A stiffness parameter and truncation error criterion for adaptive path following in structural mechanics

We explore a truncation error criterion to steer adaptive step length refinement and coarsening in incremental-iterative path following procedures, applied to problems in large-deformation structural mechanics. Elaborating on ideas proposed by Bergan and collaborators in the 1970s, we first describe an easily computable scalar stiffness parameter whose sign and rate of change provide reliable information on the local behavior and complexity of the equilibrium path. We then derive a simple scaling law that adaptively adjusts the length of the next step based on the rate of change of the stiffness parameter at previous points on the path. We show that this scaling is equivalent to keeping a local truncation error constant in each step. We demonstrate with numerical examples that our adaptive method follows a path with a significantly reduced number of points compared to an analysis with uniform step length of the same fidelity level. A comparison with Abaqus illustrates that the truncation error criterion effectively concentrates points around the smallest-scale features of the path, which is generally not possible with automatic incrementation solely based on local convergence properties.     

Numerical modelling of the propagation of fast landslides using the finite element method

This paper proposes a two‐dimensional (2D) model for the analysis of the propagation of fast landslides involving a fluidized material such as debris and mud flows, flowslides and avalanching flows. The model is based on the Navier–Stokes depth‐integrated equations. To incorporate the effect of steep slopes and centrifugal forces due to the high velocities characterizing the flowslides and the bed curvature, a curvilinear system of reference is used. The corresponding equations of motion are complemented by depth‐averaged constitutive equations and bed friction laws. The resulting set of differential equations are solved using the two‐step Taylor–Galerkin algorithm. This algorithm has been used by the authors to solve hydraulic and dam‐break problems using the finite element method. Owing to the importance of the source term compared to the advection component, the proposed algorithm follows a splitting scheme using a fourth‐order Runge–Kutta method for integrating the friction and slope components. The performance of the overall approach has been checked in a number of examples. The analysis of the results provides insights into the key elements of the model and shows the adequacy of the method to solve real problems where merging and splitting of the flow occur. Copyright © 2004 John Wiley & Sons, Ltd.     

New two‐dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes

In this paper, we introduce an extension of Van Leer's slope limiter for two‐dimensional discontinuous Galerkin (DG) methods on arbitrary unstructured quadrangular or triangular grids. The aim is to construct a non‐oscillatory shock capturing DG method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion. Unlike some splitting techniques that are limited to linear approximations on rectangular grids, in this work, the solution is approximated by means of piecewise quadratic functions. The main idea of this new reconstructing and limiting technique follows a well‐known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution. Numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters. Copyright © 2004 John Wiley & Sons, Ltd.     

Symmetric BEM formulations for 2-D steady-state and transit potential problems

This paper presents a new concept for symmetric boundary element method (SBEM) applicable to 2-D steady-state and transit potential problems. Two kinds of SBEM formulations are derived. Symmetry is obtained simply through matrix manipulation, and no hypersingularity appears. Therefore, SBEM is much easier than the traditional symmetric Galerkin BEM. Compared with the traditional asymmetric BEM, the present SBEM can reduce the computational cost for time domain problems only. However, when applied to BEM/FEM coupling procedure, SBEM can reduce the computational cost for both steady-state and time domain problems. Three numerical examples are included to illustrate the effectiveness and accuracy of the present formulations.     

Application of Galerkin Method to Dynamical Behavior of Viscoelastic Timoshenko Beam with Finite Deformation

The motion equations governing the dynamical behavior of a viscoelasticTimoshenko beam with finite deformation are derived and simplified byGalerkin method. The viscoelastic material is assumed to obey thethree-dimensional fractional derivative constitutive relation. Thedynamical behaviors of the simplified systems with order 1 and order 2are numerically computed and compared by using the computational methodpresented by the authors. The dynamical behaviors of the systems areuniform qualitatively, but there is a little deviation quantitatively.And the truncated system with order 1 is safer than the one of order 2.It is also shown that the lower order system is reasonable. Theinfluences of the load parameter and the fractional derivative parameter(material parameter) on the deflection of the beam are consideredrespectively. The numerical methods in nonlinear dynamics, such as phasediagram, and Poincaré section, are applied to reveal dynamical behaviorsof the nonlinear viscoelastic Timoshenko beam. There are plenty ofdynamical behaviors, such as periodicity, bifurcation, quasi-periodicityand chaos in the dynamical system.     

光测遥测数据联合计算速度的方法

提出了利用遥测的过载、俯仰角信息和光测的坐标联合计算弹道关机段速度的方法，从遥测结果的系统误差、随机误差和数值积分的截断误差三万面对剩余误差的影响进行了精度分析，并给出了速度精度的算法。     

Exploiting partial or complete geometrical symmetry in 3D symmetric Galerkin indirect BEM formulations

Procedures based on group representation theory, allowing the exploitation of geometrical symmetry in symmetric Galerkin BEM formulations, are investigated. In particular, this investigation is based on the weaker assumption of partial geometrical symmetry, where the boundary has two disconnected components, one of which is symmetric; e.g. this can be very useful for defect identification problems. The main development is expounded in the context of 3D Neumann elastostatic problems, considered as model problems; and then extended to SGBIE formulations for Dirichlet and/or scalar problems. Both Abelian and non‐Abelian finite symmetry groups are considered. The effectiveness of the present approach is demonstrated through numerical examples, where both partial and complete symmetry are considered, in connection with both Abelian and non‐Abelian symmetry groups. Copyright © 2003 John Wiley & Sons, Ltd.     

Thermal Analysis of CNT-Based Nano-Composites by Element Free Galerkin Method

This paper deals with the thermal analysis of carbon nanotube (CNT) based composites by meshless element free Galerkin method. Cylindrical representative volume element (cylindrical RVE) has been chosen to evaluate the thermal properties of nano-composites using multi-domain and simplified approaches. The values of temperature have been calculated at different points and plotted against RVE length and RVE radius. A sensitivity analysis of RVE as well as CNT dimensions has been carried out in detail. The present computations show that the equivalent thermal conductivity is a function of CNT length, CNT radius, RVE length and RVE radius. Based on present numerical simulations, an approximate formula is proposed to calculate the equivalent thermal conductivity of nano-composites. The results obtained by simplified approach have been found in good agreement with those obtained by multi-domain approach.     

ROI-based Watermarking Scheme for JPEG 2000

A new region of interest (ROI)-based watermarking method for JPEG 2000 is presented. The watermark is embedded into the host image based on the characteristics of the ROI to protect rights to the images. This scheme integrates the watermarking process with JPEG 2000 compression procedures. Experimental results have demonstrated that the proposed watermark technique successfully survives JPEG 2000 compression, progressive transmission, and principal attacks.     

间断Galerkin方法的最优误差限

本文考虑了数性双曲方程的离散Ｇａｌｅｒｋｉｎ方法。如果精确到光滑的并且同是几乎均匀的，证明了对于分层常数元的最优的和超收敛的误差限。