Computer-oriented Algorithm Research Articles

About local numerical solution of boundary problems of elasticity three-dimensional theory

The distinctive paper is devoted to wavelet-based multilevel method of local numerical solution of boundary problems of elasticity three-dimensional theory. As it is known, effective qualitative multilevel analysis of local and structure global stress-strain states is normally required in various technical applications. Operational and variational formulations of the problem (particularly with the use of wavelet (Haar) basis) are presented. Computer-oriented algorithms of fast direct and inverse discrete Haar transforms are described. Due to special algorithms of averaging within corresponding multigrain approach, problem reduction is provided.

Analytical solution for beams with multipoint boundary conditions on two-parameter elastic foundations

An efficient analytical method is presented for the closed form solution of continuous beams on two-parameter elastic foundations. The general form of the governing equation is reduced to a system of first-order differential equations with constant coefficients. The system is then solved using Jordan form decomposition for the coefficient matrix and construction of the fundamental solution. Common types of boundary conditions (pinned and roller support, hinge connection, fixed and free end) can be applied to an arbitrary point on the beam. The method has a completely computer-oriented algorithm, computational stability, and optimal conditionality of the resultant system and is a powerful alternative to the analytical solution of beams with multipoint boundary conditions on one- or two-parameter elastic foundations. Examples with different types of loading, boundary conditions, and foundation are presented to verify the method.

Semianalytical analysis of shear walls with the use of discrete-continual finite element method. Part 1: Mathematical foundations

The distinctive paper is devoted to the two-dimensional semi-analytical solution of boundary problems of analysis of shear walls with the use of discrete-continual finite element method (DCFEM). This approach allows obtaining the exact analytical solution in one direction (so-called “basic” direction), also decrease the size of the problem to one-dimensional common finite element analysis. The resulting multipoint boundary problem for the first-order system of ordinary differential equations with piecewise constant coefficients is solved analytically. The proposed method is rather efficient for evaluation of the boundary effect (such as the stress field near the concentrated force). DCFEM also has a completely computer-oriented algorithm, computational stability, optimal conditionality of resultant system and it is applicable for the various loads at an arbitrary point or a region of the wall.

Correct Multilevel Discrete-Continual Finite Element Method of Structural Analysis

The distinctive paper is devoted to correct multilevel discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coefficients, eliminating necessity of calculation of root vectors.

Correct Discrete-Continual Finite Element Method of Structural Analysis Based on Precise Analytical Solutions of Resulting Multipoint Boundary Problems for Systems of Ordinary Differential Equations

The distinctive paper is devoted to correct discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include uni-versality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coeffi-cients, eliminating necessity of calculation of root vectors.

Correct Wavelet-Based Multilevel Numerical Method of Local Solution of Boundary Problems of Structural Analysis

The distinctive paper is devoted to correct wavelet-based multilevel numerical method of local solution of boundary problems of structural analysis. Operational and variational formulations of the problem (particularly with the use of wavelet basis) are presented. Computer-oriented algorithms of fast direct and inverse discrete Haar transforms are described. Due to special algorithms of averaging within multigrid approach, reduction of the problem is provided.

Correct Method of Analytical Solution of Multipoint Boundary Problems of Structural Analysis for Systems of Ordinary Differential Equations with Piecewise Constant Coefficients

This paper is devoted to correct method of analytical solution of multipoint boundary problems of structural analysis for systems of ordinary differential equations with piecewise constant coefficients. Its major peculiarities include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resultant systems and partial Jordan decomposition of matrix of coefficients, eliminating necessity of calculation of root vectors.

An efficient recursive approach for computer generation of manipulator dynamic model

According to the structural characteristics of the serial robot arm, on the basis of multi-rigid-bodies dynamics, the vectorial and complete recursive dynamical equations are derived first by means of D'Alembert's principle, and a new, complete recursive algorithm is presented in this paper. These dynamical equations are succinct in form and compact in structure. The recurrence formula obtained is very simple and direct; it is suitable for robots dynamic realtime computed. Furthermore, we used the augmented body and composite system for the serial robot arm in the dynamical model; it makes the dynamical calculation simple and raises the computational efficiency. It suits to the positive or inverse problems of dynamics. It is a computer-oriented algorithm that forms and solves dynamical equations automatically.

