Just jumped on here to confirm that I'm having the same issue. I'm on a completely fresh Ubuntu 18.04 virtual machine and got the libssl.so.1.0.2 not found error. I double-checked and made sure that I had installed the rstudio-server-stretch-1.1.447-amd64.deb package for Ubuntu 17+.
Then, out of curiosity, I uninstalled the broken Ubuntu 17+ package and installed the Ubuntu 16 rstudio-server-1.1.447-amd64.deb one. This worked out-of-the-box and I now have RStudio Server running on port 8787 with no additional configuration.
To summarize: for me, the "correct" Ubuntu 17+ package didn't work, but the old Ubuntu 16 package did.