Controlling nodal displacement of pantographic structures using matrix condensation and interior-point optimization: A numerical and experimental study

Abstract

This study presents an innovative approach for the precise control of nodal displacements in pantographic structures. The method is founded on the Matrix Condensation of Force Method, seamlessly integrated with an Interior Point Optimization algorithm. This combination offers a unique advantage by allowing users to manipulate displaced nodes within a defined coordination domain. Furthermore, this approach introduces the Interior Point Optimization algorithm as an indispensable tool to eliminate inactive turnbuckles and minimize overall actuation requirements. Traditional control methods typically demand a substantial number of turnbuckles and extensive actuation efforts to attain the desired nodal coordinates. The interconnected nature of node movements, wherein changes in one node affect others, adds complexity to determining the impact of bar length alterations on each node. To address this challenge, precisely control power of the Interior Point Optimization algorithm systematically explores numerous scenarios to identify solutions that minimize both actuation and turnbuckle usage. The current technique's effectiveness is validated through rigorous comparisons with established methods, experimental modeling, and rigorous testing using SAP 2000 software. Notably, the current approach yields remarkable results, requiring a staggering 60% less actuation and reducing the reliance on turnbuckles by up to 40% compared to previous methods. This innovation promises to significantly enhance the efficiency and cost-effectiveness of controlling pantographic structures, marking a substantial advancement in this field.