Applications of Reissner's principle to structural dynamics

The analysis and prediction of the dynamic behaviour of s7ructural components plays an important role in modern engineering design. :n this work, the so-called "mixed" finite element models based on Reissnen's variational principle are applied to the solution of free and forced vibration problems, for beam and :late structures. The mixed beam models are obtained by using elements of various shape functions ranging from simple linear to complex cubic and quadratic functions. The elements were in general capable of predicting the natural frequencies and dynamic responses with good accuracy. An isoparametric quadrilateral element with 8-nodes was developed for application to thin plate problems. The element has 32 degrees of freedom (one deflection, two bending and one twisting moment per node) which is suitable for discretization of plates with arbitrary geometry. A linear isoparametric element and two non-conforming displacement elements (4-node and 8-node quadrilateral) were extended to the solution of dynamic problems. An auto-mesh generation program was used to facilitate the preparation of input data required by the 8-node quadrilateral elements of mixed and displacement type. Numerical examples were solved using both the mixed beam and plate elements for predicting a structure's natural frequencies and dynamic response to a variety of forcing functions. The solutions were compared with the available analytical and displacement model solutions. The mixed elements developed have been found to have significant advantages over the conventional displacement elements in the solution of plate type problems. A dramatic saving in computational time is possible without any loss in solution accuracy. With beam type problems, there appears to be no significant advantages in using mixed models.

Neuro-electromagnetic imaging of the human visual cortex

Methods of solving the neuro-electromagnetic inverse problem are examined and developed, with specific reference to the human visual cortex. The anatomy, physiology and function of the human visual system are first reviewed. Mechanisms by which the visual cortex gives rise to external electric and magnetic fields are then discussed, and the forward problem is described mathematically for the case of an isotropic, piecewise homogeneous volume conductor, and then for an anisotropic, concentric, spherical volume conductor. Methods of solving the inverse problem are reviewed, before a new technique is presented. This technique combines prior anatomical information gained from stereotaxic studies, with a probabilistic distributed-source algorithm to yield accurate, realistic inverse solutions. The solution accuracy is enhanced by using both visual evoked electric and magnetic responses simultaneously. The numerical algorithm is then modified to perform equivalent current dipole fitting and minimum norm estimation, and these three techniques are implemented on a transputer array for fast computation. Due to the linear nature of the techniques, they can be executed on up to 22 transputers with close to linear speedup. The latter part of the thesis describes the application of the inverse methods to the analysis of visual evoked electric and magnetic responses. The CIIm peak of the pattern onset evoked magnetic response is deduced to be a product of current flowing away from the surface areas 17, 18 and 19, while the pattern reversal P100m response originates in the same areas, but from oppositely directed current. Cortical retinotopy is examined using sectorial stimuli, the CI and CIm ;peaks of the pattern onset electric and magnetic responses are found to originate from areas V1 and V2 simultaneously, and they therefore do not conform to a simple cruciform model of primary visual cortex.

Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N0), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H2, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N0, M, and n. Asymptotic approximations of H2 are deduced and tested for both one-dimensional (1-D) and 2-D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power-law relationship, C= aMNb0, with the CPU cost index, b, indicating the weighting of N0 in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N0 determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2394–2402, 2015

Rough-terrain groundspeed measurement:a radar-based commercial solution

Off-highway motive plant equipment is costly in capital outlay and maintenance. To reduce these overheads and increase site safety and workrate, a technique of assessing and limiting the velocity of such equipment is required. Due to the extreme environmental conditions met on such sites, conventional velocity measurement techniques are inappropriate. Ogden Electronics Limited were formed specifically to manufacture a motive plant safety system incorporating a speed sensor and sanction unit; to date, the only such commercial unit available. However, problems plague the reliability, accuracy and mass production of this unit. This project assesses the company's exisiting product, and in conjunction with an appreciation of the company history and structure, concludes that this unit is unsuited to its intended application. Means of improving the measurement accuracy and longevity of this unit, commensurate with the company's limited resources and experience, are proposed, both for immediate retrofit and for longer term use. This information is presented in the form of a number of internal reports for the company. The off-highway environment is examined; and in conjunction with an evaluation of means of obtaining a returned signal, comparisons of processing techniques, and on-site gathering of previously unavailable data, preliminary designs for an alternative product are drafted. Theoretical aspects are covered by a literature review of ground-pointing radar, vehicular radar, and velocity measuring systems. This review establishes and collates the body of knowledge in areas previously considered unrelated. Based upon this work, a new design is proposed which is suitable for incorporation into the existing company product range. Following production engineering of the design, five units were constructed, tested and evaluated on-site. After extended field trials, this design has shown itself to possess greater accuracy, reliability and versatility than the existing sensor, at a lower unit cost.

On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.

Metrology enhanced tooling for aerospace (META):strategies for improved accuracy of jig built structures

The accuracy of many aerospace structures is limited by the accuracy of assembly tooling which is in turn limited by the accuracy of the measurements used to set the tooling. Further loss of accuracy results from different rates of thermal expansion for the components and tooling. This paper describes improved tooling designs and setting processes which have the potential to significantly improve the accuracy of aerospace structures. The most advanced solution described is environmentally isolated interferometer networks embedded within tooling combined with active compensation of component pick-ups. This would eliminate environmental effects on measurements while also allowing compensation for thermal expansion. A more immediately realizable solution is the adjustment of component pick-ups using micrometer jacking screws allowing multilateration to be employed during the final stages of the setting process to generate the required offsets. Copyright © 2011 SAE International.