A new class of algorithms for classical plasticity extended to finite strains. Application to geomaterials

A recently proposed methodology for computational plasticity at finite strains is re-examined within the context of geomechanical applications and cast in the general format of multi-surface plasticity. This approach provides an extension to finite strains of any infinitesimal model of classical plasticity that retains both the form of the yield criterion and the hyperelastic character of the stress-strain relations. Remarkably, the actual algorithmic implementation reduces to a reformulation of the standard return maps in principal axis with algorithmic elastoplastic moduli identical to those of the infinitesimal theory. New results in the area of geomechanics included a fully implicit return map for the modified Cam-Clay model, extended here to the finite deformation regime, and a new semi-explicit scheme that restores symmetry of the algorithmic moduli while retaining the unconditional stability property. In addition, a new phenomenological plasticity model for soils is presented which includes a number of widely used models as special cases. The general applicability of the proposed methodology is illustrated in several geomechanical examples that exhibit localization and finite deformations.Partial support provided by the Max Kade Foundation under Grant No. 2-DJA-616 and with Stanford University, and the Naval Civil Engineering Laboratory at Port Huaneme     

An analysis of a new class of integration algorithms for elastoplastic constitutive relations

An accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors, is carried out in this paper. For simplicity, attention is confined to infinitesimal deformations. The integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations. General rate-independent and rate-dependent behaviour, with plastic hardening or softening, associated or non-associated flow rules and nonlinear elastic response can be efficiently treated within the present framework. Isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding.     

A very efficient moment calculation method for uncertain linear dynamic systems

The problem of calculating the uncertainty in the dynamic response of a structure due to uncertainties related to the modeling of its dynamic behavior, is addressed. Based on a Bayesian probabilistic approach, a new approximate numerical method is proposed to investigate the resulting uncertainties in the structural response. The proposed method provides a very efficient and accurate approach to the solution of stochastic finite-element models. It can be used to quantify the uncertainties in the predicted response of a structure during its design, where engineering judgement is used to quantify the uncertainties in the modeling process.     

A local convergence analysis of bilevel decomposition algorithms

Multidisciplinary design optimization (MDO) problems are engineering design problems that require the consideration of the interaction between several design disciplines. Due to the organizational aspects of MDO problems, decomposition algorithms are often the only feasible solution approach. Decomposition algorithms reformulate the MDO problem as a set of independent subproblems, one per discipline, and a coordinating master problem. A popular approach to MDO problems is bilevel decomposition algorithms. These algorithms use nonlinear optimization techniques to solve both the master problem and the subproblems. In this paper, we propose two new bilevel decomposition algorithms and analyze their properties. In particular, we show that the proposed problem formulations are mathematically equivalent to the original problem and that the proposed algorithms converge locally at a superlinear rate. Our computational experiments illustrate the numerical performance of the algorithms.     

Study of efficient homogenization algorithms for nonlinear problems

A framework for the homogenization of nonlinear problems is discussed with respect to block LU factorization of the micro–macro coupled equation, and based on the relation between the characteristic deformation and the Schur-Complement as the homogenized tangent stiffness. In addition, a couple of approximation methods are introduced to reduce the computational cost, i.e., a simple scheme to reuse the old characteristic deformation and a sophisticated method based on the mode-superposition method developed by our group. Note that these approximation methods satisfy the equilibrium conditions in both scales. Then, using a simplified FE model, the conventional algorithm, a relative algorithm originating from the block LU factorization, and the above-mentioned algorithms with the approximated Schur-Complement are compared and discussed. Finally, a large-scale heart simulation using parallel computation is presented, based on the proposed method.     

