Nicholas Davies edited method.tex  over 7 years ago

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The pre-stressed state of the cambium from gravity and growth stresses produces the need to successively ’grow’ the mesh which is to be used so that each mesh addition is added in a non stressed state on top of a stressed surface. Mesh growth is achieved by first defining an initial state, this state can be thought of as a seedling. The seedling is subjected to gravitational forces, deformation occurs and a new deformed mesh is created. The positions of the nodes and vertices of the deformed mesh are used to calculate the positions of new vertices and nodes to be added in order to represent cambial growth in a non stressed state onto the stressed surface along with apical growth to a predefined height.   Experimental The material  constants described in Chapter 2 for \textit{Pinus radiata} were reported by --ref--  were used to parametrise the model. Fourwood  samples of Pinus radiata were chosen to represent a range of representing  extreme values of green density and stiffness for the species. species were used.  Linear interpolation was used to approximate material constants between two samples to provide a gradient of material properties from the corewood to the outerwood. The TRP of cellular properties was investigated using the gradient of elastic constants and Poisson ratios from different samples by applying simulated wind loads to stems with different radial profiles. A linear interpolation was used between two samples in order to provide the TRP over the stem. While the TRP of Pinus radiata usually follows a non-linear increase for density and a non-linear decrease for MFA (Burdon et al., 2004), during the first 15 years the trend can be approximated as linear, after this however the non-linear behaviour becomes more prevalent as the properties stabilise. It should be noted that there is much variation between individuals and this is not universal. After 15 years the properties produced by older cambial tissues become fairly consistent for a given individual and are not considered here. As the radius increases and the pattern becomes consistent the inner radial pattern will have less influence on the structural stability of the stem. The TRP was investigated by calculating the appropriate elastic and shear moduli along with Poisson ratios for each point in the stem based on a linear interpolation. The linear interpolation was calculated between two samples chosen to represent corewood and outerwood, Equation 3.2 shows the general form. λ =  −r  (λ i − λ o ) + λ i