See the files in http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/shell_solid_interface.tar .

The cantilever models therein illustrate several alternatives for
constraining shells to solids.

The *constrained_shell_to_solid approach maintains rotational continuity.
LS-PrePost has a tool for creating the necessary 
keyword data; see  Model > CreEnt > Cre > Constrained > Shell2Solid.
Final displacement = 18.84.                                                                                                         

The *constrained_nodal_rigid_body approach is pretty
straightforward with the drawback that section thinning cannot be simulated
(not important in simulating bending modes).  Final displacement = 18.86.
                                                                                                         
An unacceptable method is *constrained_tied_shell_edge_to_SURFACE.  
The main problem here is that solids do not have rotational DOF and so the 
tied contact cannot enforce rotational continuity.

*Contact_tied_shell_edge_to_SOLID (tiedse2solid_alt.key) and
*contact_tied_shell_edge_to_SOLID_constrained_offset (tiedse2solid_alt.key) 
illustate two EDGE_TO_SOLID approaches, with the latter giving a much more 
accurate solution.  The difference is especially seen in the x-stress distribution 
through the thickness of the solid part at the shell/solid interface.
Note in the preferred "alt" approach, the solid part is slave and the shell part is master.
For another example of these two EDGE_TO_SOLID approaches, 
see http://ftp.lstc.com/anonymous/outgoing/support/EXAMPLES/contact_tied_shell_edge_solid.k 
and http://ftp.lstc.com/anonymous/outgoing/support/EXAMPLES/contact_tied_shell_edge_solid_alt.k .
and the comments therein concerning *contact_tied_shell_edge_to_solid.

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Constrained_interpolation is not recommended for transitioning from
solids to shells.

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Another approach to maintain the rotational continuity would be to add extra shell element(s).
Such a method is not wholly realistic since nonphysical mass and stiffness are being added
along with the added shells.  

a)  Embed at least 1 row of shells into the solid mesh like a ruler jammed into a potato.  
You can either share nodes between the solids and embedded shells or else use 
*constrained_lagrange_in_solid (embedded shells = slave, solids = master, CTYPE=2).  
The *constrained_lagrange_in_solid approach is illustrated in 
http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/model005-r3-1.zip .

b) Coat the solid surface with added shells that share nodes with the solids.   
Then use *contact_tied_shell_edge_to_surface to tie the shell edge to the added shell surface.

Note: Null shells (*MAT_NULL) will NOT work in a) and b) above. Null shells have no stiffness. 

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Perhaps the best option is to replace your shells with tshells.
The tshells can share nodes directly with the solids, or if you want to change 
the mesh refinement at the solid/tshell juncture, *contact_tied_surface_to_surface would work.