Energy-dissipative momentum-conserving time-stepping algorithms for the dynamics of nonlinear Cosserat rods

 This paper presents the development of energy-dissipative momentum-conserving algorithms for the numerical integration of the dynamics of nonlinear Cosserat rods. The proposed numerical schemes exhibit a non-negative energy dissipation, controllable through the appropriate algorithmic parameters including an energy-conserving scheme as a particular case. These conservation/dissipation properties are proven rigorously in the general nonlinear setting, accounting specifically for the finite element implementation of the rotational degrees of freedom associated to the motion of the rod's cross-sections. In particular, we consider a direct parameterization of the director fields defining these sections, hence leading to frame-indifferent approximations of the strain measures defining the rod's mechanical response. The robustness added by these considerations when comparing the proposed numerical schemes with existing conserving schemes is illustrated with several representative numerical simulations. RID="†" ID="†" Our motivation behind the developments presented in this paper started from a number of very instructive conversations with Professor M.A. Crisfield. His insight in the numerical treatment of the structural problems considered here was unique. It was for us a great privilege to interact with him and enjoy of his friendship. These interactions were always very rewarding, given especially how contagious his enthusiasm for his work was. We would like to dedicate this modest contribution to his memory. Currently at: E.T.S.I.C.C.P., Universidad Politécnica de Madrid, Spain Dedicated to the memory of Prof. mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many years. Financial support for this research was provided by the AFOSR under contract no. F49620-00-1-0360 with UC Berkeley. This support is gratefully acknowledged.     

A new energy and momentum conserving algorithm for the non-linear dynamics of shells

A numerical time-integration scheme for the dynamics of non-linear elastic shells is presented that simultaneously and independent of the time-step size inherits exactly the conservation laws of total linear, total angular momentum as well as total energy. The proposed technique generalizes to non-linear shells recent work of the authors on non-linear elastodynamics and is ideally suited for long-term/large-scale simulations. The algorithm is second-order accurate and can be immediately extended with no modification to a fourth-order accurate scheme. The property of exact energy conservation induces a strong notion of non-linear numerical stability which manifests itself in actual simulations. The superior performance of the proposed scheme method relative to conventional time-integrators is demonstrated in numerical simulations exhibiting large strains coupled with a large overall rigid motion. These numerical experiments show that symplectic schemes often regarded as unconditionally stable, such as the mid-point rule, can exhibit a dramatic blow-up in finite time while the present method remains perfectly stable.     

Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum

We show that, for rigid body dynamics, the mid-point rule formulated in body co-ordinates exactly conserves energy and the norm of the angular momentum for incremental force-free motions, but fails to conserve the direction of the angular momentum vector. Further, we show that the mid-point rule formulated in the spatial representation is, in general, physically and geometrically meaningless. An alternative algorithm is developed which exactly preserves energy, and the total spatial angular momentum in incremental force-free motions. The implicit version of this algorithm is unconditionally stable and second order accurate. The explicit version conserves exactly angular momentum in incremental force-free motions. Numerical simulations are presented which illustrate the excellent performance of the proposed procedure, even for incremental rotations over 65 degrees. The procedure is directly applicable to transient dynamic calculations of geometrically exact rods and shells.     

Simulation of a confined polymer in solution using the dissipative particle dynamics method

The dynamics of a bead-and-spring polymer chain suspended in a sea of solvent particles are examined by dissipative particle dynamics (DPD) simulations. The solvent is treated as a structured medium, comprised of particles subject to both solvent-solvent and solvent-polymer interactions and to stochastic Brownian forces. Thus hydrodynamic interactions among the beads of the polymer evolve naturally from the dynamics of the solvent particles. DPD simulations are about two orders of magnitude faster than comparable molecular dynamics simulations. Here we report the results of an investigation into the effects of confining the dissolved polymer chain between two closely spaced parallel walls. Confinement changes the polymer configuration statistics and produces markedly different relaxation times for chain motion parallel and perpendicular to the surface. This effect may be partly responsible for the gap width-dependent theological properties observed in nanoscale rheometry.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Damage identification in three-dimensional structures using single-objective evolutionary algorithms and finite element model updating: evaluation and comparison

This study presents a methodology which integrates single-objective evolutionary algorithms (EAs) and finite element (FE) model updating for damage inference in three-dimensional (3D) structures. First, original well-known EAs, namely the genetic algorithm, differential evolution (DE) and particle swarm optimization (PSO), are combined with FE model updating for detecting damage in a 3D four-storey modular structure and their performances are compared. Next, to obtain more accurate results, hybrid Lévy flights–DE and hybrid artificial bee colony–PSO are developed for enhancing damage identification. With each method, the objective function composed of modal strain energy and mode shape residuals, taken from the FE model of the intact structure and the simulated damage responses, is initially created. Then, the performance of each algorithm combined with FE model updating for damage detection is assessed in terms of three characteristics: consistency, computational cost and accuracy, and the best performing algorithm is recommended.     

