Search results

To the Editor. SIR: I should like to make some comments on the article by E. W. Parkes on ‘Linear Simultaneous Equations’ on p. 48 of the February issue. This article does not paint a fair picture of this operation.

A very simple redundant structure is subjected to temperature cycling, primarily to determine the influence of the yield stress/temperature relation on its behaviour: the range and periodic time of the temperature cycle are included as subsidiary variables. It is found that improving the strength of the material at elevated temperatures may have the undesirable effect of hastening incremental collapse of the structure, and that the most rapid incremental collapse is not necessarily associated with maximum values for the range and periodic time of the temperature cycle. It is also found that the common assumption that the strength of the material is independent of temperature may in some circumstances be ambiguous, since there may be a sudden discontinuity in behaviour between a structure made from a material having a slight negative strength/temperature gradient and one made from a material having a slight positive gradient.

This paper discusses the problem of a panel attached along two of its edges to heavy members which respond only slowly to external temperature change and thereby prevent its free (hernial expansion, and along the other two edges, parallel to the direction of loading, to light members which permit free expansion. It is shown that the load‐bearing capacity of such a panel is generally small, if buckling is to be avoided, but that much greater loads can be carried in the post‐buckling condition, provided that a small degree of rippling can be tolerated. The paper includes a number of numerical examples, in one of which the concept of a load‐temperature envelope is introduced.

WHEN a structure is subjected to a recurrent cycle of loading a number of different types of deformation may be set up. The structure may remain elastic throughout, returning to its original configuration at the end of each cycle. It may shake down to an elastic configuration which differs from the initial one, but which, once established, is the same at the end of each cycle. The structure may suffer inelastic deformation in each cycle of loading, with net value zero, so that again the configuration is the same at the end of each cycle: this condition is usually known as alternate plasticity and may lead to strain fatigue. Finally, the structure may suffer inelastic deformation in each cycle which has a non‐zero net value, so that the deformation changes progressively with each cycle of loading: this is known as incremental collapse.

An analysis is given for the stresses in an insulated plate in the neighbourhood of a local hot spot. The stresses depend upon the relative size and flexibilities of plate and heated area.

When an aircraft changes its speed or altitude, large thermal strains may be set up in the wing structure; sometimes these are of sufficient magnitude for the accompanying stresses to exceed the clastic limit of the material. During its life the aircraft may suffer a large number of cycles of thermal stress. Under repeated thermal loading it is found that four types of stress‐strain system may be set up: permanent elasticity and shakedown to an clastic state, which are safe, and alternate plasticity and incremental collapse, which are dangerous. The present paper investigates these stress‐strain systems and determines the conditions for their occurrence.

The following paper investigates the dependence of the thermal stresses which are set up when an aircraft suffers an external temperature change, upon the degree of insulation of the outer skin, and upon the speed with which the external temperature change takes place. It is shown that quite thin insulating layers, such as are provided by the aircraft paintwork, can produce considerable alleviation of the thermal stresses. We should not generally, however, expect any appreciable reduction in the stresses due to the finite time taken for the external temperature to change, since effectively instantaneous variations of temperature can occur in practice, particularly when the external surface is insulated.

THE procedure usually adopted for the design of a redundant structure is to assume some initial distribution of material and then to stress this by strain energy methods. From the knowledge of the load distribution thus acquired a second structure is designed and stressed and the process is repeated, if necessary, until a reasonably uniform stress is obtained.

The following paper discusses the transient thermal stresses set up in a cellular wing structure when the aircraft is subjected to a change of speed or of altitude. It is found rftac for nings with little or no insulation (fie maximum stress in the wing is usually between 70 per cent and 85 per cent of the value given by Young's modulus for webs × coefficient of expansion for the skin × external temperature change: it is therefore concluded that of the metallic materials, the combination of Hfcht alloy webs with a steel skin is admirable in its effect in reducing the thermal stresses. The analysis used is exact within the limits of its assumptions and comparisons are made with an earlier solution of the same problem by Hoff, who used an approximate method.

An approximate method is employed to derive the transient temperature distributions and thermal stresses in an idealized insulated multi‐spar wing subjected to aerodynamic heating. Approximate formulae obtained by this method arc compared with exact solutions for a number of special cases, and are found to be in good agreement.