Finite element programming and C

In finite element programming, data have to be dealt with which are of different types but belong together in a logical sense. It would be very effective, with respect to program readability and maintainability, to store these data as a single unit. Effcient software design requires that all parts of information, which belong together logically, are stored as a single data unit. This can be accomplished utilizing structured data types.

Dynamic memory allocation allows the definition of dynamic variables which can be created and destroyed during run-time. Dynamic memory management is handled in C by pointers. In other conventional languages, e.g. Fortran 77, the programmer has the responsibility to select adequate array sizes for the largest problem to be solved. This often leads in engineering practice to array oversizing and to memory wasting. By allocating memory dynamically during program execution according to actual problem size, wasting can be avoided.

The combination of structured data and pointers along with the dynamic memory allocation capabilities of C allows the creation of linked lists. Utilizing these concepts, an effective and easy-to-read C program has been written for finite element analysis. The C program presented demonstrates the use of these techniques for interactive finite mesh generation. The strengths of C are compared to that of Fortran 77 and Fortran 90. It has been found that for finite element programming C is in many aspects superior to Fortran 77. However, it has some disadvantages in comparison with Fortran 90 concerning array processing.     

Skeletal based programming for dynamic programming on MultiGPU systems

Current parallel systems composed of mixed multi/manycore systems and/with GPUs become more complex due to their heterogeneous nature. The programmability barrier inherent to parallel systems increases almost with each new architecture delivery. The development of libraries, languages, and tools that allow an easy and efficient use in this new scenario is mandatory. Among the proposals found to broach this problem, skeletal programming appeared as a natural alternative to easy the programmability of parallel systems in general, but also the GPU programming in particular. In this paper, we develop a programming skeleton for Dynamic Programming on MultiGPU systems. The skeleton, implemented in CUDA, allows the user to execute parallel codes for MultiGPU just by providing sequential C++ specifications of her problems. The performance and easy of use of this skeleton has been tested on several optimization problems. The experimental results obtained over a cluster of Nvidia Fermi prove the advantages of the approach.     

Finite element MAC scheme in general curvilinear coordinates

A combined study of F.D. and F.E. methods for 2-D incompressible Navier-Stokes flows is undertaken. In primitive variable formulation, major difficulties are connected to spurious numerical oscillations which may arise from the enforcement of the incompressibility constraint. With regard to this problem, various F.D. schemes differ essentially according to the variable location on the mesh points, while F.E. schemes are analogously differentiated by the interpolation functions adopted for the different variables. In the present paper, we propose an F.E. analog of MAC scheme, which can be accomplished by different interpolation functions for the two velocity components. This new F.E. scheme-although based on low order approximations-eliminates all spurious oscillations. The extension to curvilinear quadrilateral elements—which is needed in order to achieve geometrical versatility—requires the problem to be formulated in general curvilinear coordinates and the contravariant velocity components to be assumed as variables. Some numerical results are presented and discussed, in order to assess the capabilities of the proposed model.     

Transformation-based diagnosis of student programs for programming tutoring systems

A robust technology that automates the diagnosis of students' programs is essential for programming tutoring systems. Such technology should be able to determine whether programs coded by a student are correct. If a student's program is incorrect, the system should be able to pinpoint errors in the program as well as explain and correct the errors. Due to the difficulty of this problem, no existing system performs this task entirely satisfactorily, and this problem still hampers the development of programming tutoring systems. This paper describes a transformation-based approach to automate the diagnosis of students' programs for programming tutoring systems. Improved control-flow analysis and data-flow analysis are used in program analysis. Automatic diagnosis of student programs is achieved by comparing the student program with a specimen program at the semantic level after both are standardized. The approach was implemented and tested on 525 real student programs for nine different programming tasks. Test results show that the method satisfies the requirements stated above. Compared to other existing approaches to automatic diagnosis of student programs, the approach developed here is more rigorous and safer in identifying student programming errors. It is also simpler to make use of in practice. Only specimen programs are needed for the diagnosis of student programs. The techniques of program standardization and program comparison developed here may also be useful for research in the fields of program understanding and software maintenance.     

Generic programming techniques for parallelizing and extending procedural finite element programs

We outline an approach for extending procedural finite-element software components using generic programming. A layer of generic software components consisting of C++ containers and algorithms is used for parallelization of the finite-element solver and for solver coupling in multi-physics applications. The advantages of generic programming in connection with finite-element codes are discussed and compared with those of object-oriented programming. The use of the proposed generic programming techniques is demonstrated in a tutorial fashion through basic illustrative examples as well as code excerpts from a large-scale finite-element program for serial and parallel computing platforms.

Finite element analysis based on stochastic Hamilton variational principle

A stochastic Hamilton variational principle (SHVP) is formulated for dynamic problems of linear continuum. The SHVP allows incorporation of probabilistic distributions into the finite element analysis. The formulation is simplified by transformation of correlated random variables to a set of uncorrelated random variables through a standard eigenproblem. A procedure based on the Fourier analysis and synthesis is presented for eliminating secularities from the perturbation approach. The algorithms developed can readily be adapted to existing deterministic finite element codes.     

Finite element based tracking of deforming surfaces

We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on the object’s surface. Our method combines the use of prior information on the geometry of the object modeled by a smooth template and the use of a linear finite element method to predict the deformation. This allows the accurate reconstruction of both the observed and the unobserved sides of the object. We present tracking results for noisy low-quality point clouds acquired by either a stereo camera or a depth camera, and simulations with point clouds corrupted by different error terms. We show that our method is also applicable to large non-linear deformations.     

