A hybrid,finite element—finite difference approach to simplified large deflection analysis of structures

A new and considerably simplified solution technique for geometrically nonlinear problems is introduced. In contrast to the existing numerical methods, the present approach obtains an approximate large deflection pattern from the linear displacement vector by successively employing updated correction factors. Conservation of energy principle yields a general expression for these subsequent corrections. While the linear portion of the strain energy can be computed using finite element approach, evaluations of its nonlinear counterparts often require mathematical discretization techniques. The simple, self-correcting iterative procedure is unconditionally stable and its fast oscillatory convergence offers further computational efficiency. To illustrate the application of the proposed method and to assess its accuracy, moderately large deflections of beam, plate and flexible cable structures have been computed and compared with known analytical solutions. If required, the obtained results—which are acceptable for most design purposes—can be further improved.     

A numerical approach to the analysis of circular cylindrical water tanks

This paper presents a novel numerical approach to the solution of differential equations governing the deformation of a circular cylindrical water tank whose axis is vertical. The approach is a combination of the Runge-Kutta numerical method of solution of ordinary differential equations and of numerical optimization methods. The results obtained using this approach are compared with the results from other methods. The usefulness of the method is discussed.     

The HaLoop approach to large-scale iterative data analysis

The growing demand for large-scale data mining and data analysis applications has led both industry and academia to design new types of highly scalable data-intensive computing platforms. MapReduce has enjoyed particular success. However, MapReduce lacks built-in support for iterative programs, which arise naturally in many applications including data mining, web ranking, graph analysis, and model fitting. This paper (This is an extended version of the VLDB 2010 paper “HaLoop: Efficient Iterative Data Processing on Large Clusters” PVLDB 3(1):285–296, 2010.) presents HaLoop, a modified version of the Hadoop MapReduce framework, that is designed to serve these applications. HaLoop allows iterative applications to be assembled from existing Hadoop programs without modification, and significantly improves their efficiency by providing inter-iteration caching mechanisms and a loop-aware scheduler to exploit these caches. HaLoop retains the fault-tolerance properties of MapReduce through automatic cache recovery and task re-execution. We evaluated HaLoop on a variety of real applications and real datasets. Compared with Hadoop, on average, HaLoop improved runtimes by a factor of 1.85 and shuffled only 4 % as much data between mappers and reducers in the applications that we tested.     

A novel matrix approach to observability analysis of finite automata

In this paper, the observability of finite automata (acronym is FA) that contain both deterministic finite automata and non-deterministic finite automata is investigated under the framework of the semi-tensor product of matrices. For both initial state and current state cases, two different observability definitions with or without input information are considered, respectively. First, we show that how the observability problem of initial state of FA can be transformed to the construction problem of an initial state-outputs matrix that presents the relationship between initial state and outputs. Second, a current state-outputs matrix to verify the observability problem of current state is given. When two matrices are obtained, four theorems to verify the observability of initial state and current state are presented, respectively. In particular, compared with the existing approach, the proposed approach not only provides a unified verification for the two types of observability of both initial state and current state but also reduces the computational complexity considerably. An illustrative example is presented to show the theoretical results.     

Nonlinear finite element analysis of curved beams

Mixed curved-beam finite elements are developed for the geometrically nonlinear analysis of deep arches. The analytical formulation is based on a form of the nonlinear deep-arch theory with the effects of transverse shear deformation and bending-extensional coupling included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch. The generalized stiffness matrix is obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Numerical studies are presented to demonstrate the high accuracy of the solutions obtained by the mixed models and to show that their performance is considerably less sensitive to variations in the arch geometry than that of the displacement models.     

A finite element approach to global-local modeling in composite laminate analysis

A finite element model is described to study interlaminar stresses within polymer composite laminated materials. This model is based upon a global-local model proposed by Pagano and Soni in 1983. The development of solution procedures includes an out-of-core memory solving technique. The numerical results generated for simple plate problems with and without holes in the center under uniaxial loading are reported. Comments regarding the finite-element mesh-size, numerical stability, problem size and sensitivity of results to substructuring of the laminate into global and local regions have also been discussed.     

Geometrically nonlinear finite element analysis of tapered beams

A novel finite element methodology is developed capable of analyzing the geometrically nonlinear behavior of thin-walled framed structures composed of non-prismatic members. The pertinent element matrices are formulated on the basis of a modified version of the variational theorem of Hellinger and Reissner. Finite geometry changes are consistently described by using an updated Lagrangian (U.L.) formulation. Validity, accuracy and reliability of the proposed scheme are examined on the basis of several well-selected test examples.     