Computer-oriented closed-form algorithm for constrained multibody dynamics for robotics applications

An alternative computer-oriented algorithm for generating the equations of motion for constrained multibody systems subject to control is presented. The algorithm is derived from the principle of virtual work and includes the effect of a moving reference frame. The equations of motion are expanded in a closed form in terms of a minimum set of variables. Symbolic implementation, simplification and linearization are discussed. Computer-based models of a biped robot walking on a vibrating platform are generated. Dynamic behavior of the biped is simulated by implementing the optimal control theory. The study shows that this closed-form formalism holds promise in the simulation of constrained robotic systems.

Spatially coupled vibrations of a suspension bridge under random highway traffic

AbstractThe problem of spatial dynamic response of a suspension bridge to the passage of trains of concentrated forces with random values is considered. The arrival of forces at the bridge is assumed to constitute a Poisson process of events. Such an excitation process is an appropriate model of vehicular traffic loads acting on the bridge. The bridge is idealized by a single‐span thin‐walled beam underslung to two cables. The response of the bridge in the space‐time domain is described by a coupled system of non‐linear, integro‐differential equations. The dynamic influence functions of vertical and horizontal deflections at each cross‐section point are obtained for the linear case. Cumulants and probability density functions of response are determined. Numerical methods have been used to develop a computer‐oriented algorithm aimed at the numerical solution of the problem. As examples, numerical results for a particular bridge with some practical load cases are presented and illustrated by graphs.

Influence of Mass Distribution, Shear Deformation, and Rotatory Inertia on Flutter Loads

Classical problems of columns under tangential (follower) loads are analyzed for stability. A generalized Ritz technique is used in conjunction with a computer-oriented algorithm suitable for the flutter analysis of complex structural systems. A brief description of this technique is presented. The numerical approach allows for easy consideration of additional effects in classical problems such as the Beck and Leipholz columns. The influence of shear deformation, rotatory inertia, and concentrated mass at the tip of the column is shown in graphs and discussed.

Singular perturbation modelling of large-scale systems with multi-time-scale property

The problem is investigated of singular perturbation modelling, which plays an important role in cases of the application of the singular perturbation method to the design and analysis of large-scale systems. In both continuous- and discrete-time versions, modelling concepts based on structural properties are studied, and computer-oriented algorithms are developed. The results of two-time-scale systems are extended to multi-time-scale cases. Furthermore, in order to verify the validity of these studies, some numerical examples are given.

A simplified computer-oriented algorithm for obtaining stable reduced-order models by using Routh approximations

A simplified computer-oriented algorithm for obtaining stable reduced-order models by Routh approximations is proposed. Simplicity of the proposed algorithm is demonstrated through a numerical example.

Additive Decomposition of Finite Processes

In various branches of the random process analysis it is a common practice to split measured signals into trend and stochastic components (Anderson, 1971; Bendat, 1980). This is invariably the case, when performing identification, prediction and spectrum evaluation. The problem is characterized by inherent ambiguity if only a limited fraction of the process is available for measurement. A new approach to the finite process decomposition, based on two principal concepts, is discussed. The first concept may be considered as the extension of the Fourier analysis on the case of a non-orthogonal trigonometric basis. A broad variety of finite functions may be represented by trigonometric series with arbitrary frequencies, generally providing more economic expansion as compared to the Fourier series. Such representations are named as perfect trigonometric expansions (PE) of finite functions. The second concept may be formulated as harmonic kernel (HK) extraction, the term referring to the time-invariant portion of a signal. It is shown that HK provides an unbiased and consistent estimate for an almost periodic trend of a process. To illustrate the practical possibilities a spectral density estimator with minimum absolute value bias for a given sample size is constructed. The discussion completes with brief remarks on computer-oriented algorithms.

