On the work theorems for finite and incremental elastic deformations with discontinuous fields: A unified treatment of different versions

Starting from the statical and kinematical relations in three different versions characterized by the use of Piola's, Kirchhoff's or Biot's (Jaumann's) stresses respectively and the corresponding deformation quantities a unified abstract formulation of the basic equations is given. Because of certain properties of the statical and geometrical operators various material independent work theorems follow including the (generalized and modified) principles of virtual displacements and virtual forces. For a hyperelastic body under conservative loading these are transformed into generalized variational principles and strengthened to complementary extremum principles. Finally the abstract formulation is applied to the incremental equations. The admissible functions are allowed to have relaxed continuity properties. Therefore the presented work theorems may be used as a basis for a consistent finite element approximation according to the mixed version or to the classical displacement formulation.     

Application of the quadratic functional to nonconservative problems of elastic stability

Two methods for solving nonconservative problems by applying the quadratic functional are presented. The corresponding approximate methods of solution are obtained by using suitable polinomial trial functions and are illustrated by solving Beck's and Leipholz's rods.     

Increasing tree search efficiency for constraint satisfaction problems

In this paper we explore the number of tree search operations required to solve binary constraint satisfaction problems. We show analytically and experimentally that the two principles of first trying the places most likely to fail and remembering what has been done to avoid repeating the same mistake twice improve the standard backtracking search. We experimentally show that a lookahead procedure called forward checking (to anticipate the future) which employs the most likely to fail principle performs better than standard backtracking, Ullman's, Waltz's, Mackworth's, and Haralick's discrete relaxation in all cases tested, and better than Gaschnig's backmarking in the larger problems.     

Comparisons of practical hierarchical control methods for interconnected dynamical systems

This paper gives a brief survey of possible methods which can be used for the practical control of large interconnected dynamical systems. The development is in two parts, i.e. optimal methods and suboptimal methods. In the first part, a brief outline is given of infeasible methods like Goal co-ordination and the Takara-Sage algorithm. In the general study of infeasible methods, Tamura's three-level method, Tamura's time-delay method and Pearson's pseudo-model co-ordination method are also included. It is seen that both the algorithms of Tamura as well as the Takahara-Sage method are particularly suited to systems with slow dynamics whereas Pearson's pseudo-model co-ordination method could be used advantageously for systems with fast dynamics.A practical example is then given of optimal traffic control using an infeasible method, in this case the time-delay method of Tamura. The main conclusion to emerge from this part is that optimal methods will require multiple processors for on-line dynamic optimization although for systems with slow dynamics like the traffic example, fairly large problems could nevertheless be tackled using only one processor.There are certain classes of systems for which it may be possible to obtain virtually optimal control using only a single processor even when the number of subsystems is very large. One such class of problems is of serially connected dynamical systems. In the second part of this paper a suboptimal approach is described for the control of serial systems and the method is demonstrated using river pollution as an example. Finally, a new method is developed which enables a significant improvement to be made for serial systems with conflicts between the subsystems and an example illustrates this approach.     

Improved shooting techniques for linear boundary value problems

Various methods are available for the solution of linear boundary value problems that arise, amongst other situations, in hydrodynamic stability theory. The principal difficulty in such cases is the parasitic growth of one or more independent solutions when a standard shooting technique, such as the Runge-Kutta method, is used for integration. Four methods of reducing or removing the parasitic errors are critically examined: (a) Kaplan's filtering technique, (b) Davey's complete orthonormalization method, (c) the Gram-Schmidt orthonormalization procedure and (d) an initial value method based on the use of compound matrices. One of them is recommended for overall economy and accuracy.     

Mixed finite elements based upon marguerre theory for the study of geometrically nonlinear behavior of thin shells

Simple triangular and quadrangular finite elements based on Marguerre's theory are proposed and are shown to greatly improve the solution over plane shell elements for a small additional computation cost.Several features of the developments are worth noting, namely: The presentation of a dual approach for the derivation of Marguerre's theory of shallow shells with moderate rotations, based on Fraeijs de Veubeke's variational principle, with a precise statement of hypotheses and applicability; the choice of hybrid connectors for solving the compatibility problem generated by Kirchhoff's hypothesis; a treatment of pressure loading, body forces and inextensional bending modes which employs a ‘static approach’ for the membrane; and discussion about the performance of some algorithms used to solve elastic stability problems. Numerical studies indicate that accurate results may be obtained by the approach advocated.     

