Optimal Time History Analysis of 2d Trusses Using Free-Scaled Wavelet Functions

This paper presents an improved approach where the wavelet functions are developed for particularly two-dimensional (2D) trusses. In the proposed scheme, a clear-cut formulation in a fluent manner has been derived to numerically solve the second-ordered differential equation of motion governing 2D trusses using two different types of basis functions including, complicated Chebyshev and simple Haar wavelet functions. For this aim, a simple step-by-step algorithm is implemented to calculate corresponding dynamic quantities of 2D trusses. In addition, validity and effectiveness of the proposed approach are demonstrated by one example, compared with some of the existent numerical integration methods such as family of Newmark-β, Wilson-θ and central difference method. Finally, it is shown that the time history analysis of 2D trusses is optimally achieved by lesser computational time and high accuracy of responses, using a long-time increment.