Three-dimensional Green’s function and its derivatives for anisotropic elastic, piezoelectric and magnetoelectroelastic materials

This thesis mainly deals with the Green’s function for linear generally anisotropic materials in the infinite three-dimensional space, also called the fundamental solution. The detailed derivations and the numerical results of the explicit expressions of the Green’s function and its first and second derivatives based on the residue calculus method (RCM), Stroh formalism method (SFM) and unified explicit expression method (UEEM) are presented. The numerical examples of the three different methods are compared with each other for the anisotropic elasticity. All three methods are accurate for an arbitrary point in non-degenerate cases. For nearly degenerate cases, both the RCM and the SFM become unstable while the UEEM keeps accurate. Moreover, the SFM is more stable than the RCM. To overcome the difficulty in nearly degenerate cases and degenerate cases, some material constants are slightly changed in the RCM and the SFM. Although the UEEM has some advantages compared with the RCM and the SFM, it is difficult to be extended to the multifield coupled materials. The RCM and SFM are extended to the piezoelectric materials and compared with each other. Since the SFM has a better performance than the RCM for the piezoelectric materials, it is extended further to the magnetoelectroelastic materials. The UEEM is implemented into a Boundary Element Method (BEM) as an application. Some demonstrative anisotropic elastic problems are solved by the developed BEM.