Tremendous advances in nanoscience during the past decades have drawn a new horizon for the future of science. Many biological and structural elements such as DNA, bio-membranes, nanotubes, nanowires and thin films have been studied carefully in the past decades. In this work we target to speed up the computational methods by incorporating the structural symmetries that nanostructures have. In particular, we use the Objective Structures (OS) framework to speed up molecular dynamics (MD), lattice dynamics (phonon analysis) and multiscale methods. OS framework is a generalization of the standard idea for crystal lattices of assuming periodicity of atomic positions with a large supercell. OS not only considers the translational periodicity of the structure, but also other symmetries such as rotational and screw symmetries. In addition to the computational efficiency afforded by Objective Structures, OS provides us with more flexibility in the shape of the unit cell and the form of the external deformation and loading, comparing to using the translational periodicity. This is because the deformation and loading should be consistent in all cells and not all deformations keep the periodicity of the structures. For instance, bending and twisting cannot be modeled with methods using the structure's periodicity. Using OS framework we then carefully studied carbon nanotubes under non-equilibrium deformations. We also studied the failure mechanism of pristine and twisted nanotubes under tensile loading. We found a range of failure mechanisms, including the formation of Stone-Wales defects, the opening of voids, and the motion of atoms out of the cross-section. We also used the OS framework to make concrete analogies between crystalline phonons and normal modes of vibration in non-crystalline but highly symmetric nanostructures.