1 Numerical Methods in Continuum Mechanics 2000, Liptovsky Ján, Slovak Republic Symbolic c.pdfVIP

Numerical Methods in Continuum Mechanics 2000, Liptovsky Ján, Slovak Republic1 Symbolic computations for random fields using second order perturbation method Marcin Kaminski Department of Civil Engineering, George Brown School of Engineering Rice University, 6100 Main Street, Houston, 77005-1892 TX, USA e-mail: kaminski@ruf.rice.edu Division of Mechanics of Materials, Technical University of Lodz Al. Politechniki 6, 93-590 Lodz, POLAND e-mail: marcin@kmm-lx.p.lodz.pl Abstract The main idea is to show the application of symbolic computations in analysis of engineering systems with random parameters. The general computational methodology is based on the stochastic second order perturbation method and its implementation in the mathematical package MAPLE 6. The entire approach is displayed on the example of simple single degree of freedom dynamical system with random spring stiffness. The results of symbolic computations are derived numerically in the form of probabilistic moments of the structural response computed for the whole analysis time domain. The general methodology can be applied to all these engineering problems where the response can be derived symbolically in deterministic case, while input parameters of the system are random variables, fields or processes characterized by the probability density function (PDF) of any type. 1 Introduction Symbolic computations became recently more popular in numerical methods in engineering what is observed thanks to the enormous progress in the mathematical software developed in this area and, on the other hand, results from the limitation of accuracy of widely used discrete numerical methods (Finite, Boundary Element Methods, Finite Difference Method or meshless approaches worked out last years). Instantaneous progress in numerical error analysis, visualization techniques as well as general software and hardware development made renaissance of classical mathematical methods in a new, pure computational symbolical language