Fission-Fusion Adaptivity in Finite Elements for Nonlinear Dynamics of Shells
Final technical rept. 1 Oct 1987-30 Aug 1990,
NORTHWESTERN UNIV EVANSTON IL DEPT OF CIVIL ENGINEERING
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The objective of this work was to develop adaptive finite element analysis methods for nonlinear structural dynamics. Adaptive methods are particularly promising for nonlinear problems involving failure, because in failure and near-failure states of structures, three predominant phenomena are buckling, shear banding, and fracture. These phenomena are associated with localization of the deformation, by which is meant the development of large strains in small regions of the structure, which is accompanied by large gradients in the strain. While strains are distributed in elastic buckling, once plasticity develops a large part of the deformation of beams or shells usually occurs over narrow zone called hingelines. Shear banding is a result of strain softening material behavior and is also associated with narrow bands of highly strained material. In fracture, high strain gradients occur at the crack tip, and in addition the displacement field is discontinuous behind the crack tip. In this work, adaptive methods are developed for the nonlinear dynamics of shells with both geometric and material nonlinearities. The localization phenomenon which is of primary interest in this class of problems is hingeline formation, but aspects of this work should be applicable to other localization phenomena in structural dynamics.
- Structural Engineering and Building Technology