The work described in this paper forms part of a programme on the local buckling of long thin flat-walled structures, such as integrally stiffened panels or corrugated core sandwich panels, with the individual flats subjected to combined longitudinal compression and shear. When buckling occurs, the line junctions between adjoining flats remain straight, but rotations occur about the junctions. These rotations vary sinusoidally in the longitudinal direction but, because of the shear, the rotations at the two edges of an individual flat are out of phase with each other. In order to picture the buckling mode it is essential to have at least a qualitative idea of the shape of the nodal lines in the flats. The analysis of this paper is entirely concerned with this problem.

The main purpose of this paper is to illustrate the use of the stability functions for long plates in combined compression and shear defined in a previous paper by the authors. The panel is supported on its two edges and on a series of N intermediate simple supports. Each of the two edges is either clamped or simply-supported and numerical results are given for each of the three possible combinations, with varying numbers of supports. In all cases it is found that a simple parabolic interaction formula between shear and compression is extremely accurate. Also simple approximate formulae are given for calculating the wavelength of the buckle and the lead of the nodal lines for any combination of compression, shear, edge conditions and number of supports.

A method for calculating the growth of a turbulent wall jet in streaming flow has been developed. The flow is assumed to be two-dimensional, incompressible and over a plane, smooth wall. Downstream variations of pressure are permitted and separation in an adverse pressure gradient may be predicted. The method incorporates procedures for matching the flow to that at the blowing slot, although it is postulated that the upstream boundary layer there is thin enough that the wall jet develops without an unmixed wake (i.e. there is not a minimum in the mean-velocity profile).

The method incorporates four integral momentum equations taken from the wall to various points in the flow. The calculation of the outer shearing stress, although empirical, is based on the large-eddy equilibrium hypothesis and therefore has some foundation. The remaining empiricism in the method is based on measurements in self-preserving wall jets.

The method has been used to predict the jet-momentum coefficient required to suppress separation over a trailing-edge flap attached to a thin aerofoil. Plausible curves have been obtained Using assumed values of upstream boundary layer at the slot. Of some practical interest is the indication that large savings in power are possible if the upstream boundary layer is removed. This indicates that blowing combined with upstream suction, or multiple-slot blowing, may give useful savings in the application of blowing to prevent separation.

Nishihara’s combined bending and torsion out-of-phase fatigue limit data are analysed. The Tresca shear stress failure criterion predicts strengths up to 30 per cent higher than observed. It thus appears that renewed attention should be given to the basic problem of developing reliable combined stress failure criteria. It is suggested that new test methods will be required for this purpose.

The governing equations for bending of truncated conical shells with multi-layer anisotropic construction are developed by a variational method. The shell is considered to consist of an arbitrary number of alternating soft and hard layers. It is assumed further that the n hard membrane layers are isotropic and may possess different elastic properties, while the (n-1) soft core layers are orthotropic in general and may take transverse shear only. The variations of stresses across the membranes are neglected, as are the surface-parallel stresses in the cores. These assumptions are consistent with those usually employed in single-core sandwich shells. The energy functional is formulated with the stresses considered as independent variables. The stresses are also dependent variables defined in the set of two curvilinear co-ordinates defining the surface of the shell. The stress resultants are introduced as constraint conditions utilising Lagrange multipliers. Successful definition of an elastic neutral surface ensures the uniqueness of shell constants and the equations obtained may be in a form comparable to that of classical shell theory. The system of equations is reduced to a form where Galerkin’s method can be applied directly.

The paper presents a solution to the buckling under shear stress of infinitely long plates orthogonally reinforced by stiffeners having both flexural and torsional rigidity. Each family of stiffeners is assumed to consist of equally spaced identical stiffeners. Numerical results are given for the case of a plate with transverse stiffeners and a central longitudinal stiffener for the following three cases:

• (i) Transverse and longitudinal stiffeners of closed tubular cross-section.

• (ii) Transverse stiffeners of closed tubular cross-section, longitudinal stiffeners possessing only flexural rigidity.

• (iii) Transverse stiffeners possessing only flexural rigidity, the longitudinal stiffeners being of closed tubular cross-section.

Relationships between the buckling stress parameter K and the flexural rigidity parameter γ of the stiffeners are presented for each of the three cases when the identical transverse stiffeners are placed at spacings of d, 0·8d and 0·5d, where d is the depth of the webplate.

Case (i) has provided values of the buckling coefficient K for finite rectangular plates clamped on three edges and simply-supported on the remaining edge.

Measurements of the pitot pressure between the body and shock on a 15° semi-vertex angle, spherically blunted cone were made in the RARDE Hypersonic Gun Tunnel at a Mach number of 8·6. Using these measurements, together with the measured shock shape, the other flow field parameters were calculated. The results were compared with results of inviscid theoretical calculations for a similar cone at a Mach number of 10.