Bending Of Circular Plate On Elastic-Foundation

The governing differential equation of linear, elastic, thin, circular plate of uniform thickness, subjected to uniformly distributed load and resting on Winkler-Pasternak type foundation is solved using ``Chebyshev Polynomials''. Analysis is carried out using Lenczos' technique, both for simply supported and clamped plates. Numerical results thus obtained by perturbing the differential equation for plates without foundation are compared and are found to be in good agreement with the available results. The effect of foundation on central deflection of the plate is shown in the form of graphs.

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

Microprocessor-based polynomial generator

A new method of generating polynomials using microprocessors is proposed. The polynomial is generated as a 16-bit digital word. The algorithm for generating a variety of basic 'building block' functions and its implementation is discussed. A technique for generating a generalized polynomial based on the proposed algorithm is indicated. The performance of the proposed generator is evaluated using a commercially available microprocessor kit.

A cryptographic system based on finite field transforms

In this paper, we develop a cipher system based on finite field transforms. In this system, blocks of the input character-string are enciphered using congruence or modular transformations with respect to either primes or irreducible polynomials over a finite field. The polynomial system is shown to be clearly superior to the prime system for conventional cryptographic work.

A Novel Cache Architecture and Placement Framework for Packet Forwarding Engines

Packet forwarding is a memory-intensive application requiring multiple accesses through a trie structure. With the requirement to process packets at line rates, high-performance routers need to forward millions of packets every second with each packet needing up to seven memory accesses. Earlier work shows that a single cache for the nodes of a trie can reduce the number of external memory accesses. It is observed that the locality characteristics of the level-one nodes of a trie are significantly different from those of lower level nodes. Hence, we propose a heterogeneously segmented cache architecture (HSCA) which uses separate caches for level-one and lower level nodes, each with carefully chosen sizes. Besides reducing misses, segmenting the cache allows us to focus on optimizing the more frequently accessed level-one node segment. We find that due to the nonuniform distribution of nodes among cache sets, the level-one nodes cache is susceptible t high conflict misses. We reduce conflict misses by introducing a novel two-level mapping-based cache placement framework. We also propose an elegant way to fit the modified placement function into the cache organization with minimal increase in access time. Further, we propose an attribute preserving trace generation methodology which emulates real traces and can generate traces with varying locality. Performanc results reveal that our HSCA scheme results in a 32 percent speedup in average memory access time over a unified nodes cache. Also, HSC outperforms IHARC, a cache for lookup results, with as high as a 10-fold speedup in average memory access time. Two-level mappin further enhances the performance of the base HSCA by up to 13 percent leading to an overall improvement of up to 40 percent over the unified scheme.

Finite element analysis of laminated anisotropic thin-walled open-section beams

A finite element analysis of thin-walled open-section laminated anisotropic beams is presented herein. A two-noded, 8 degrees of freedom per node thin-walled open-section laminated anisotropic beam finite element has been developed and used. The displacements of the element reference axes are expressed in terms of one-dimensional first order Hermite interpolation polynomials and line member assumptions are invoked in the formulation of the stiffness matrix. The problems of: 1. (a) an isotropic material Z section straight cantilever beam, and 2. (b) a single-layer (0°) composite Z section straight cantilever beam, for which continuum solutions (exact/approximate) are possible, have been solved in order to evaluate the performance of the finite element. Its applicability has been shown by solving the following problems: 3. (c) a two-layer (45°/−45°) composite Z section straight cantilever beam, 4. (d) a three-layer (0°/45°/0°) composite Z section straight cantilever beam.

A laminated anisotropic curved beam and shell stiffening finite element

The details of development of the stiffness matrix of a laminated anisotropic curved beam finite element are reported. It is a 16 dof element which makes use of 1-D first order Hermite interpolation polynomials for expressing it's assumed displacement state. The performance of the element is evaluated considering various examples for which analytical or other solutions are available.

Application of partition method to vibration problems of plates

The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

Divide-and-Correct Algorithm for Division in a Negative Base

A divide-and-correct algorithm is described for multiple-precision division in the negative base number system. In this algorithm an initial quotient estimate is obtained from suitable segmented operands; this is then corrected by simple rules to arrive at the true quotient.

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

Microprocessor-based polynomial generator

A new method of generating polynomials using microprocessors is proposed. The polynomial is generated as a 16-bit digital word. The algorithm for generating a variety of basic 'building block' functions and its implementation is discussed. A technique for generating a generalized polynomial based on the proposed algorithm is indicated. The performance of the proposed generator is evaluated using a commercially available microprocessor kit.

Application of partition method to vibration problems of plates

The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

Divide-and-Correct Algorithm for Division in a Negative Base

A divide-and-correct algorithm is described for multiple-precision division in the negative base number system. In this algorithm an initial quotient estimate is obtained from suitable segmented operands; this is then corrected by simple rules to arrive at the true quotient.

Natural frequencies of polar orthotropic annular plates

The classical Rayleigh-Ritz method with simple polynomials as admissible functions has been used for obtaining natural frequencies of transversely vibrating polar orthotropic annular plates. The method in conjunction with transformations introduced in the analysis has been found to be quite effective, particularly for large hole sizes. Estimates of natural frequencies corresponding to modes with one as well as two nodal diameters are obtained for the nine combinations of clamped, simply supported and free edge conditions and for various values of rigidity ratio and hole sizes. Based on the variation of eigenvalue parameter with rigidity ratio, the frequencies of these modes as well as those of axisymmetric modes have been expressed by means of simple formulae in terms of rigidity ratio and the frequencies of corresponding modes in the isotropic case. These formulae have been used in determining the fundamental frequencies of orthotropic plates.

Finite element analysis of curved anisotropic laminated hollow bars

Curved hollow bars of laminated anisotropic construction are used as structural members in many industries. They are used in order to save weight without loss of stiffness in comparison with solid sections. In this paper are presented the details of the development of the stiffness matrices of laminated anisotropic curved hollow bars under line member assumptions for two typical sections, circular and square. They are 16dof elements which make use of one-dimensional first-order Hermite interpolation polynomials for the description of assumed displacement state. Problems for which analytical or other solutions are available are first solved using these elements. Good agreement was found between the results. In order to show the capability of the element, application is made to carbon fibre reinforced plastic layered anisotropic curved hollow bars.