... finite element analysis Monte Carlo methods nanoindentation porosity Young's modulus In clinical practice, the prediction of bone fracture is commonly based on osteodensitometry quantified by bone mineral density (BMD), which is measured macroscopically and can be imprecise [( 1 2...

... 2007 19 09 2009 22 01 2010 22 01 2010 Monte Carlo methods oscillators stochastic processes white noise nonlinear oscillator generalized FPK equation probability density function Poisson white noise Poisson white noise represents a discrete excitation process...

... ) ‖ and describes the almost-sure or sample stability of the system. When the largest Lyapunov exponent λ is negative, system 1 is asymptotically stable with probability 1. diffusion linear differential equations Lyapunov methods Monte Carlo methods numerical analysis stability stochastic...

.... , 1998 , “ Stochastic Linearization: The Theory ,” J. Appl. Probab. 0021-9002 10.1239/jap/1032265219 , 35 ( 3 ), pp. 718 – 730 . Rubinstein , R. Y. , 1981 , Simulation and the Monte Carlo Method , Wiley , New York . Yazici , A. , Atlas , I. , and Ergenc , T. , 2005...

.... 09 09 2004 25 01 2006 turbines blades beams (structures) vibrations crack detection finite difference methods Young's modulus Monte Carlo methods manufacturing processes Effective failure detection requires a good understanding of the characteristics of the monitored...

... after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 03 January 2004 17 September 2004 15 03 2005 Monte Carlo methods Lyapunov methods stochastic systems white noise stability Stochastic differential equations are encountered...

..., a greatly simplified model is obtained. 17 October 2002 19 September 2003 22 06 2004 damping elastic hysteresis Monte Carlo methods nonlinear differential equations In the past few decades, various phenomenological models of hysteresis have been proposed. One of the most...

... integrations and the spectral processing required by the Monte Carlo method. Similar results have been obtained for the response variable x 2 t ; they are not shown here for brevity. 3 Spectrum of the response x 1 by using the wavelet method 4 Spectrum...

... of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS . 30 Nov 2001 20 Aug 2002 11 06 2003 Monte Carlo methods elasticity finite element analysis digital simulation boundary-elements methods The commonly used numerical methods in physics and engineering can...