DIMENSIONAL REDUCTION FOR THE BEAM IN ELASTICITY ON AN UNBOUNDED DOMAIN

1999 ◽  
Vol 09 (03) ◽  
pp. 415-444 ◽  
Author(s):  
KANG-MAN LIU
Keyword(s):  
Hilbert Space ◽  
Unbounded Domain ◽  
Dimensional Reduction ◽  
Fourier Transformation ◽  
Reduction Method ◽  
Rates Of Convergence ◽  
Reduction Technique ◽  
Systems Of Equations ◽  
Basic Tool ◽  
Dimensional Reduction Method

The dimensional reduction method is investigated for solving boundary value problems of the beam in elasticity on domain Ωd:=ℝ×(-d,d) by replacing the problems with systems of equations in ℝ. The basic tool to analyze the dimensional reduction technique for problems in an unbounded domain Ωd is using of Fourier transformation. The error estimates between the exact solution and the dimensionally reduced solution in a Hilbert space are obtained when d and N are given. The rates of convergence depend on the smoothness of the data on the faces.

Dimensional Reduction for Helmholtz's Equation on an Unbounded Domain

1997 ◽  
Vol 07 (01) ◽  
pp. 81-111 ◽  
Author(s):  
Kang-Man Liu
Keyword(s):  
Hilbert Space ◽  
Unbounded Domain ◽  
Dimensional Reduction ◽  
Fourier Transformation ◽  
Reduction Method ◽  
Rates Of Convergence ◽  
Reduction Technique ◽  
Systems Of Equations ◽  
Basic Tool ◽  
Dimensional Reduction Method

The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain Ωd := ℝn × (-d,d) by replacing them with systems of equations in ℝn are investigated. Basic tool to analyze dimensional reduction technique for problems on an unbounded domain Ωd is the use of Fourier transformation. The error estimates between the exact solution and the dimensionally reduced solution in some Hilbert space are obtained when d and N are given. The rates of convergence depend on the smoothness of the data on the faces.

Computationally Efficient Reliability Analysis of Mechanisms Based on a Multiplicative Dimensional Reduction Method

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Xufang Zhang ◽  
Mahesh D. Pandey ◽  
Yimin Zhang
Keyword(s):  
Reliability Analysis ◽  
Dimensional Reduction ◽  
System Reliability ◽  
Reduction Method ◽  
Maximum Output ◽  
Computationally Efficient ◽  
Output Error ◽  
System Reliability Analysis ◽  
Dimensional Reduction Method ◽  
Fractional Moments

The paper presents a computationally efficient method for system reliability analysis of mechanisms. The reliability is defined as the probability that the output error remains within a specified limit in the entire target trajectory of the mechanism. This mechanism reliability problem is formulated as a series system reliability analysis that can be solved using the distribution of maximum output error. The extreme event distribution is derived using the principle maximum entropy (MaxEnt) along with the constraints specified in terms of fractional moments. To optimize the computation of fractional moments of a multivariate response function, a multiplicative form of dimensional reduction method (M-DRM) is developed. The main benefit of the proposed approach is that it provides full probability distribution of the maximal output error from a very few evaluations of the trajectory of mechanism. The proposed method is illustrated by analyzing the system reliability analysis of two planar mechanisms. Examples presented in the paper show that the results of the proposed method are fairly accurate as compared with the benchmark results obtained from the Monte Carlo simulations.

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