By B. M. Fraeijs de Veubeke (auth.)
This e-book is predicated on lecture notes of the past due Professor de Veubeke. the topic is gifted at a degree compatible for graduate scholars in engineering, physics, or arithmetic. a few publicity to linear algebra, complicated research, variational calculus, or simple continuum mechanics will be useful. the 1st 3rd of the publication includes the basics of the speculation of elasticity. Kinematics of continuing media, the notions of pressure and equilibrium, conservation of strength, 'and the elastic constitutive legislations are every one handled first in a nonlinear context, then really expert to the linear case. the rest of the ebook is given to 3 vintage functions of the speculation, every one supplemented by means of unique re sults in line with using complicated variables. each of the 3 themes - Saint-Venant's conception of prismatic beams, aircraft deformations, and the bending of plates - is first pre sented and analyzed regularly, then rounded out with quite a few particular and occasionally novel examples. the next notational conventions are typically in strength, other than the place famous on the contrary: decrease case boldface letters denote vectors or triples of Cartesian co ordinates, higher case boldface letters denote three x three matrices, repeated decrease case Latin subscripts are summed over (1,2,3), and non-repeated reduce case Latin subscripts are assumed to diversity over (1,2,3).
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Extra resources for A Course in Elasticity
3 MECHANICS OF SNOW COVERED TERRAIN In this section we will present details of an in-situ experimental method that may be used to obtain snow characteristics and related snow physical properties. The method may also be used to obtain the snow’s essential compression and shear deformation properties. These properties are necessary for calculation of the bearing capacity of a snow covered terrain or alternately of the thrust or drag of a tracked over-snow vehicle or wheeled snow remover during driving or braking action on a snow covered terrain.
37) In the triaxial compression test, depending on the drainage conditions utilised the experimental method can be classed into three different test regimes – namely the unconsolidated undrained shear test (UU Test), the consolidated undrained shear test (CU Test) and the drainage shear test (D Test). In the field of terramechanics, the undrained shear test (UU Test) is commonly used because of the large strain rates encountered and the undrained condition typically encountered in the field. Although the standard triaxial compression test typically uses a quite fast strain rate of 1%/min, the required strain rate of the soil in terramechanics work is very much higher.
51) where α is a constant value which is determined by the snow sample and the shear rate etc. If one assumes that the distribution of shear resistance τ acting on the vertical peripheral shear surface and the horizontal bottom shear surface of the vane cone of height of H and of radius r becomes uniform, then the normal stress σ and the shear resistance τ can be calculated from the penetration force F and the maximum torque Tmax . This latter factor is measured in correspondence to the maximum shear resistance τmax at X = 0 .