A new genetic programming framework based on reaction systems

This paper presents a new genetic programming framework called Evolutionary Reaction Systems. It is based on a recently defined computational formalism, inspired by chemical reactions, called Reaction Systems, and it has several properties that distinguish it from other existing genetic programming frameworks, making it interesting and worthy of investigation. For instance, it allows us to express complex constructs in a simple and intuitive way, and it lightens the final user from the task of defining the set of primitive functions used to build up the evolved programs. Given that Evolutionary Reaction Systems is new and it has small similarities with other existing genetic programming frameworks, a first phase of this work is dedicated to a study of some important parameters and their influence on the algorithm’s performance. Successively, we use the best parameter setting found to compare Evolutionary Reaction Systems with other well established machine learning methods, including standard tree-based genetic programming. The presented results show that Evolutionary Reaction Systems are competitive with, and in some cases even better than, the other studied methods on a wide set of benchmarks.     

基于ANSYS Workbench的变速自行车车架的有限元分析

采用Soldworks软件建立了车架的三维模型,并通过ANSYS Workbench软件建立了装配体的有限元分析模型,对自行车架进行了结构的强度、刚度校核及模态分析,在形状优化基础上进行了改进.     

Evolving recursive programs by using adaptive grammar based genetic programming

The publisher apologizes for an error that occurred in the above mentioned article. The error appears in the printed version, as well as in the html and pdf version online. Man Leung Wong is the sole author of this article. His affiliation is listed below. The online version of the original article can be found at     

Finite element analysis of large displacements in flexural systems

The fictitious load procedure developed for prismatic beam elements by Kohnke[1] is compared to the widely used general procedure outlined by Zienkiewicz[2]. Applied to a problem involving only axial strains the two methods are found to yield practically identical results. Applied to a problem involving flexural effects, on the other hand, the general method performs poorly. This is found to be owing to the lack of any allowance for large displacements in the evaluation of the flexural strains. A simple means of making such allowance is then proposed and found to greatly improve the results given by the general incremental method.     

Construction of composition programming systems based on the identification relation

Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 38–44, November–December, 1995.     

基于ABAQUS的复合薄膜热结构有限元分析

半导体硅基复合薄膜悬臂梁在温度场、加速度以及二者耦合场作用下,挠度和应力会发生变化.通过加热可使得驱动元件本身的温度升高,结构内部将会产生热应力,会导致两种薄膜各自产生线应变,线膨胀系数小的薄膜受到拉力作用,线膨胀系数大的薄膜受到压力作用,自由端会受到力矩作用而向线膨胀系数小的薄膜方向弯曲,从而导致悬臂梁的挠度发生变化.当弯曲悬臂梁有加速度作用时,会产生一个与加速度方向相同的力作用在悬臂梁上,同样会导致悬臂梁的挠度发生变化[1].通过ABAQUS软件仿真[2],分别给出不同物理场中弯曲悬臂梁相对位移的大小,所得的结论为半导体硅基复合薄膜弯曲悬臂梁的应用装置提供了理论依据.     

Finite element implementation of nearly-incompressible rheological models based on multiplicative decompositions

The present work is concerned with the numerical integration of finite viscoelastic or viscoplastic models. A numerical integration scheme based on the definition of a flow direction and a flow amplitude as in elastoplasticity is proposed. The most original feature of this approach resides in a local correction of the direction and amplitude with a sub-stepping strategy. Comparisons with the results obtained using a classical tensorial integrator based on a Runge-Kutta–Fehlberg scheme are provided. The reliability of the present numerical scheme is investigated with three rheological models two are viscoelastic (Zener and Poynting–Thomson) and one is viscoplastic.     

Finite element analysis of flexible multibody systems with fuzzy parameters

A computational procedure is presented for predicting the dynamic response and evaluating the sensitivity coefficients of flexible multibody systems whose characteristics include fuzzy parameters. Time-histories of the possibility distributions of the response and the sensitivity coefficients are generated. These coefficients measure the sensitivity of the dynamic response to variations in the material, geometric and external force parameters of the system. The five key components of the procedure are: a) a corotational frame approach used in conjunction with a total Lagrangian formulation; b) beam and shell elements with the Cartesian coordinates of the nodes selected as degrees of freedom, and with continuous inter-element slopes; c) use of an approximate method of extension, based on the α-cut representation, called the ‘vertex method’ for generating the possibility distributions of the desired response quantities and their sensitivity coefficients; d) semi-explicit temporal integration technique for generating the dynamic response; and e) direct differentiation approach for evaluating the sensitivity coefficients. The effectiveness of the procedure and the usefulness of the fuzzy output are demonstrated through numerical examples, including an articulated space structure consisting of beams, shells and revolute joints.     

Finite state based testing of P systems

In this paper, we propose an approach to P system testing based on finite state machine conformance techniques. Of the many variants of P systems that have been defined, we consider cell-like P systems which use non-cooperative transformation and communication rules. We show that a (minimal) deterministic finite cover automaton (DFCA) (a finite automaton that accepts all words in a given finite language, but can also accept words that are longer than any word in the language) provides the right approximation for the computation of a P system. Furthermore, we provide a procedure for generating test sets directly from the P system specification (without explicitly constructing the minimal DFCA model).