neural networks (ANNs). The first training set consisted of all proteins (38 in total) and the second consisted of only the significantly different proteins expressed (12 in total) between at least two patient groups. Both ANNs obtained high levels of sensitivity and specificity, with the first and second ANN each diagnosing 100% of test set patients correctly. These results were then verified by re-investigating the entire dataset using a decision tree algorithm. We show that ANNs can be used for the accurate differentiation between serum samples of patients with OA, a diagnosed RA patient comparator cohort and normal/control cohort. Using neural network and systems biology approaches to manage large datasets derived from high-throughput proteomics should be further explored and considered for diagnosing diseases with complex pathologies.     

Device for converting linear displacements into electric pulses

Translated from Izmeritel'naya Tekhnika, No. 4, p. 14, April, 1993.     

A general approach for transferring hydrophobic nanocrystals into water

Hydrophobic inorganic nanocrystals have been transferred from organic solvent to aqueous solution through a robust and general ligand exchange procedure. Polyelectrolytes such as poly(acrylic acid) and poly(allylamine) are used to replace the original hydrophobic ligands on the surface of nanocrystals at an elevated temperature in a glycol solvent and eventually render the nanocrystals highly water soluble. The physical properties of the nanocrystals, such as superparamagnetism, photocatalytic activity, and photoluminescence, are maintained or improved after ligand exchange.     

A general rotation averaging method for granular materials

In order to study the rotational behavior of granular materials, rotation averaging methods are required. Most of the existing rotation averaging methods are only for 2D cases and limited by the shape, position and size of the averaging volumes. Hence, a general rotation averaging method is proposed in this paper. Our approach is simple yet works for both 2D and 3D cases with very little restriction. The performance of this method is shown by both hypothetical examples and DEM simulations of plane strain tests with different boundary conditions.     

A new multiscale computational method for elasto-plastic analysis of heterogeneous materials

A new multiscale computational method is developed for the elasto-plastic analysis of heterogeneous continuum materials with both periodic and random microstructures. In the method, the multiscale base functions which can efficiently capture the small-scale features of elements are constructed numerically and employed to establish the relationship between the macroscopic and microscopic variables. Thus, the detailed microscopic stress fields within the elements can be obtained easily. For the construction of the numerical base functions, several different kinds of boundary conditions are introduced and their influences are investigated. In this context, a two-scale computational modeling with successive iteration scheme is proposed. The new method could be implemented conveniently and adopted to the general problems without scale separation and periodicity assumptions. Extensive numerical experiments are carried out and the results are compared with the direct FEM. It is shown that the method developed provides excellent precision of the nonlinear response for the heterogeneous materials. Moreover, the computational cost is reduced dramatically.     

A novel computational method for solving Troesch's problem with high-sensitivity parameter

Troesch's problem is a nonlinear boundary value problem arising in the confinement of a plasma column by radiation pressure, and also in the theory of gas porous electrodes. It is well known that finding numerical solutions to this problem is challenging, especially when the sensitivity parameter is large. In this article, we present an efficient and accurate numerical method for solving Troesch's problem. The method presented in this work is capable of computing the solution, even for extremely high-sensitivity parameter. The method is based on the the Newton–Raphson–Kantorovich approximation method in function space combined with the standard finite difference method. Although, available numerical solvers fail to provide accurate numerical solutions when the sensitivity parameter λ becomes large (λ exceeds 100) [1–5], the method proposed here is able to provide accurate numerical solutions for extremely large values of this sensitivity parameter, up to λ = 500. Numerical experiments are provided to show the accuracy of the method compared to existing solvers, as well as its capability to compute the solution for high values of the sensitivity parameter λ.     

A computational method for optimal structural design II: Continuous problems

A method for solving structural design problems that allows a continuous distribution of material along structural elements is presented. The method is an extension of the generalized steepest descent method presented in Reference 1. Inequality constraints on design variables, displacement, natural frequency, and buckling are explicitly treated and a minimum weight cost function is employed. A steepest descent method for boundary-value state equations is developed and a computational algorithm is given. Several example problems in minimum weight structural design are solved and compared with results obtained by discretization techniques.     

A finite element method for the computational modelling of cohesive cracks

The present contribution is concerned with the computational modelling of cohesive cracks in quasi‐brittle materials, whereby the discontinuity is not limited to interelement boundaries, but is allowed to propagate freely through the elements. In the elements, which are intersected by the discontinuity, additional displacement degrees of freedom are introduced at the existing nodes. Therefore, two independent copies of the standard basis functions are used. One set is put to zero on one side of the discontinuity, while it takes its usual values on the opposite side, and vice versa for the other set. To model inelastic material behaviour, a discrete damage‐type constitutive model is applied, formulated in terms of displacements and tractions at the surface. Some details on the numerical implementation are given, concerning the failure criterion, the determination of the direction of the discontinuity and the integration scheme. Finally, numerical examples show the performance of the method. Copyright © 2005 John Wiley & Sons, Ltd.     

A new method of reconstructing spectra

A theoretical method is proposed for accurate reconstruction of the spectrum using bounded sets of discrete values of the spectrum intensities. The method is based on a well known measurement theorem from optics. This method was used to solve the corresponding integral equation to eliminate instrumental distortions and to accurately reconstruct the spectra using the appropriate discrete values. Institute of Applied Physics Problems, Armenian Academy of Sciences Pis’ma Zh. Tekh. Fiz. 24, 5–9 (July 26, 1998)