Enhanced Solution Scheme for Nonlinear Analysis of Force-Based Beam for Large Rotations, Multiple Critical Points, and Random Quasi-Static Loading Input

Abstract

AbstractThis paper attempts to enhance (1) the flexibility-corotational beam formulation for simulating highly geometrically nonlinear problems, and (2) the arc length method of integration to develop a robust and economical solution scheme for random quasi-static loading input. The existing flexibility-corotational formulation of a three dimensional beam is improved by (1) updating the rotation matrices by using the quaternions, and (2) proposing novel methods for tracking the displacement compatibility. Further, the cylindrical arc length method is modified by (1) introducing capabilities for handling random quasi-static loading, and (2) proposing automatic adjustment of the arc length. By using these developments several classical geometric nonlinearity problems are solved and path independency for buckling and postbuckling path with the random quasi-static loading is verified. The proposed variation in the arc length solution scheme is also shown to be better than the implementation of the arc length ...