Matrix analysis of nonlinear trusses using Prandtl-2 Neural Networks

A new method, based on the concepts of matrix analysis as well as the learning capabilities of neural networks, for the analysis of nonlinear trusses under dynamic loading is presented. The method can be applied to static trusses too. While there have been attempts in the past to use neural networks to identify and model different structures based on data measured on structural response directly, the main feature and advantage of this new method is in its capability to model a nonlinear truss by assembling the data collected on the response of its members. The basics of the method are: (1) for each truss member, a neural network is trained to learn and simulate its load–response behavior, (2) the member neural networks are then assembled to build another neural network which can simulate the load–response behavior of the whole truss. Noticing test at member level is generally easier than at structure level, this can make the building of a neural network to simulate the response of the truss more affordable. Also this has potential application when it is hard to find a mathematical model from experimental data to describe the internal force vector for a truss, as well as identification and control of trusses where precise modeling of the structure is a key point to the success of the application. Prandtl Neural Network, developed recently by the authors for modeling of nonlinear hysteretic materials, has been improved and used in this study too. The improved version has been called Prandtl-2 Neural Network (PNN2) in this paper. The method has been applied to the static and dynamic analysis of a 3-bar and a 10-bar benchmark truss successfully, the results of which are reported in this paper.