Monomial (single-termed power function) approximation more faithfully models the power function behavior of the structural system, while at the same time, becomes a linear form when transformed into log space. Thus, computational tools based on linear algebra remain useful and effective. Since the monomial approximation provides a much higher quality approximation to the nonlinear phenomena exhibited in structural applications, incremental and iterative methods become much more effective since the local approximation allows significantly larger steps to be taken. The net result is an increase in reliability of the solution process and a significant reduction in computational effort. The main goal of this research is to develop efficient and reliable methods for structural analysis and design based on this monomial approximation. The scope will include treatment of geometric nonlinearities in structures modeled by finite elements, including trusses, frames and continuation structures. A general load increment method based on the monomial approximation will be developed. The project will also consider material nonlinearities. The typical stress-strain relationship for a nonlinearly elastic material nonlinearities. The typical stress-strain relationship for a nonlinearly elastic material is remarkably monomial in shape. The monomial approximation will model this behavior very well and should produce a very effective analysis tool.
