Australian Journal of Basic and Applied Sciences, 8(19) Special 2014, Pages: 127-130 AENSI Journals Australian Journal of Basic and Applied Sciences ISSN:1991-8178 Journal home page: www.ajbasweb.com Corresponding Author: Seyed Hossein Mahdavi, University of Malaya, Department of Civil Engineering, Box.50603. Kuala Lumpur. Malaysia; Tel: 0060122977526; E-mail: s.h.mahdavii@gmail.com Optimal Time History Analysis of 2d Trusses Using Free-Scaled Wavelet Functions Seyed Hossein Mahdavi and Hashim Abdul Razak StrucHMRS Group, Department of Civil Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia ARTICLE INFO ABSTRACT Article history: Received 15 April 2014 Received in revised form 22 May 2014 Accepted 25 October 2014 Available online 10 November 2014 Keywords: Integration approach; Optimal structural dynamics; Wavelet function; 2D truss. 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. © 2014 AENSI Publisher All rights reserved. To Cite This Article: S.H.Mahdavi and H.A.Razak, Optimal Time History Analysis Of 2d Trusses Using Free-Scaled Wavelet Functions Title of paper. Aust. J. Basic & Appl. Sci., 8(19): 127-130, 2014 INTRODUCTION Numerical and step-by-step time integration methods are widely utilized in the computational analysis and evaluation of dynamic systems. Precise and efficient numerical integration schemes have been the focus of significant interest to solve Multi-Degrees-of-Freedom (MDOF) problems of structural dynamics. As a result, because of complexity of not only nonlinear but also large-scaled structures, time integration methods are only options to investigate about responses of the system. In general, there are two basic categories of time integration approaches. First, direct integration schemes whereby the quantities of the dynamic system are being calculated through a direct space vector in the step-by-step solution of the equation of motion. Second, indirect integration schemes involving all corresponding equations being numerically transformed into a new space vector, e.g. from the time domain to the frequency domain. Afterwards, step-by-step dynamic analysis is accordingly performed and fulfilled on the current space vector (Bathe, K.J., 1996). Theoretically, it has been perceived that direct methods are most applicable for structural dynamics, where the response is computed in set of short time increments through the accurate approximation of external excitations. Consequently, it requires high amounts of storage capacity to gain a proper time history analysis of large-scaled structures. What is more, responses calculated by direct algorithms are not numerically optimal over the wide range of natural frequencies i.e. large-scaled and 2D trusses (Chang, S.Y., 2010). Mathematically, researchers have proposed wavelet procedure to examine many types of differential equations. However, It has been observed that solution of time dependent equation is being constrained only in a unit time step (Yuanlu, L., 2010; Babolian, B., F. Fatahzadeh, 2010). Generally, wavelet functions are characterized into the two main categories. The first being 2D wavelet whereby a definite basis function of wavelet is being shifted for all scaled functions. The other category is three-dimensional (3D) wavelet involving used of an improved wavelet basis function being shifted on each new scale of the mother wavelet (Mahdavi, S.H. and H.A. Razak, 2013). In this paper, a straightforward and comprehensive formulation is improved for MDOF systems by representing the basis function of Haar and Chebyshev wavelet. Subsequently, to confirm validity of the analytical schemes in this study, case study involving a 2D Howe truss under an impact loading is presented and discussed. The characteristics of Haar wavelet and Chebyshev wavelet functions are cited to some relevant references (Yuanlu, L., 2010; Lepik, U., 2005).