Energy-Based Analysis of Time-Dependent Deformations in Viscoelastic Truss Systems

Abstract

Truss systems are essential structural elements widely utilized for their lightweight design, high load-bearing capacity, and structural efficiency. This study introduces a novel energy-based method for analyzing time-dependent deformations in viscoelastic truss systems, applicable to both statically determinate and indeterminate configurations. The primary objective is to develop a total potential energy (TPE) functional that explicitly incorporates viscoelastic effects, system parameters, material properties, and loading conditions. Unlike conventional methods that treat viscous terms as non-conservative and lacking a clear energy representation, the proposed approach facilitates a direct and efficient energy-based formulation of the governing equations. The methodology employs the Laplace transform to simplify the problem and an inverse Laplace transform to recover solutions in the time domain. This systematic approach ensures accurate results while reducing computational effort, making it both time-efficient and straightforward to implement. A key advantage of the proposed method is its adaptability to various viscoelastic material models, such as the Kelvin-Voigt and Standard Linear Solid (SLS) models, and its applicability to diverse loading conditions, including step and impulsive loads. To validate the method, numerical analyses are conducted on truss systems subjected to different time-dependent loading scenarios. The results demonstrate the method's capability to accurately predict the time-dependent behavior of viscoelastic trusses, addressing a significant gap in the literature by providing benchmark solutions. The proposed framework offers a computationally efficient alternative for analyzing viscoelastic structures, facilitating their integration into practical structural design and improving the prediction of long-term deformation behavior. This study provides a reliable and innovative solution for analyzing viscoelastic truss systems, making it a valuable tool for engineers and researchers working with time-dependent materials in structural applications.