Finite Element Formulation [chapter]

2008 Finite Element Analysis of Antennas and Arrays  
An incremental and piecewise linear finite element theory is developed for the large displacement, large strain regime with particular reference to elastic-plastic behavior in metals. The resulting equations, though more complex, are in a similar form to those previously developed for large displacement, small strain problems, the only additional term being an initial load stiffness matrix which is dependent on current loads. This similarity in form means that existing nonlinear general purpose
more » ... ear general purpose programs may easily be extended to include finite strains. A large displacement, small strain formulation (as applicable to problems of structural stability) is obtained from this theory by assuming that changes in length of line elements and relative rotation of orthogonal line elements arc negligible compared to unity. The simplified equations are in essential agreement with previous formulations in the literature. The only difference which is observed is the persistence of the initial load stiffness matrix, which may be significant in some cases.
doi:10.1002/9780470409732.ch2 fatcat:ftzv744d5fb5tjoq327uxkur54