A monomial‐based method for non‐linear structural analysis

The analysis of certain structures must be performed with due consideration to non‐linear behavior, such as material and geometric non‐linearities. The existing methods for treating non‐linear structural behavior generally make use of repeated linearization, such as load increment methods. This paper demonstrates that there is an alternative type of linearization that appears to have significant advantages when applied to the analysis of non‐linear structural systems. Briefly stated, this alternative linearization can be thought of as a “monomialization”. This monomial (single‐termed power function) approximation more faithfully models the power function behavior inherent in typical structural systems. Conveniently, it becomes a linear form when transformed into log space. Thus, computational tools based on linear algebra remain useful and effective. Preliminary results indicate that the monomial approximation provides a higher quality approximation to non‐linear phenomena exhibited in structural applications. Consequently, incremental and iterative methods become more effective because larger steps can be taken. The net result is an increase in reliability of the solution process and a significant reduction in computational effort. Two examples are presented to demonstrate the method.