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S U M M A R YWe present a new 1-D earth model for the crust and upper mantle beneath the Archaean core of southern Africa. The crustal structure is constrained by published seismic refraction/reflection data and by the modelling of teleseismic receiver function data. The mantle structure is constrained by traveltime measurements for P, and S, waves, by waveform inversion of multimode surface waves, and by forward modelling of P,, waveforms for regional earthquakes. The 42 km thick crust of southern Africa consists of four layers: a 2 km thick 5.05 km s-' surface layer, a 5 km thick 6.08 km s-' upper crust, a 20 km thick 6.30 km s-l mid-crust and a 15 km thick 6.73 km s-' lower crust. Below the crust there is an 80 km thick upper-mantle lid. V, and V, are 8.09 and 4.62 km s-l, respectively, at the top of the lid, and the compressional-and shearvelocity gradients through the lid are 0.0008 s-l and 0.0013 s-', respectively. Below the lid there is a substantial shear-wave LVZ, with the shear-wave velocity dropping from 4.72 km s-l in the lower part of the lid to 4.32 km s-' at 250 km depth. The shear-wave LVZ is required to fit both the V,= measurements and the regional surface waveforms. Forward modelling of P,, suggests that no upper-mantle P-wave LVZ exists. There is an increase in the P-wave velocity gradient at 125 km depth to 0.0015 s-' and a second increase at 250 km depth to 0.0035 s-'. Velocities and densities in the seismic model of the lid agree closely with velocity and density estimates from the geochemical analysis of garnet periodotite nodules from kimberlites of the Kaapvaal Craton, implying that the estimates from kirnberlites are representative of a wider region of the Archaean core of southern Africa-not just of the restricted region beneath which the kimberlites are found. A comparison of the southern African seismic model with seismic models for other shield regions where nodule data are not available shows that the nodule results may also be representative of the upper mantle in those regions.

An analytical model is developed for the deformation response of clamped circular sandwich plates subjected to shock loading in air and in water. The deformation history is divided into three sequential stages and analytical expressions are derived for the deflection, degree of core compression, and for the overall structural response time. An explicit finite element method is employed to assess the accuracy of the analytical formulas for the simplified case where the effects of fluid-structure interaction are neglected. The sandwich panel response has only a low sensitivity to the magnitude of the core compressive strength and to the degree of strain hardening in the face-sheets. The finite element results confirm the accuracy of the analytical predictions for the rigid ideally plastic sandwich plates. The analytical formulas are employed to determine optimal geometries of the sandwich plates that maximize the shock resistance of the plates for a given mass. The optimization reveals that sandwich plates have a superior shock resistance relative to monolithic plates of the same mass.

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As a result of repeating carbon nanotube Y junctions periodically, super honeycomb structures have recently been proposed. In this paper, the mechanical properties of these structures are investigated by using the shell model of the finite element method. The study shows that the super honeycomb structures have great flexibility and outstanding capability in force transferring; the network configuration increases the ductility of the nanomaterials. Furthermore, it can be concluded that the equivalent tensile modulus and Poisson's ratio of super structures are dependent on the number of junctions in the width direction.