By James R. Smith
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Extra info for Basic geodesy : an introduction to the history and concepts of modern geodesy without mathematics
If a weight function is known for a particular body then stress intensity factors may be obtained for different loadings on the same body by a simple integration. To see how this function relates to the stress intensity factor, we will determine the change in energy introduced by a new crack. Weight functions are discussed in more detail by Parker (1980). For simplicity, we consider the mode I opening of a crack problem which is symmetric about the x-axis. 17(b) the normal stress is assumed to be a known function — p(x) along the dashed line in the uncracked region.
Since the crack does not open, the SIF for this case Kb = 0. Finally, in part (c), the stresses closing the crack in (b) are applied in reverse thus opening the crack and giving rise to a stress intensity factor Kc. 5) Superposition 39 The stress intensity factor for any linear elastic region may therefore always be found from the original problem or from the same geometry with no external loads and the appropriate stresses applied to the crack surface. If the SIF is to be obtained from a number of different cracked configurations, then any of these may have overlapping crack surfaces providing that the total configuration does not.
However, we can consider briefly how elastic regions and cracks are modelled since this is vital to the accuracy of results. 1 a curve is approximated (or modelled) by a polynomial which passes through a number of sample points on the true curve. Since polynomials are easy to deal with mathematically, they may be used to approximate an integral form of the rather complicated equations of elasticity. The simplified equations can then be solved numerically. This is the basis of the finite element (FEM) and boundary element (BEM) methods.