Mechanical Engineering Commons^™

Computational Methods For Nonlinear Systems Analysis With Applications In Mathematics And Engineering, Geoffrey Kenneth Rose

Mechanical & Aerospace Engineering Theses & Dissertations

An investigation into current methods and new approaches for solving systems of nonlinear equations was performed. Nontraditional methods for implementing arc-length type solvers were developed in search of a more robust capability for solving general systems of nonlinear algebraic equations. Processes for construction of parameterized curves representing the many possible solutions to systems of equations versus finding single or point solutions were established. A procedure based on these methods was then developed to identify static equilibrium states for solutions to multi-body-dynamic systems. This methodology provided for a pictorial of the overall solution to a given system, which demonstrated the possibility …