Response Limits for a Class of Nonlinear Systems

A system is called simple if its equilibrium configuration can be characterized by the extremum of a state function that is homogeneous in the state variables. A simple system is considered near a state of equilibrium, and it is shown that the properties of the passive system under proportional loading are expressible through a single parameter. It is further shown how accurate upper and lower bounds can be established for this parameter. The analysis is illustrated by an example (a hydraulic network). Other potential applications are found in analysis of structures of nonlinear materials such as concrete, grey iron, or aluminum, statically determinate and indeterminate.