Handsketching as a human factor aspect in graphical interaction

For some years a lot of effort has been put into improving the human-computer interface in CAD-systems. After a short introduction on input problems in design processes, some of this work is reported here as well as a fairly new method, handsketching. In the third part of this paper a special system called CASUS is thoroughly explained from the user's point of view. A fourth part deals with the authors' conviction that psychological theories and methods are necessary in order to create still better interfaces. In the last chapter the system presented with all its interface features is compared to some human factor considerations discussed before. No attention is paid to the fact that very often the quality of work is changed by introducing CAD-systems. Though the designer's situation can be very often improved much more by designing his entire work, this paper lays claim only to designing a tool for the designer's hand.     

The mechanical discovery of certain problem symmetries

This paper presents several methods for analysing finite state problems to discover certain types of symmetry. The methods are based on techniques used in Sequential Machine Theory, especially the use of partitions that have the Substitution Property. Amarel's investigations of a type of time-reverse symmetry have also been extended to a wider class of problems. All the symmetries discussed enable substantial savings in search effort to be obtained by effectively reducing the size of the search space.     

Discontinuous finite elements and godunov-type methods for the eulerian equations of gas dynamics

We investigate the numerical solution of typical problems in gas dynamics by discontinuous finite element methods, and compare the results with computations performed with variants of Godunov's conservative method.A one-dimensional shock wave problem with reflection, and a three-dimensional shock tube-type problem with convergent-divergent nozzle geometry are analyzed. For the one-dimensional problem we also present results obtained with a variant of Glimm's method. In one dimension, finite elements give valuable results, although they need a substantially larger computing time; in three space dimensions discontinuous elements appear to be too cumbersome, in the present form, to lend themselves to an efficient treatment of time-dependent shock wave problems.     

Fitting three-parameter lognormal models by numerical global optimization — an improved algorithm

The theoretical maximum likelihood point estimates of the parameters of the three-parameter lognormal distribution (LD) for complete, ungrouped samples are infeasible values for which the likelihood function is positively infinite. This has prompted the search for usable point estimates which are called local-maximum likelihood estimates (LMLE's) and which correspond to the largest finite local maximum of the log-likelihood function (LLF). Previously published work has shown that an effective way to obtain LMLE's is to numerically maximize the conditional LLF of the observations using sequential interior penalty and barrier function methods. These methods are robust but necessitate the numerical solution of a sequence of maximization problems.This paper describes an algorithm for computing LMLE's which involves only a single numerical maximization of a suitably transformed conditional LLF. The results of computational tests indicate that the algorithm, when implemented using computationally efficient and reliable univariate global optimization methods, is a computationally robust method for computing LMLE's of LD parameters.     

The expected linearity of a simple equivalence algorithm

The average time needed to form unions of disjoint equivalence classes, using an algorithm suggested by Aho, Hopcroft, and Ullman, is shown to be linear in the total number of elements, thereby establishing a conjecture of Yao. The analytic methods used to prove this result are of interest in themselves, as they are based on extensions of Stepanov's approach to the study of random graphs. Several refinements of Yao's analyses of related algorithms are also presented.     

A higher order numerical scheme for scalar transport

The computational principles of a numerical scheme for the solution of the two-dimensional scalar transport equation are presented. The scheme is designed for use in transient flow situations where accurate simulation of the advective process is important. Advective transport is computed by the method of characteristics in which the scalar field is represented by a Hermitian polynomial complete through the third degree in both coordinate directions, while diffusion is computed by central differencing. The superior accuracy of the new method is demonstrated by analysing its propagation characteristics and by comparing its performance on standard test problems with that of some well-known lower order methods. Finally, the method's applicability is demonstrated in several examples involving tracer releases into channel flows. Where possible the results of these simulations are compared with analytical solutions.     

