Stiffened elastic constant

In piezoelectric media, the strain energy is multiplied by the factor (1 + due to piezoelectric stiffening of the elastic constants. Thus, the strain energy includes electrical stored energy in this case. To calculate the magnitude of the electrical energy density Ue independent of the strain energy, the relation... 

Figure 17 The evolution of the computed C44 elastic constant of albite with temperature and differing degrees of AFSi order, Qod- The C44 elastic constant in analbite acts almost as the critical elastic constant as it most softens to zero. Increasing Al/Si order stiffens the elastic constant (after Wood 1998).

Summing up, the overall decrease in the contact area with increasing speed can be predicted by assuming that at zero speed the elastic contact condition prevails. However, at high speed the material is viscoelastic, giving rise to the aforementioned stiffening, and it is assumed that the new (and smaller) area of contact is related to the viscoelastic moduli in a similar way. Finally, at very high speed, the contact tends to also be constant. 

Consider a thin plate of homogeneous, isotropic and linearly elastic material with modulus of elasticity E and Poisson ratio v, having constant thickness hp and occupying the two dimensional multiply connected region of the x,y plane bounded by the piecewise smooth fC-fl curves ro,ri,...,rx-i,rx, as shown in Fig. 1. The plate is stiffened by a set of /= 1,2,..., 7 arbitrarily placed parallel beams of arbitrary doubly symmetric cross section of homogeneous, isotropic and linearly elastic material with modulus of elasticity and Poisson ratio which may have either internal or boundary point supports. For the sake of convenience the x axis is taken parallel to the beams. The stiffened plate is subjected to the lateral load g = g(x, r), x x,y, t>0. For the analysis of the aforementioned problem a global coordinate system Oxy for the analysis of the plate and local coordinate ones O x y corresponding to the centroid axes of each beam are employed as shown in Fig. 1. 

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