I'm not aware of any algorithm for indicating ply angles and number of plies. That's
your job! Some FE optimizers can help you make these decisions more quickly but in the end it is the analyst's responsibility to make a final decision based on the margins of safety indicated by suitable failure criteria.
Some mechanical aspects of a design to check, for which there may be analytical tools available: max stress [y], max strain [y], dangerous deflections [y], composite quadratic failure criteria (e.g. Tsai-Wu) [y], interlaminar shear [y], Brazier radius through-thickness tension [y], plate and shell buckling (shear, compression, multi-axial loading) [y], column buckling [y], beam column failure, compression crippling, local skin instabilities for sandwich [y], stress concentration effects [y], effects of cracks, laminate coupling [y], fatigue damage [y], vibration and resonance, impact and birdstrike [y]... This is hardly a comprehensive list and many non-mechanical criteria also have to be taken into account (e.g. thermal). (A 'y' means I have seen something addressing analysis of the issue for composites, although some are so general (max stress, etc.) that they are covered in many publications and involve general analysis. And you can of course often adapt references written for isotropic materials for composites.)
Primes (e.g., Airbus, Boeing, Bombardier, Lockheed Martin, etc.) all have suitable stress manuals which have simplified methods which are very useful. These are of course copyright and not necessarily readily available, but you may find something online. NASA technical reports, technical memos, conference publications and contractor reports are free and very useful, with approaches to many of the issues I mention above. See
and
.
Usually you have many behaviors to check with criteria indicating unacceptable behavior and you must check them all. For tools to do so you could check textbooks (search Eng-Tips for 'reference' or 'text book') or websites such as
or
). Do let us know if find any others.