Browsing by Author "Hemp, W. S."

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    The buckling in compression of panels with square top-hat section stringers
    (College of Aeronautics, Cranfield, 1949-06) Hemp, W. S.; Griffin, K. H.
    A simplified panel model is described, together with a number of assumptions about the mode of its bucking. The approach to the calculation of the buckling stress is by splitting the panel into a number of flat plates and treating these by the ordinary plate theory. Use of the boundary conditions between these plates leads to a relation between the buckling stress and the variables of the panel geometry. The results thus obtained are compared with two sets of recent experimental work; and an appendix is included to show the effect of initial panel irregularities on the experimental determination of buckling stresses.
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    Note on the dynamics of a slightly deformable body
    (College of Aeronautics, Cranfield, 1947-02) Hemp, W. S.
    The purpose of this note is to develop the equations of motion of a slightly deformable body. Appeal to general principles shows the independence of the translation (Para.2). Moving axis are defined in papa.3 which can be taken to define the rotation. Motion relative to these axes is described by normal co-ordinates (Para.4) and the kinetic energy of the motion relative to the centre of mass is split into two parts; the energy of rotation and the energy of vibration (Para.5). Equations for the vibration are then formulated (Para.6). Attention is drawn to the coupling between rotation and vibration, which only vanishes when the angular velocities are small (Para.7).
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    Notes on the problem of the optimum design of structures
    (College of Aeronautics, 1958-01) Hemp, W. S.
    The urgent need for a systematic approach to the problems of the optimum design of structures is stressed and ideal formulations of these problems are considered. Differential equations and a variational principle are derived for the case of plates loaded in their own planes; these can form the basis for approximate solutions, in the form of optimum distributions of plate thickness and the corresponding stress distributions which are required to equilibrate given systems of external loads.
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    On a theory of sandwich construction
    (College of Aeronautics, 1948-03) Hemp, W. S.
    The theory of sandwich construction developed in this paper proceeds from the simple assumption that the filling has only transverse direct and shear stiffnesses, corresponding to its functional requirements (§1). This supposition permits integration of the equilibrium equations for the filling (§2). The resulting integrals are used to study the compression buckling of a flat sandwich plate (§3). The formulae obtained are complex, but may be simplified in practical cases (§4). A second approach to sandwich problems is made in §5, where a theory of "bending" of plates is outlined. This generalises the usual theory, making allowance for flexibility in sheer. This approach is applied to overall compression buckling of a plate in §6, and agreement with the previous calculations is found. This suggests the possibility of calculating buckling loads for curved sandwich shells. A simple example, the symmetrical buckling of a circular cylinder in compression is worked out in §7. The theory developed would seem applicable to all cases of buckling of not too short a wave length (§8).
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    On the analysis of statically indeterminate structures
    (College of Aeronautics, Cranfield, 1946-11) Hemp, W. S.
    This report develops a general method for the analysis of statically indeterminate structures. It concerns itself both with a rigorous demonstration of the validity of the methods and with recommendations for their successful practical application. Continues ...
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    On the application of oblique coordinates to problems of plane elasticity and swept-back wing structures
    (College of Aeronautics, Cranfield, 1950-01) Hemp, W. S.
    The object of this report is two-fold. On the mathematical side it seeks to illustrate the use of oblique coordinates in applications to Elasticity and Structure Theory. On the practical side it seeks to provide methods by which designers can solve problems of stress distribution and deflection for the case of swept-back wing structures, whose ribs lie parallel to the direction of flight. Continues …
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    On the natural frequencies of a reinforced circular cylinder
    (College of Aeronautics, Cranfield, 1949-03) Hemp, W. S.
    This report is concerned with the calculations of the natural frequencies of an ideal structure somewhat representative of an aircraft fuselage. The results are based upon a simplified “shell” theory which permits proper allowance to be made for the shear stresses and the corresponding displacements. No use is made of the so-called “shear deflection”, but it is shown in the Appendix that, for the special case considered, this approach would yield the same answer. Numerical results are given in x7 and comparison is made with both the usual beam theory results and the frequencies calculated on the assumption that flexibility in shear is of primary importance.
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    Optimum structures
    (College of Aeronautics, 1965-07) Hemp, W. S.; Chan, H. S. Y.
    The design of the best structure for a given purpose depends upon the criterion used for optimisation. Structures may be designed to safely transmit a given system of forces using the least weight of material.. They may also be designed to have maximum stiffness of a certain type for a given weight or alternatively to have the greatest possible fundamental frequency of vibration. These problems, although in general distinct from one another, are closely related and much can be achieved towards maximisation of stiffness and frequency by the use of minimum weight designs. In fact it can be shown that a minimum weight framework is the stiffest structure of that weight for the force system, which it is designed to carry.x The present report is concerned exclusively with the problem of the design of structures of minimum weight, which are required to transmit specified forces. Some attention will be given to frameworks because, in particular, methods of approximate numerical analysis are more readily formulated for this type of structure, but the main emphasis will be placed upon the design of structures formed from plates of variable thickness reinforced by direct load carrying members. See para,l.4
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    Plastic buckling of a plate in shear
    (College of Aeronautics, 1957-05) Hemp, W. S.
    This note derives the mathematical equations for the analysis of the shear buckling of a plate, in the case where the initial stresses exceed the elastic limit of the material. It is hoped at a later stage to apply this theory to test results, which are being obtained using rectangular torsion boxes.
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    Solution of a load diffusion problem by relaxation methods
    (College of Aeronautics, 1954-11) Vaisey, Gillian; Hemp, W. S.
    SUMMARY The need. to generalise the usual assumptions made in the analysis of load diffusion problems has been emphasised by recent experimental work (Ref. 3)1 which has shown the importance of bending of the edge members. Direct mathematical solution of the plate problems, which arise, is hardly feasible and so in this report a numerical solution using the 'relaxation method' is carried out. Results show the method to be suitable for design purposes/ but comparison with experiment still shows the need for further physical generalisations. These will form the subject of future work.
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    Theory of structural design
    (College of Aeronautics, 1958-08) Hemp, W. S.
    The Theory of Structures is for the most part concerned with the calculation of stresses in a given structure under given external conditions of loading and temperature. The real problem of structural design, however, in aeronautics at any rate, is to find that structure, which will equilibrate the external loads, without failure or undue deformation, under such conditions of temperature, as may be appropriate, and which at the same time will have the least possible weight. The solution of this general design is obviously very difficult and cannot be resolved at the present time. However, on the basis of certain classical theorems due to Maxwell and Michell and using methods and suggestions derived from these theorems by H.L. Cox, one can make certain progress, and in addition point the way to profitable lines of research. The present paper reviews the classical results and their current application, develops the mathematical theory for the two-dimensional case and derives a number of special solutions. It is hoped that its publication will encourage research in this very important field.