Static interaction of arbitrary shaped solid plate and transversely isotropic half-space

Increase in the number of newly constructed industrial structures and the importance of structural design of the foundations during the last decade has led researches to solve the contact problem of solid plate with infinite half-spaces. Assuming the half-space having engineering characteristics very similar to that of thetransversely isotropic materials, logically assures the solution to be more reliable. Furthermore, solving thiscontact problem for an arbitrary shaped solid plate gives the engineers the opportunity to choose the foundation’s shape from various types.In this research, after writing the equations of equilibrium in the polar coordinates for a transversely isotropic media, a method of potential functions accompanied with integral transforms is applied to derivedisplacement and stresses Green’s functions for a half-space. Then, the integrals indicating thedisplacement will be calculated in such a way that adaptive gradient elements to be applied for evaluation of the integrals for arbitrary shapes of rigid foundations. For the ease of calculations for the structural engineering purposes, the solution is derived for a unit radius circle. At the end, the displacements and stresses will be easily calculated and graphically shown. By comparison with the results reported in the literature for isotropic half-spaces, the validity and accuracy will be proved

Keywords:

Elasticity , Contact problem , Transversely isotropic , Arbitrary shaped solid plate