Mesoflowers: A new class of highly efficient surface-enhanced Raman active and infrared-absorbing materials

A method for the synthesis of a new class of anisotropic mesostructured gold material, which we call “mesoflowers”, is demonstrated. The mesoflowers, unsymmetrical at the single particle level, resemble several natural objects and are made up of a large number of stems with unusual pentagonal symmetry. The mesostructured material has a high degree of structural purity with star-shaped, nano-structured stems. The mesoflowers were obtained in high yield, without any contaminating structures and their size could be tuned from nano- to meso-dimensions. The dependence of various properties of the mesoflowers on their conditions of formation was studied. The near-infrared-infrared (NIR-IR) absorption exhibited by the mesoflowers has been used for the development of infrared filters. Using a prototypical device, we demonstrated the utility of the gold mesoflowers in reducing the temperature rise in an enclosure exposed to daylight in peak summer. These structures showed a high degree of surface-enhanced Raman scattering (SERS) activity compared to spherical analogues. SERS-based imaging of a single mesoflower is demonstrated. The high SERS activity and NIR-IR absorption property open up a number of exciting applications in diverse areas. Electronic Supplementary Material  Supplementary material is available in the online version of this article at http://dx.doi.org/ and is accessible free of charge.     

Computer algorithms for calculating efficient initial vectors for subspace iteration method

In this paper, the effects of selecting initial vectors on computation efficiency for a subspace iteration method are investigated. Four algorithms are used for selecting the initial vectors. First, arbitrary starting iteration vectors are chosen according to Bathe and Wilson's algorithm.¹ In the other algorithms, the initial vectors are the retrieved eigenvectors from the Guyan and quadratic reduction methods. Improvement of the eigenvalue approximations of the subspace iteration method over reduction methods is presented. The computation effort is examined for the various algorithms used for initial iteration vectors.     

Epidemic algorithms for reliable and efficient information dissemination in vehicular

Vehicular ad hoc networks (VANET), which are created by vehicles equipped with short- and mediumrange wireless communication, have an array of important applications in intelligent transport systems. Many of these applications require reliable, bandwidth-efficient dissemination of traffic and road information via ad hoc network technology. This is a difficult task since inter-vehicular networks often lack continuous end-to-end connectivity and are characterised by large variations in node density. A new epidemic algorithm for information dissemination in highly dynamic and intermittently connected VANET is introduced. It is shown through realistic simulations in highway traffic that the proposed algorithm is capable of reliable and efficient information dissemination in VANET in the face of frequent network fragmentation and large density variations.     

A class of generalized mid-point algorithms for the Gurson–Tvergaard material model

We investigate the generalized mid-point algorithms for the integration of elastoplastic constitutive equations for the pressure-dependent Gurson–Tvergaard yield model. By exact linearization of the algorithms and decomposition of the stresses into hydrostatic and deviatoric parts, a formula for explicitly calculating the consistent tangent moduli with the generalized mid-point algorithms is derived for the Gurson–Tvergaard model. The generalized mid-point algorithms, together with the consistent tangent moduli, have been implemented into ABAQUS via the user material subroutine. An analytical solution of the Gurson–Tvergaard model for the plane strain tension case is given and the performances of the generalized mid-point algorithms have been assessed for plane strain tension and hydrostatic tension problems and compared with the exact solutions. We find that, in the two problems considered, the generalized mid-point algorithms give reasonably good accuracy even for the case using very large time increment steps, with the true mid-point algorithm (α = 0·5) the most accurate one. Considering the extra non-symmetrical property of the consistent tangent moduli of the algorithms with α < 1, the Euler backward algorithm (α = 1) is, perhaps, the best choice.     

First excursion probabilities for linear systems by very efficient importance sampling

An analytical study of the failure region of the first excursion reliability problem for linear dynamical systems subjected to Gaussian white noise excitation is carried out with a view to constructing a suitable importance sampling density for computing the first excursion failure probability. Central to the study are ‘elementary failure regions’, which are defined as the failure region in the load space corresponding to the failure of a particular output response at a particular instant. Each elementary failure region is completely characterized by its design point, which can be computed readily using impulse response functions of the system. It is noted that the complexity of the first excursion problem stems from the structure of the union of the elementary failure regions. One important consequence of this union structure is that, in addition to the global design point, a large number of neighboring design points are important in accounting for the failure probability. Using information from the analytical study, an importance sampling density is proposed. Numerical examples are presented, which demonstrate that the efficiency of using the proposed importance sampling density to calculate system reliability is remarkable.     

