The imperfection sensitivity of the effective elastic properties is numerically explored for three planar isotropic lattices: fully triangulated, the Kagome grid, and the hexagonal honeycomb. Each lattice comprises rigid-jointed, elastic Euler–Bernoulli beams, which can both stretch and bend. The imperfections are in the form of missing bars, misplaced nodes, and wavy cell walls. Their effect on the macroscopic bulk and shear moduli is numerically investigated by considering a unit cell containing randomly distributed imperfections, and with periodic boundary conditions imposed. The triangulated and Kagome lattices have sufficiently high nodal connectivities that they are stiff, stretching dominated structures in their perfect state. In contrast, the perfect hexagonal honeycomb, with a low nodal connectivity of 3, is stretching dominated under pure hydrostatic loading but is bending dominated when the loading involves a deviatoric component. The high connectivity of the triangulated lattice confers imperfection insensitivity: Its stiffness is relatively insensitive to missing bars or to dispersed nodal positions. In contrast, the moduli of the Kagome lattice are degraded by these imperfections. The bulk modulus of the hexagonal lattice is extremely sensitive to imperfections, whereas the shear modulus is almost unaffected. At any given value of relative density and level of imperfection (in the form of missing bars or dispersed nodal positions), the Kagome lattice has a stiffness intermediate between that of the triangulated lattice and the hexagonal honeycomb. It is argued that the imperfections within the Kagome lattice switch the deformation mode from stretching to a combination of stretching and bending. Cell-wall waviness degrades the moduli of all three lattices where the behavior of the perfect structure is stretching dominated. Since the shear response of the perfect hexagonal honeycomb is by bar bending, the introduction of bar waviness has a negligible effect on the effective shear modulus.
A review of existing mathematical models for velodrome cycling suggests that cyclists and cycling coaches could benefit from an improved simulation tool. A continuous mathematical model for cycling has been developed that includes calculated slip and steering angles and, therefore, allows for resulting variation in rolling resistance. The model focuses on aspects that are particular, but not unique, to velodrome cycling but could be used for any cycling event. Validation of the model is provided by power meter, wheel speed and timing data obtained from two different studies and eight different athletes. The model is shown to predict the lap by lap performance of six elite female athletes to an average accuracy of 0.36% and the finishing times of two elite athletes competing in a 3-km individual pursuit track cycling event to an average accuracy of 0.20%. Possible reasons for these errors are presented. The impact of speed on steering input is discussed as an example application of the model.
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