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.

Algorithms for Constructing Hierarchical Graphs

An algorithm is described for developing a hierarchy among a set of elements having certain precedence relations. This algorithm, which is based on tracing a path through the graph, is easily implemented by a computer.

Algorithms for Constructing Hierarchical Graphs

An algorithm is described for developing a hierarchy among a set of elements having certain precedence relations. This algorithm, which is based on tracing a path through the graph, is easily implemented by a computer.

Non-linear response of a gyrostabilized platform to transient input

In this paper the response of a gyrostabilized platform subjected to a transient torque has been analyzed by deliberately introducing non-linearity into the command of the servomotor. The resulting third-order non-linear differential equation has been solved by using a transformation technique involving the displacement variable. The condition under which platform oscillations may grow with time or die with time are important from the point of view of platform stabilization. The effect of deliberate addition of non-linearity with a view to achieving the ideal response—that is, to bring the platform back to its equilibrium position with as few oscillations as possible—has been investigated. The conditions under which instability may set in on account of the small transient input and small non-linearity has also been discussed. The analysis is illustrated by means of a numerical example. The results of analysis are compared with numerical solutions obtained on a digital computer.

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

Homogenization of periodic structures via Bloch decomposition

In this paper, the classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coefficients is considered. Using Bloch wave decomposition, a new proof of convergence is furnished. It sheds new light and offers an alternate way to view the classical results. In a natural way, this method leads us to work in the Fourier space and thus in a framework dual to the one used by L. Tartar [Problemes d'Homogeneisation dans les Equations aux: Derivees Partielles, Cours Peccot au College de Prance, 1977] in his method of homogenization. Further, this technique offers a nontraditional way of calculating the homogenized coefficients which is easy to implement in the computer.

Computer simulation of protein—carbohydrate complexes: application to arabinose-binding protein and pea lectin

The CCEM method (Contact Criteria and Energy Minimisation) has been developed and applied to study protein-carbohydrate interactions. The method uses available X-ray data even on the native protein at low resolution (above 2.4 Å) to generate realistic models of a variety of proteins with various ligands.The two examples discussed in this paper are arabinose-binding protein (ABP) and pea lectin. The X-ray crystal structure data reported on ABP-β-l-arabinose complex at 2.8, 2.4 and 1.7 Å resolution differ drastically in predicting the nature of the interactions between the protein and ligand. It is shown that, using the data at 2.4 Å resolution, the CCEM method generates complexes which are as good as the higher (1.7 Å) resolution data. The CCEM method predicts some of the important hydrogen bonds between the ligand and the protein which are missing in the interpretation of the X-ray data at 2.4 Å resolution. The theoretically predicted hydrogen bonds are in good agreement with those reported at 1.7 Å resolution. Pea lectin has been solved only in the native form at 3 Å resolution. Application of the CCEM method also enables us to generate complexes of pea lectin with methyl-α-d-glucopyranoside and methyl-2,3-dimethyl-α-d-glucopyranoside which explain well the available experimental data in solution.

Fast matrix transposition computer implementation

Eklundh's (1972) algorithm to transpose a large matrix stored on an external device such as a disc has been programmed and tested. A simple description of computer implementation is given in this note.

A computerized methodology for structural synthesis of kinematic chains: Part 2 - Application to several fully or partially known cases

The reliability of the computer program for structural synthesis and analysis of simple-jointed kinematic chains developed in Part 1 has been established by applying it to several cases for whuch solutions are either fully or partially available in the literature, such as 7-link, zero-freedom chains; 8- and 10-link, single-freedom chains; 12-link, single-freedom binary chains; and 9-link, two-freedom chains. In the process some discrepancies in the results reported in previous literature have been brought to light.