Two new decoding algorithms for Reed-Solomon codes

The subject of decoding Reed-Solomon codes is considered. By reformulating the Berlekamp and Welch key equation and introducing new versions of this key equation, two new decoding algorithms for Reed-Solomon codes will be presented. The two new decoding algorithms are significant for three reasons. Firstly the new equations and algorithms represent a novel approach to the extensively researched problem of decoding Reed-Solomon codes. Secondly the algorithms have algorithmic and implementation complexity comparable to existing decoding algorithms, and as such present a viable solution for decoding Reed-Solomon codes. Thirdly the new ideas presented suggest a direction for future research. The first algorithm uses the extended Euclidean algorithm and is very efficient for a systolic VLSI implementation. The second decoding algorithm presented is similar in nature to the original decoding algorithm of Peterson except that the syndromes do not need to be computed and the remainders are used directly. It has a regular structure and will be efficient for implementation only for correcting a small number of errors. A systolic design for computing the Lagrange interpolation of a polynomial, which is needed for the first decoding algorithm, is also presented.This research was supported by a grant from the Canadian Institute for Telecommunications Research under the NCE program of the Government of Canada     

A new local high-order laminate theory

A new local high-order deformable theory of laminated composite/sandwich plates is presented here. The displacement fields of each discrete layer were assumed in the present theory to be of a high-order polynomial series through layer-thickness. The displacement and traction continuity conditions at the interface between layers and the traction conditions at the outer surfaces were imposed as the constraint conditions, and introduced into the potential energy functional by the Lagrange multiplier method. The equations of motion and admissible boundary conditions were given on the basis of the present theory by using the generalized variational principle. Pagano's 3-D elasticity solutions of generally rectangular laminated composite/sandwich plates, fully simply supported, subjected to transverse sinusoidal loading were used for assessment of the present theory and other theories discussed in previous literature. The present theory was found to agree very closely with 3-D elasticity solutions.     

MINIT: A new gas detector for very low threshold particle identification

We report on the first results of in-beam tests performed with the MINIT detection technique. Its modular structure of multilayer ionization chamber with proportional avalanche multiplication allows to detect and identify heavy ions with a very low energy threshold. Its simple mechanical structure, based on a glass microstrip plate, should allow the realization of cheap large-area arrays of similar detectors, in view of the next generation of experiments with radioactive ion beams.     

A new efficient mixed formulation for thin shell finite element models

A nine node shell element is developed by a new and more efficient mixed formulation. The new shell element formulation is based on the Hellinger–Reissner principle with independent strain and the concept of a degenerate solid shell. The new formulation is made more efficient in terms of computing time than the conventional mixed formulation by dividing the assumed strain fields into a lower order part and a higher order part. Numerical results demonstrate that the present nine node element is free of locking even for very thin plates and shells and is also kinematically stable. In fact the stiffness matrix associated with the higher order assumed strain plays the role of a stabilization matrix.     

A new efficient factorization algorithm for polynomials over small finite fields

We present a new deterministic factorization algorithm for polynomials over a finite prime fieldF _p . As in other factorization algorithms for polynomials over finite fields such as the Berlekamp algorithm, the key step is the linearization of the factorization problem, i.e., the reduction of the problem to a system of linear equations. The theoretical justification for our algorithm is based on a study of the differential equationy ^(p –1)+y ^p =0 of orderp–1 in the rational function fieldF _p(x). In the casep=2 the new algorithm is more efficient than the Berlekamp algorithm since there is no set-up cost for the coefficient matrix of the system of linear equations.     

均匀B样条曲线的高效细分公式

主要研究在n次均匀B样条初始节点序列中每两个节点间一次性地均匀插入m-1个新节点的算法,导出了原始n次均匀B样条基函数与插入新节点后的基函数之间的明确关系式,进一步得到了原始B样条曲线的新旧控制顶点之间的明确关系式.该结果几何直观性强,新旧控制顶点对应明确,丰富了绘制均匀B样条曲线的方法.     

A new method for fast and efficient magnetic selection of hard Ferrites

A new method for fast and efficient magnetic selection of hard ferrites is described in which a procedure of magnetization with transient periodical oscillations (MTPO) is used. This method was evaluated during the determination of remanent induction Brand coercive forceBHcof hard ferrites. The equivalent circuit of an instrument for magnetization, measuring, selection, and demagnetization (MMSD) using the MTPO procedure also is given.