Multibody structural dynamics including translation between the bodies

New and recently developed concepts useful for obtaining and solving equations of motion of multibody mechanical systems with translation between the respective bodies of the system, is presented. The incorporation of translation effects make the analysis applicable to a much broader class of problems than was possible with previous analyses which are restricted to linked multibody systems.The concepts developed in the analysis include the use of Euler parameters, Lagrange's form of d'Alembert's principle, quasi-coordinates, relative coordinates, and body connection arrays. Procedures for the development of efficient computer algorithms for evaluating the coefficients of the governing equations of motion are outlined.The methods presented are directly applicable in the analysis of biodynamic and human models, finite segment cable models, mechanisms, manipulators and robots.     

A use of microcomputers in training at ICI

This paper describes a computer-managed training package developed for use by ICI at various works in the Organics Division. The package was produced to assist with the training of plant operators manning refrigeration plant and deals with the general principles of refrigeration, how these principles are applied in the construction and operation of a large-scale ice-making plant, and typical faults which occur in the day-by-day operation of the plant. The aim of the package is to improve the trainee's understanding of the principles of a refrigeration cycle as applied to plant used by ICI and hence improve efficiency and minimise wastage caused by mechanical failure.     

Lipski's approach to incomplete information data bases restated and generalized in the setting of Zadeh's possibility theory

The main purpose of this paper is to make clear the connection between Lipski's approach to incomplete information databases and Zadeh's possibility theory which both appeared recently, quite simultaneously, but in different contexts. Lipski's approach is extended by introducing [0, 1]-valued levels of possibility in order to take into account the fact that our incomplete knowledge about properties of objects in databases may be based on soft (non-binary) information or on statistical-like data. Moreover, possibility theory, enlarged by the introduction of the concept of necessity, seems easier to manipulate than the semantics of usual modal logic used by Lipski. The problems of dependencies, of “yes-no” queries or of queries involving the cardinalities of specified sets when available information is incomplete are considered. Two illustrative examples are dealt with.     

CAI in digital logic design,debugging, and programming

This paper describes design techniques for generative computer-assisted instruction (CAI) systems. These are systems which are capable of generating problems for students and deriving and monitoring the solutions to these problems. The difficulty of the problem, the pace of instruction, and the depth of monitoring are all tailored to the individual student. Parts of the solution algorithms can also be used to analyze an incorrect student response and determine the exact nature of the student's error in order to supply him with meaningful remedial comments.A generative CAI system which teaches logic design and machine-language programming will be discussed. This CAI system covers the material in an introductory course in digital systems aimed at electrical engineering juniors. It does not replace classroom lectures or the textbook, but instead serves to provide practice and instruction in applying this material to solve problems.In addition, a companion system to teach laboratory principles has been designed. This system teaches a student how to construct a combinational or sequential logic circuit using standard integrated circuits. The student's logic circuit is automatically interfaced to the computer and tested; the computer then aids the student in debugging his circuit. In addition to teaching the student how to use integrated circuits to realize a paper design, the system also teaches the student good debugging techniques.     

Iterative methods for the solution of the navier equations of elasticity

The numerical solution of the Navier equations discretized by finite elements is studied by various forms of pre-conditioned conjugate gradient methods. In particular, the dependence of the number of iterations is examined as a function of Poisson's ratio. A comparison is made with direct solution methods, and the dependence of the discretization error on Poisson's ratio is also discussed.     

Data structuring to efficiently implement the primal-dual transportation algorithm

This paper focuses on the computer implementation of Ford and Fulkerson's primaldual method for solving the transportation problem. It explores the practical implications of improving the efficiency with which transportation problems can be solved.By using appropriate techniques for storing data elements and manipulating their structural relationships, a computer procedure, which is quite efficient in terms of central processor execution time and core storage requirements, is developed. Computational results using a FORTRAN program on test problems ranging in size from 15 sources and 25 destinations to 30 sources and 400 destinations are presented and discussed. These results indicate that the method of implementation is instrumental in reducing the effect of problem size on computational requirements.The paper emphasizes the general principles of the implementation rather than those aspects which are specifically related to the language and computer used for experimentation. Also, the applicability of the research is extended by an investigation of the potential for using the implementation concepts with other algorithms.     

A parsing automata approach to LR theory

Two simple but powerful tools are introduced in LR theory, viz. item grammars and parsing automata. Parsing automata are used to define a large class of correct prefix parsers operating in linear time. DeRemer's and Pager's parsing methods turn out to be special cases. LL and LC tests, as well as inclusion theorems for the classes of LL, LC, and LR grammars will be based on parsing automata, too.