Questioning numerical integration methods for microsphere (and microplane) constitutive equations

In the last few years, more and more complex microsphere models have been proposed to predict the mechanical response of various polymers. Similarly than for microplane models, they consist in deriving a one-dimensional force vs. stretch equation and to integrate it over the unit sphere to obtain a three-dimensional constitutive equation. In this context, the focus of authors is laid on the physics of the one-dimensional relationship, but in most of the case the influence of the integration method on the prediction is not investigated.Here we compare three numerical integration schemes: a classical Gaussian scheme, a method based on a regular geometric meshing of the sphere, and an approach based on spherical harmonics. Depending on the method, the number of integration points may vary from 4 to 983,040! Considering simple quantities, i.e. principal (large) strain invariants, it is shown that the integration method must be carefully chosen. Depending on the quantities retained to described the one-dimensional equation and the required error, the performances of the three methods are discussed. Consequences on stress–strain prediction are illustrated with a directional version of the classical Mooney–Rivlin hyperelastic model. Finally, the paper closes with some advices for the development of new microsphere constitutive equations.     

A comparison of transformation methods for evaluating two‐dimensional weakly singular integrals

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two‐dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one‐dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub‐regions are considered as well as non‐splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non‐linear transformation approach (GSSNT) is applied to various two‐dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two‐dimensional weakly singular integrals studied. Copyright © 2002 John Wiley & Sons, Ltd.     

Integration framework for intelligent manufacturing processes

In this article, we describe a new approach to applying distributed artificial intelligence techniques to manufacturing processes. The construction of intelligent systems is one of the most important techniques among artificial intelligence research. Our goal is to develop an integrated intelligent system for real time manufacturing processes. An integrated intelligent system is a large knowledge integration environment that consists of several symbolic reasoning systems (expert systems) and numerical computation packages. These software programs are controlled by a meta-system which manages the selection, operation and communication of these programs. A meta-system can be implemented in different language environments and applied to many disciplines. This new architecture can serve as a universal configuration to develop high performance intelligent systems for many complicated industrial applications in real world domains.To whom all correspondence should be addressed.     

Reduced modified quadratures for quadratic membrane finite elements

Reduced integration is frequently used in evaluating the element stiffness matrix of quadratically interpolated finite elements. Typical examples are the serendipity (Q8) and Lagrangian (Q9) membrane finite elements, for which a reduced 2 × 2 Gauss–Legendre integration rule is frequently used, as opposed to full 3 × 3 Gauss–Legendre integration. This ‘softens’ these element, thereby increasing accuracy, albeit at the introduction of spurious zero energy modes on the element level. This is in general not considered problematic for the ‘hourglass’ mode common to Q8 and Q9 elements, since this spurious mode is non‐communicable. The remaining two zero energy modes occurring in the Q9 element are indeed communicable. However, in topology optimization for instance, conditions may arise where the non‐communicable spurious mode associated with the elements becomes activated. To effectively suppress these modes altogether in elements employing quadratic interpolation fields, two modified quadratures are employed herein. For the Q8 and Q9 membrane elements, the respective rules are a five and an eight point rule. As compared to fully integrated elements, the new rules enhance element accuracy due to the introduction of soft, higher‐order deformation modes. A number of standard test problems reveal that element accuracy remains comparable to that of the under‐integrated counterparts. Copyright © 2004 John Wiley & Sons, Ltd.     

Healing the psyche through music, myth, and ritual.

According to Carl Jung, a person's symptoms occur as a result of the psyche's creative attempt to self-regulate. These symptoms are viewed as the symbol-making function of the psyche. Music therapy as a therapeutic tool is also viewed as having a symbol-making function in that the physical act of making music involves conceptualizing one's symptoms into sounds. The sound serves as a musical symbol of the symptom. The myth of Orpheus is offered as an example of how early man amplified the creative potential contained in music to heal from life's woes. The Orphic archetype illustrates that music serves as a medium for healing and as an expression of Self. That psyche can be healed by music is a reminder of the connection between music therapy and the myth of Orpheus. In using the therapeutic tool of music one can transcend, through the symbol making process inherent in music therapy, the tension of opposites that are created at the crossroads of disease and wellness. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Applications of the discrete element method in mechanical engineering

Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples. Commemorative Contribution.     

Local Exact Particle Tracing on Unstructured Grids

For analyzing and interpreting results of flow simulations, particle tracing is a well established visualization method. In addition, it is a preliminary step for more advanced techniques such as line integral convolution. For interactive exploration of large data sets, a very efficient and reliable particle tracing method is needed. For wind channel experiments or flight simulations, large unstructured computational grids have become common practice. Traditional approachs, based on numerical integration methods of ordinary differential equations however fail to deliver sufficiently accurate path calculation at the speed required for interactive use. In this paper we extend the local exact approach of Nielson and Jung in such a way that it can be used for interactive particle tracing in large data sets of steady flow simulation experiments. This will be achieved by sophisticated preprocessing using additional memory. For further visual enhancement of the streamline we construct an implicitly defined smooth Bézier curve that is used for ray tracing. This allows us to visualize additional scalar values of the simulation as attributes to the trajectory and enables the display of high‐quality smooth curves without creating any visualization geometry and providing a good impression of the spatial situation at the same time. ACM CSS: I.3.3 Computer Graphics—Line and curve generation; I .3.7 Computer Graphics—Raytracing; G.1.2 Numerical Analysis—Spline and piecewise polynomial approximation     

中国民航信息系统现状及发展展望

介绍了中国民航信息系统的现状和与实际业务需求的差距,接着从系统设计理念、核心系统、新系统新功能和信息系统整合等多个方面详细阐述了民航信息系统的发展思路,最后强调了建立新一代民航信息系统的紧迫性,具备很强的指导意义。     

应用型机械本科专业教学体系改革研究与实践

根据当前高等教育改革与发展的指导思想，紧紧围绕国家实施制造业信息化建设工程为背景，积极配合打造浙江先进制造业基地建设，结合现代机械专业结构调整，本着交叉、复合、应用型人才的培养目标，塑造具有宽口径、厚基础和强创新意识的人才培养理念，以数字化设计制造为核心，以机械技术、电子技术、信息技术和管理学科结合为主线，突出知识综合与创新能力，强调专业实践与专业知识的有效结合，有的放矢实施机械专业教学改革与实践。