A method is presented for testing whether or not two n-simplices in R(n) intersect, and if so, deciding whether or not the intersection has a nonempty interior. The algorithm is an application of a method by Stewart f...
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A method is presented for testing whether or not two n-simplices in R(n) intersect, and if so, deciding whether or not the intersection has a nonempty interior. The algorithm is an application of a method by Stewart for solving linear inequalities [1].
We investigate the generalized mid-point algorithms for the integration of elastoplastic constitutive equations for the pressure-dependent Gurson-Tvergaard yield model. By exact linearization of the algorithms and dec...
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We investigate the generalized mid-point algorithms for the integration of elastoplastic constitutive equations for the pressure-dependent Gurson-Tvergaard yield model. By exact linearization of the algorithms and decomposition of the stresses into hydrostatic and deviatoric parts, a formula for explicitly calculating the consistent tangent moduli with the generalized mid-point algorithms is derived for the Gurson-Tvergaard model. The generalized mid-point algorithms, together with the consistent tangent moduli, have been implemented into ABAQUS via the user material subroutine. An analytical solution of the Gurson-Tvergaard model for the plane strain tension case is given and the performances of the generalized mid-point algorithms have been assessed for plane strain tension and hydrostatic tension problems and compared with the exact solutions. We find that, in the two problems considered, the generalized mid-point algorithms give reasonably good accuracy even for the case using very large time increment steps, with the true mid-point algorithm (alpha = 0.5) the most accurate one. Considering the extra non-symmetrical property of the consistent tangent moduli of the algorithms with alpha < 1, the Euler backward algorithm (alpha = 1) is, perhaps, the best choice.
Lisp, one of the oldest higher-level programming languages, has rarely been used for fast numerical (floating-point) computation We explore the benefits of Common Lisp, an emerging new language standard with some exce...
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Lisp, one of the oldest higher-level programming languages, has rarely been used for fast numerical (floating-point) computation We explore the benefits of Common Lisp, an emerging new language standard with some excellent implementations, for numerical computation. We compare it to Fortran in terms of the speed of efficiency of generated code, as well as the structure and convenience of the language. There are a surprising number of advantages to Lisp, especially in cases where a mixture of symbolic and numeric processing is needed.
The scaled Popov criterion is used to derive an upper bound for the worst-case H-2 norm over a set of linear, time-invariant, norm-bounded, block-structured parameter perturbations. This upper bound provides the basis...
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The scaled Popov criterion is used to derive an upper bound for the worst-case H-2 norm over a set of linear, time-invariant, norm-bounded, block-structured parameter perturbations. This upper bound provides the basis for a robust controller synthesis procedure that minimizes the upper bound and guarantees asymptotic stability of the closed-loop system for ail real parameter perturbations in the specified set. numerical examples demonstrate the tradeoff between achievable H-2 performance and guaranteed robustness to real parameter perturbations as web as the reduction in conservatism due to the scaling matrix. Controllers designed for flexible structures using this technique are shown to have similarities to maximum entropy controllers designed for the same examples.
This is the story of exactly how the Pentium floating-point division problem was discovered, and what you need to know about the mathematics and computer engineering involved before deciding whether to replace the chi...
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This is the story of exactly how the Pentium floating-point division problem was discovered, and what you need to know about the mathematics and computer engineering involved before deciding whether to replace the chip, install the workaround provided here, or do nothing.
An electrical power system usually includes machines with their regulators and controls linked through power lines, transformers, capacitor banks, reactors, and loads. In stability analysis, two distinct strategies ar...
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An electrical power system usually includes machines with their regulators and controls linked through power lines, transformers, capacitor banks, reactors, and loads. In stability analysis, two distinct strategies are possible for solving the differential equations and network equations describing such a system: a simultaneous approach and a partitioned approach. For real-time numerical simulation, the partitioned approach is easier to distribute over parallel processors [2,11] and is therefore more appropriate in this case. In order to demonstrate the feasibility of the real-time simulation of power system stability, this paper presents an implementation of the partitioned approach using parallel digital signal processors (DSP). A network of typical size consisting of 8 machines and 50 buses is simulated. The synchronous machine model has been developed using the block diagram implementation technique. Two algorithms applied to the solution of the network algebraic equations are described and their performances are evaluated on different processors.
We present a nerv algorithm for determining minimal length paths between two regions on a three dimensional surface, The numerical implementation is based on finding equal geodesic distance contours from a given area,...
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We present a nerv algorithm for determining minimal length paths between two regions on a three dimensional surface, The numerical implementation is based on finding equal geodesic distance contours from a given area, These contours are calculated as zero sets of a bivariate function designed to evolve so as to track the equal distance curves on the given surface, The algorithm produces all paths of minimal length between the source and destination areas on the surface given as height values on a rectangular grid.
A general and robust solution procedure for non-linear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is ortho...
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A general and robust solution procedure for non-linear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state. The method implements the physical condition that the orthogonal residual force will neither increase nor decrease the magnitude of the current displacement increment vector. The orthogonality condition is formulated directly in terms of conjugate variables and therefore does not contain any scaling parameters. Passage of load and displacement limit points is discussed as well as the relation to line search, minimum residual, and are-length methods. The method is illustrated by two examples.
Three solution algorithms, explicit under relaxation, point implicit, and lower-upper symmetric Gauss-Seidel, are used to compute nonequilibrium flow around the Apollo 4 return capsule at the 62-km altitude point in i...
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Three solution algorithms, explicit under relaxation, point implicit, and lower-upper symmetric Gauss-Seidel, are used to compute nonequilibrium flow around the Apollo 4 return capsule at the 62-km altitude point in its descent trajectory. By varying the Mach number, the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness. The performance of the solution algorithms degraded as the Mach number and stiffness of the flow increased. At Mach 15 and 30, the lower-upper symmetric Gauss-Seidel method produces an eight order of magnitude drop in the energy residual in one-third to one-half the Cray C-90 computer time as compared to the point implicit and explicit under-relaxation methods. The explicit under-relaxation algorithm experienced convergence difficulties at Mach 30 and above. At Mach 40 the performance of the lower-upper symmetric Gauss-Seidel algorithm deteriorates to the point that it is out performed by the point implicit method. The effects of the viscous terms are investigated. Grid dependency questions are explored.
A study of the time-dependent effects of interfacial layers and matrices on the mechanical properties of laminated composites with various fiber-matrix volume fractions. The study considered elastic and viscoelastic ...
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A study of the time-dependent effects of interfacial layers and matrices on the mechanical properties of laminated composites with various fiber-matrix volume fractions. The study considered elastic and viscoelastic constitutive relations for the matrix. An analysis of the effects of interphase mechanical properties was performed from a microscopic perspective on overall laminated composite properties using finite element methods.
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