Measurements of cosmic rays by experiments such as ATIC, CREAM and PAMELA indicate a hardening of the cosmic ray energy spectrum at TeV energies. In our recent work, we showed that the hardening can be due to the effect of nearby supernova remnants. We showed it for the case of protons and helium nuclei. In this paper, we present an improved and more detailed version of our previous work, and extend our study to heavier cosmic ray species such as boron, carbon, oxygen and iron nuclei. Unlike our previous study, the present work involves a detailed calculation of the background cosmic rays and follows a consistent treatment of cosmic ray source parameters between the background and the nearby components. Moreover, we also present a detailed comparison of our results on the secondary-to-primary ratios, secondary spectra and the diffuse gamma-ray spectrum with the results expected from other existing models, which can be checked by future measurements at high energies.