Newly observed $\Lambda_c(2860)^+$ at LHCb and its \emph{D}-wave partners $\Lambda_c(2880)^+$, $\Xi_c(3055)^+$ and $\Xi_c(3080)^+$

New resonance Λc(2860)+, reported by the LHCb Collaboration, is a key to establish the D-wave charmed and charmed-strange baryon families. In this work, we first carry out an analysis of mass spectra of the λ-mode excited charmed and charmed-strange baryon states, which may reveal the relation of Λc(2860)+, Λc(2880)+, Ξc(3055)+, and Ξc(3080)+, i.e., Λc(2860)+ and Λc(2880)+ can form a D-wave doublet [3/2+,5/2+], while Ξc(3055)+ and Ξc(3080)+ are the strange partners of Λc(2860)+ and Λc(2880)+, respectively. Further study of their two-body Okubo-Zweig-Iizuka-allowed decays supports Λc(2860)+ and Ξc(3055)+ as the D-wave charmed and charmed-strange baryons, respectively, with JP=3/2+. For Λc(2880)+ and Ξc(3080)+, however, there exist some difficulties under the D-wave assignment with JP=5/2+, since the experimental widths, and some ratios of partial width of Λc(2880)+ and Ξc(3080)+, cannot be reproduced in our calculation.