Analyzing Fe–Zn system using molecular dynamics, evolutionary neural nets and multi-objective genetic algorithms

Failure behavior of Zn coated Fe is simulated through molecular dynamics (MD) and the energy absorbed at the onset of failure along with the corresponding strain of the Zn lattice are computed for different levels of applied shear rate, temperature and thickness. Data-driven models are constructed by feeding the MD results to an evolutionary neural network. The outputs of these neural networks are utilized to carry out a multi-objective optimization through genetic algorithms, where the best possible tradeoffs between two conflicting requirements, minimum deformation and maximum energy absorption at the onset of failure, are determined by constructing a Pareto frontier.     

材料不平衡凝聚非线性行为的研究及数值模拟

材料设计是指通过理论与计算预报新材料的组分、结构与性能。对材料不平衡凝聚非线性行为的研究发展过程、应用前景进行了评述。介绍了非线性行为在材料设计中的理论意义,分析了几种数值计算方法的优缺点。提出了材料研究微观模拟的发展方向。     

多学科设计优化的数值算法及其组合算法比较的研究

针对多学科设计优化的数值算法比较研究上存在的不足,提出了算法在进行优化时所需的时间、解决问题个数及选用目标函数的相对精度等三项评估标准相结合的三维算法比较方法,首次将精度作为算法比较的一个重要指标,由此得到的算法比较三维模型,为算法选择提供了更加合理的理论依据.在理论研究的基础上,对组合算法和数值算法进行了比较,突破了传统算法比较局限在数值算法的不足.结果表明,在时间变化不大的情况下,组合算法的精度比单纯的数值算法有大幅度的提高,为工程应用提供了更全面的支持.在此基础上给出了数值算法及其组合的算法选择流程.最后,通过手机的多学科设计优化实例,验证了所提出的算法选择流程的合理性和可行性.     

低温微创手术高真空绝热治疗探杆研制

介绍低温微创手术高真空绝热治疗探杆的结构和制作方法,对制作过程中小直径簿壁不锈钢套管焊接;微小间隙抽真空以及真空检漏等应注意的问题进行探讨.临床应用表明,探杆采用真空度1×10-4Pa的高真空绝热能够实现良好的绝热性能;可以满足低温微创手术对探杆绝热的要求.     

Structure and hot-rolled reinforcement rods properties evolution in the process of long service life

The physical nature of mechanical properties of hot-rolled reinforcement rods degradation during long-life operation is established by methods of transmission diffraction electron microscopy. It is shown that strength and plasticity properties decrease is due to cementite plates cutting and dissolution, microcracks formation process as a result of interstitial phase inclusions creation in the near-surface layer of material.     

Hypervelocity penetration modeling: momentum vs. energy and energy transfer mechanisms

Analytic penetration modeling usually relies on either a momentum balance or an energy-rate balance to predict depth of penetration by a penetrator based on initial geometry and impact velocity. In recent years, fairly sophisticated models of penetration have arisen that develop the three-dimensional flow field within a target. Based on the flow field and constitutive assumptions, it is then possible to derive a momentum or an energy-rate balance. This paper examines the use of assumed flow fields within a target created by impact and then examines the resulting predicted behavior based on either momentum conservation or energy conservation. It is shown that for the energy-rate balance to work, the details of the energy transfer mechanisms must be included in the model. In particular, how the projectile energy is initially transferred into target kinetic energy and elastic compression energy must be included. As impact velocity increases, more and more energy during the penetration event is temporarily deposited within the target as elastic compression and target kinetic energy. This energy will be dissipated by the target at a later time, but at the time of penetration it is this transfer of energy that defines the forces acting on the projectile. Thus, for an energy rate balance approach to successfully model penetration, it must include the transfer of energy into kinetic energy within the target and the storage of energy by elastic compression. Understanding the role of energy dissipation in the target clarifies the various terms in analytic models and identifies their origin in terms of the fundamental physics. Understanding the modes of energy transfer also assists in understanding the hypervelocity result that penetration depth only slowly increases with increasing velocity even though the kinetic energy increases as the square of the velocity.     

