Analysis of imperfect column buckling under intermediate velocity impact

In this paper, three-dimensional Greenʹs functions for anisotropic bimaterials are studied based on Stroh formalism and two-dimensional Fourier transforms. Although the Greenʹs functions can be expressed exactly in the Fourier transform domain, it is dicult to obtain the explicit expressions of the Greenʹs functions in the physical domain due to the general anisotropy of the material and a geometry plane involved. Utilizing Fourier inverse transform in the polar coordinate and combining with Mindlinʹs superposition method, the physical-domain bimaterial Greenʹs functions are derived as a sum of a full-space Greenʹs function and a complementary part. While the full-space Greenʹs function is in an explicit form, the complementary part is expressed in terms of simple regular line-integrals over [0, 2pŠ that are suitable for standard numerical integration. Furthermore, the present bimaterial Greenʹs functions can be reduced to the special cases such as half-space, surface, interfacial, and full-space Greenʹs functions. Numerical examples are given for both half-space and bimaterial cases with isotropic, transversely isotropic, and anisotropic material properties to verify the applicability of the technique. For the half-space case with isotropic or transversely isotropic material properties, the Greenʹs function solutions are in excellent agreement with the existing analytical solutions. For anisotropic half-space and bimaterial cases, numerical results show the strong dependence of the Greenʹs functions on the material properties