Premium
Derivation of general algebraic constraint conditions for ‘weak’ C 1 continuity for thin shells
Author(s) -
Mang Herbert A.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620111009
Subject(s) - constraint (computer aided design) , a priori and a posteriori , mathematics , algebraic equation , element (criminal law) , algebraic number , metric (unit) , system of linear equations , shell (structure) , independence (probability theory) , algebraic operation , mathematical analysis , geometry , nonlinear system , physics , engineering , statistics , quantum mechanics , political science , law , philosophy , operations management , epistemology , civil engineering
Employing C 0 conforming thin shell elements, a derivation of general algebraic equations for enforcing C 1 interelement continuity in a ‘weak’ (that is, integral) sense is presented. ‘Restoration’ of strict C 1 continuity is treated as a special case of the proposed concept. The cónstraint equations do not depend on the metric of the given shell. While, for smooth shells, this is automatically the case, if strict C 1 continuity is ‘restored’, the constraint equations usually depend on the metric of the shell, if only ‘weak’ C 1 continuity is enforced. The independence of the proposed constraint equations of the metric of the shell facilitates the computer implementation of the proposed approach. It is demonstrated that linear dependencies among the constraint equations can easily be detected and a priori be eliminated. It is also shown that, in certain cases, it is very easy to switch from an (intrinsically) element‐interface‐oriented concept to an element‐oriented technique of generating constraint equations with the help of the digital computer. The latter mode offers computational advantages, if an element‐oriented mode of solving the global system of algebraic equations (equilibrium and constraint equations), such as Irons' wave front technique, is adopted.