Perforation of aluminum plates with ogive-nose steel rods at normal and oblique impacts

Perforation experiments were conducted with 26.3 mm thick, 6061-T651 aluminum plates and 12.9 mm diameter, 88.9 mm long, 4340 R_c = 44 ogive-nose steel rods. For normal and oblique impacts with striking velocities between 280 and 860 m/s, we measured residual velocities and displayed the perforation process with X-ray photographs. These photographs clearly showed the time-resolved projectile kinematics and permanent deformations. In addition, we developed perforation equations that accurately predict the ballistic limit and residual velocities.     

水基铁磁流体磁致凝聚行为的三维耗散粒子动力学研究

用耗散粒子动力学方法对铁磁流体在外加恒定磁场作用下的凝聚行为进行了三维模拟.基于Flory-Huggins相混理论得到包括磁性颗粒珠子间的通常意义上的相互作用参数;利用Ewald方法把单磁畴结构的磁性颗粒长程的磁性相互作用转换成短程加和形式,从而得到磁偶极子的磁性相互作用参数.模拟结果表明,外加磁场强度是形成凝聚结构的...     

RC beams strengthened with NSM CFRP rods and modeling of peeling-off failure

The aim of the experimental programme developed in this work was to investigate the possibility of using Carbon Fibre-Reinforced Polymer (CFRP) rods to strengthen concrete structural members with the Near Surface Mounted reinforcement (NSM) technique. The global behaviour of reinforced cantilever concrete beams strengthened by the NSM technique and subjected to flexure is investigated. The specific problem of cantilever beams (strengthening outward pressure) was studied. The global behaviour of the cantilever concrete beams was compared with that of beams subjected to flexure with four points load test. A carbon–epoxy pultruded FRP (CFRP) rod of 6 mm in diameter was used. The study was carried out up to the failure load, and focused on the modifications in mechanical behaviour, cracking and failure mode of the beams. An analytical and Finite Element models to predict the peeling-off failure mode were compared.     

Influence of non degenerated joint on the global and local behavior of joined rods

We consider transport (thermoconductivity, diffusion, etc.) problem in a system of joined n-dimensional (n = 2, 3) thin rods, We assume that the joint has the size compared with the characteristic diameter of the rods and the joint is made of materials with transport properties similar to the transport properties of materials of the rods (such joint is referred as non degenerated joint). Using a technique of local perturbation, we construct asymptotic representations of the solution and obtain the limit model for some types of rods and joints. In all the cases, we find that the non degenerated joint is ignored on the global level (e.g., in framework models) and it manifests itself on the local level (in particular, it determines the gradient of the solution in and near the joint).     

Exact three-dimensional piezothermoelasticity solution for dynamics of rectangular cross-ply hybrid plates featuring interlaminar bonding imperfections

An exact three-dimensional (3D) piezothermoelasticity solution is presented for static, free vibration and steady state harmonic response of simply supported cross-ply piezoelectric (hybrid) laminated rectangular plates with interlaminar bonding imperfections. The bonding imperfection is modeled by considering the jump in the displacements, electric potential and temperature across the non-rigid interface proportional, respectively, to the associated tractions, transverse electric displacement and heat flux. The solution includes the case when electric potentials are prescribed at the interfaces for effective actuation. Numerical results are presented for hybrid composite and sandwich plates with varying imperfection compliance. The effect of location of imperfect bonding on the response is investigated for mechanical, electric potential and thermal load cases. The effect of weak bonding at elastic–piezoelectric interface on the actuation authority of the piezoelectric layer is also investigated. These results would serve as benchmark for assessing 2D plate theories incorporating interlaminar bonding imperfections.     

Rheology and thermodynamics from nonequilibrium molecular dynamics

We review some of the recent developments in nonequilibrium molecular dynamics (NEMD) simulations of fluids. One of the areas which has been profoundly influenced by this new technique is the study of systems undergoing steady planar Couette flow. Attention has been focused on developments which have taken place since the 1982 Conference on Nonlinear Fluid Behaviour. Since that time many questions concerning the formal justification of NEMD algorithms have been successfully answered. There have also been extensions of the range of properties studied by the technique.Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Stochastic approximation algorithms: Overview and recent trends

Stochastic approximation is a common paradigm for many stochastic recursions arising both as algorithms and as models of some stochastic dynamic phenomena. This article gives an overview of the known results about their asymptotic behaviour, highlights recent developments such as distributed and multiscale algorithms, and describes existing and potential applications, and other related issues. The work of the second author is supported by the DST grant III 5(12)/96-ET.