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higher order shell theories and finite elements
Recently I faced few questions in a course that I am attending:
1) Outline the salient features of different higher order shell theories.
2)Explain why some shell theories are not suitable as the basis of element formulation.
3) Discuss any limitations of elements being used in relation to their underlying formulation ( e.g use of shallow shell theory or cylindrical shell theory).
For question 1, I am only aware of two theories applied to shell elements, the Kirchoff theory and the Mindlin theory . I am not aware of what is meant by "higher order shell theories". Can somebody throw some light on the same , including reference of ny text book where I can find information on the same?
For question 2, the books that I have read ( Cook, Malkus, Plesha and RH McNeal) do not have answer to this question, can somebody help ? References will be additional advantage.
Question 3: I could not comprehend this question properly. Kind help will be highly appreciated.