DR analysis of beams using graded finite differences

A graded finite-difference implementation of the DR method for small-deflection beam analysis is presented. The advantages of this type of formulation, namely increased flexibility and/or solution accuracy without computational penalty, are emphasised. These features are illustrated via the solution of three simple beam-flexure problems.     

A finite element analysis of deep beams with cutouts considering four supports

Using the finite element method, the biaxial stress distribution has been determined for a wide-flange deep beam, with rectangular cutouts placed at various locations, on four supports. An elastic plane state of stress is assumed for the web of the beam and an elastic uniaxial state of stress is assumed for the flanges. The influence that cutouts indeterminate supports have on the stress distribution in deep beams is illustrated by plotting the stress distribution, at several longitudinal locations, for the homogeneous beam and the beam with cutouts, on both determinate and indeterminate supports. Several convergence studies have been performed to determine the proper mesh sizes for the given problems.     

A state space approach to the finite automata

This paper proposes a state space approach for analyzing the finite automata. A Ψ-representation transforms a set of words into a formal power series for establishing the state equation of a finite automaton. We investigate the structure of the automaton via its corresponding state equation. It is shown that the solution of the state equation always exists and is unique. Furthermore, we prove that the solution field is a separable algebraic extension of the coefficient field. Finally, the concept of the substitution property of a partition is shown to be equivalent to that of invariant subspaces of the associated state space.     

An efficient general iterative algorithm for dataflow analysis

Summary Existing iterative algorithms for global dataflow analysis have demonstrable shortcomings; either they can be used only for a limited class of problems or they are needlessly inefficient in some cases. We review several algorithms, pointing out weaknesses and develop a new algorithm that can be used for a wide class of problems and has a runtime that compares favorably ro runtimes of existing algorithms.     

On a numerical approach to shakedown analysis of structures

Two alternative ways of performing the shakedown analysis of structures subjected to variable repeated loads are presented. The first one enables one to check whether the structure shakes down (i.e. responds elastically after a few elastoplastic cycles) or not. Such a check is done by reproducing incrementally a critical cyclic load which corresponds to a cyclic repetition of piecewise-proportional load path that contains all the vertices of the variable load domain. The second approach enables one to find a safety factor for the limit of shakedown capability. The problem is one of convex or linear programming, depending on the kind of yield condition used. Numerical results presented in the paper show that the general purpose software that performs incremental elastoplastic calculations can be successfully used for shakedown analysis.     

A general numerical model for grounding analysis in layered soils

Safety of persons, protection of equipment and continuity of power supply are the main objectives of the grounding system of a large electrical installation. For its accurate design, it is essential to determine the potential distribution on the earth surface and the equivalent resistance of the system. In this paper, we present a numerical approach based on the boundary element method for grounding analysis in layered soils. The feasibility of this formulation is discussed by means of its application to a real grounding system with different kinds of layered soil models.     

A triangular finite difference scheme for large deflection problems

A lumped triangular element formulation is developed based on a finite difference approach for the large deflection analysis of plates and shallow shells. The presented formulation is independent of the boundary condition (unlike the finite difference formulation) and uses energy principles to derive a set of nonlinear algebraic equations which are solved by using an incremental Newton-Raphson iterative procedure. A study of the large deflection behaviour of thin plates is made for various edge conditions and aspect ratios, and the results obtained are compared with those using a finite element scheme. Representative nondimensional solutions for deflections and stresses are presented in the form of graphs.     

A general approach to classification problems

In the classification problem the value of the discrete random variable I must be estimated from that of a random variable X given a random sample (I₁, X₁),(I₂, X₂),…,(I_n, X_n). A classification rule giving such an estimate can be based on most nonparametric density estimators which are based on delta sequences. The rate at which the nonerror rate for this rule converges to the optimal is calculated. It is found to be $\text{O(n}{}^{\mathrm{<mtext>?1</mtext><mtext>(2d\; +\; 2)</mtext>}}\text{log}{}^{\mathrm{d}}\text{n}$, where d is the dimension of the variable X under mild assumptions on the densities. A procedure for choosing an associated parameter for small samples is given.     

An approach to backward analysis for linear and nonlinear iterative methods

In this paper a general model for the analysis of the limiting accuracy of linear and nonlinear iterative methods under the influence of approximation and roundoff errors is presented. A number of numerical methods for which this question up to now has been answered by the use of specialized and rather complicated techniques only can be treated with great ease and generality.