Two questions often crop up about turtle shells:

1. Is the shell created by the endoskeleton (ribs, verts) or an exoskeleton (dermal ossicles)? Or both?
2. Why do the ribs on the inside of the carapace (ventral view) appear to arise not from the midpoint of each centra, but from the joints between vertebrae (Fig. 1)?

Figure 1. Softshell turtle carapace in dorsal, ventral and median elements in lateral views. In dorsal view, the ribs match up to the the vertebrae, but in ventral view the middle ribs line up with vertebral joints for added strength.

Here’s the situation in graphic form (Fig. 1)
A dorsal/ventral view of the soft-shell turtle shell demonstrates the problem. Note the shifting of the ribs in ventral view so that they appear to arise from the joints between the vertebrae! Very odd, at first glance…

Figure 2. Some parts of the soft-shell turtle plastron have their origins in the interclavicle and clavicle of other tetrapods. Other parts are not modified gastralia because outgroups do not have gastralia.

Hirasaw et al. 2013
cleared up the issue when they reported, “For the past 200 years, the origin of the turtle carapace has remained unclear, and several different hypotheses about incorporation of the exoskeletal components into the costal and neural plates. 

“One hypothesis assumes that costo-neural elements contain both the endo- and exoskeletal materials—in particular, dermal elements called the osteoderm. For shell acquisition, the osteoderms of the ancestral animal was thus thought to have fused with the axial skeletal elements (ribs and vertebrae) underneath.”

“The second hypothesis assumes the endoskeletal origin of the costo-neural carapace, maintaining that the costal and neural plates were simply acquired by modification of the axial skeleton and, therefore, that the major parts of the carapace were formed solely from the endoskeleton.”

“Lastly, in the third hypothesis, superficially translocated endoskeletal elements were thought to induce heterotopically exoskeletal osteogenesis of the carapace. Recent observations of the embryonic turtle suggest that heterotopic shifts of the ribs occur during development: rib primordia translocated into the dermis induce membranous ossification to differentiate flanges on the craniocaudal aspects of the rib shafts and thus complete the costal plate. The superficial shift of the ribs, initially arising endochondrally, is thought to cause a new tissue interaction in the new location (that is, the dermis).

“Here through a comparative developmental analysis, we demonstrate that the costal and neural plates are assigned to be hypertrophied ribs and vertebrae, respectively. These results indicate that the major part of the turtle carapace evolved solely by modification of the endoskeleton (that is, second hypothesis).”

In short:
turtle ribs rise into the dermis where they induce further ossification.

Turtles are weird in many ways. 
They also incorporate the interclavicle and clavicle into the plastron (Fig. 2), the bones of which are not homologous with gastralia. No sister taxa (pareiasaurs) have gastralia. When you discount the former interclavicle and clavicle, there are only three remaining paired elements in the primitive bony plastron. Overlying scales mask what happens underneath among the traditional and novel bones (Fig. 3).

Figure 3. Turtle carapace and plastron bones and scales

Turtle dorsal vertebrae
are distinctive in having a flat top, with no trace of a neural spine. Where else in the reptile tree do you find such a vertebra?  You don’t find a flat-top dorsal vertebra on the proximal outgroups to turtles, Sclerosaurus (soft-flat- shells) and Bunostegos (hard-domed-shells), but as pareiasaurs these taxa had small ossicles surrounding the neural spines, which could have fused together to create the flat-tip verts. Curiously, the basalmost pareiasaur (almost a diadectid) Stephanospondylus has a flat-top dorsal vertebra (Fig. 4), but its phylogenetic distance from turtles indicates convergence, not homology.

Figure 4. Stephanospondylus has a flat-top dorsal vertebrae convergent with turtles.

References
Hirasawa T, Nagashima H & Kuratani S 2013. The endoskeletal origin of the turtle carapace. Nature Communications 4:2107. online