Computer-Oriented Algorithm for Modeling Active Spatial Mechanisms for Robotics Applications

Based on a comparison of the computational complexity of different spatial mechanisms dynamics formulations it is shown that the most appropriate one is the Newton-Euler formulation using recurrence relations for velocities, accelerations, and generalized forces. This is based on numerical efficiency and intermediate results. A general algorithm which solves both the direct and inverse problem of dynamics for an open-chained spatial mechanism of an arbitrary mechanical configuration is developed and realized. It is pointed out that for control algorithms which assume knowledge of system dynamics in real time, it is necessary to compute the inertial matrix and the term taking into account the rest of the dynamical effects separately. The "accelerated" computational algorithm for real-time implementation with this property has been developed and realized. Up to now reported real-time computational schemes do not have this feature directly implementable. Depending on the control law, manipulator configuration, type of functional tasks, and given ranges of operational speed it can appear that it is sufficient to compute only the dominant dynamical influences and not the complete dynamics. The criterion for the optimal choice of the level of the approximation of the dynamical model is formulated based on nominal regimes for specific functional tasks. For this purpose the algorithm for generation of the mathematical model of variable complexity is developed and realized. The procedure is implemented on two typical manipulator mechanical configurations of six degrees of freedom (d.o.f.) and a comparison of exact and various approximate models is performed.

Magnitude ordering of degree complements of certain node pairs in an undirected graph and an algorithm to find a class of maximal subgraphs

An undirected or a symmetric graph consists of a set of nodes and a set of nonoriented edges connecting between pairs of nodes. In widely differing disciplines of science and engineering, symmetric graphs find important uses. In many of these application areas, an often encountered problem is that of finding all the maximal complete subgraphs of a symmetric graph. In this paper, borrowing the concept of strong connectedness in a nonsymmetric graph, the idea of minimally strongly connected (MSC) and maximal minimally strongly connected (MMSC) subgraphs in a symmetric graph is introduced. The MMSC subgraphs play a kind of role identical to that played by maximal complete subgraphs in symmetric graphs. Many important properties of MMSC subgraphs are discussed in the paper, and an explicit, computer-oriented algorithm is developed for finding all the MMSC subgraphs, given an undirected graph.

An algorithm for the minimum-length least-squares solution of a set of observation equations

A new computer-oriented algorithm GSO is presented for solving overdetermined systems of linear observation equations according to the principle of the least-squares method. The matrix of the system of observation equations may be of deficient rank. In this case the algorithm leads to the vector of unknowns with a minimum Euclidean norm. Alternatively, it is possible to minimize the norm of a subvector formed by a selected group of unknowns. The weight coefficient matrix, corresponding to the vector (subvector) of unknows, has the least possible trace. The algorithm GSO is based on the Gram-Schmidt Orthogonalization of suitably defined augmented matrices. The establishing and solving of normal equations is not necessary. Apart from the unknowns and residuals, GSO also determines the factorized weight coefficient matrices of the adjusted values.

Strong connectivity in symmetric graphs and generation of maximal minimally strongly connected subgraphs

In nonsymmetric graphs strong connectivity is an important concept. In this paper, extending the concept of strong connectivity of nonsymmetric graphs to the case of symmetric graphs, the idea of minimally strongly connected (MSC) and maximal minimally strongly connected (MMSC) subgraphs in a symmetric graph is introduced, and theoretical results are developed that pertain to certain useful properties of these subgraphs. A computer-oriented algorithm is also proposed for finding the MMSC subgraphs from a given symmetric graph, that seems efficient and simple, and tends to reduce computation in generating the subgraphs.

Mathematical Programming Problems in the Computer-Aided Design of Large Scale Data Processing Systems

Some aspects of computer-aided, design of large scale data processing systems are being discussed in this paper. The object of research is a centralized data collecting network. The optimal Design prob-lem is treated as a non-linear mathematical programming task. A non-standard computer-oriented algorithm is proposed for its solution, which proves an efficient tool for system design. An example is presented with numerical results obtained through the suggested approach.

Formulation of state equations in active RLC networks

The derivation of state equations in linear active RLC networks is considered and a computer-oriented algorithm for their formulation is given. In this work, the dependent sources are assumed to be controlled by other sources as well as the passive elements, and it is shown that all the state variables still can be chosen among inductor currents and capacitor voltages. In previous works, either one of these cases was not considered. The active RLC networks considered in this paper are general enough to contain ideal transformers, gyrators, and other types of elements which can be represented by dependent sources.