Free-parameter perturbation-method solutions of the nonlinear stability of shallow spherical shells

2004 ◽  
Vol 25 (9) ◽  
pp. 963-970 ◽  
Author(s):  
Chen Shan-lin ◽  
Li Qi-zhong
Keyword(s):  
Perturbation Method ◽  
Nonlinear Stability ◽  
Free Parameter ◽  
Parameter Perturbation ◽  
Spherical Shells ◽  
Parameter Perturbation Method

scholarly journals Application of Multi-Parameter Perturbation Method to Functionally-Graded, Thin, Circular Piezoelectric Plates

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 342 ◽  
Author(s):  
Xiao-Ting He ◽  
Zhi-Xin Yang ◽  
Yang-Hui Li ◽  
Xue Li ◽  
Jun-Yi Sun
Keyword(s):  
Perturbation Method ◽  
Electrical Potential ◽  
Functionally Graded ◽  
Parameter Perturbation ◽  
Graded Materials ◽  
Cylindrical Coordinate ◽  
Stress Functions ◽  
Perturbation Parameters ◽  
Parameter Perturbation Method ◽  
Piezoelectric Plates

In this study, a multi-parameter perturbation method is used for the solution of a functionally-graded, thin, circular piezoelectric plate. First, by assuming that elastic, piezoelectric, and dielectric coefficients of the functionally-graded materials vary in the form of the same exponential function, the basic equation expressed in terms of two stress functions and one electrical potential function are established in cylindrical coordinate system. Three piezoelectric coefficients are selected as perturbation parameters, and the established equations are solved by the multi-parameter perturbation method, thus obtaining up to first-order perturbation solutions. The validity of the perturbation solution obtained is verified by numerical simulations, based on layer-wise theory. The perturbation process indicates that adopting three piezoelectric coefficients as perturbation parameters follows the basic idea of perturbation theory—i.e., if the piezoelectricity may be regarded as a kind of introduced disturbance, the zero-order solution of the disturbance system corresponds exactly to the solution of functionally-graded plates without piezoelectricity. The result also indicates that the deformation magnitude of piezoelectric plates is smaller than that of plates without piezoelectricity, due to the well-known piezoelectric stiffening effect.

Interval Back Analysis on Mechanical Parameter of Geotechnical Engineering

2012 ◽  
Vol 170-173 ◽  
pp. 399-402
Author(s):  
Shi Jun Liu ◽  
Hong Chun Wang
Keyword(s):  
Perturbation Method ◽  
Back Analysis ◽  
Measured Data ◽  
Mechanical Parameter ◽  
Electric Power Station ◽  
Mechanical Parameters ◽  
Interval Parameter ◽  
Analysis Model ◽  
Parameter Perturbation ◽  
Parameter Perturbation Method

The measured data and mechanical parameters were considered unknown but bounded property and interval numbers were used to denote the measured data and mechanical parameters. The interval parameter perturbation method was presented to solve interval FEM and the interval inverse analysis model was established. Based on the interval parameter perturbation method, the mean and deviation of the mechanical parameters were obtained by the back analysis. For the example of the mechanical parameter back analysis of rock mass cave in the large hydro-electric power station, the effect on the measured data precision was studied. From the results it can be found that the method is reasonable and feasible.

An Interval Parameter Perturbation Method for Predicting the Natural Frequency Bounds of Intelligent Truss Structures with Uncertain-But-Bounded Parameters

2007 ◽  
Vol 347 ◽  
pp. 569-574
Author(s):  
Wen Ying Chen ◽  
Fu Lei Chu ◽  
Shao Ze Yan ◽  
Ke Yun Wang
Keyword(s):  
Lower Bound ◽  
Perturbation Method ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Truss Structure ◽  
Truss Structures ◽  
Interval Parameter ◽  
Parameter Perturbation ◽  
Interval Extension ◽  
Parameter Perturbation Method

The upper and lower bound estimation of natural frequencies for intelligent truss structure with uncertain-but-bounded parameters is studied in this paper. Firstly, following the finite element method, the expressions of the interval stiffness and interval mass matrix of piezoelectric intelligent truss structures are derived directly from the interval parameters. Then, based on the matrix perturbation and interval extension theory, an interval parameter perturbation method is proposed for solving the upper and lower bound of natural frequencies. Finally, a 16-bar planar intelligent truss structure is used as an example to illustrate the applicability and validity of the presented method, and some useful conclusions are obtained.

Fast Frechet derivative calculation using an auxiliary source array method: An application to array resistivity measurements

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1364-1371
Author(s):  
Tsili Wang ◽  
Alberto Mezzatesta
Keyword(s):  
Perturbation Method ◽  
Potential Difference ◽  
Parameter Perturbation ◽  
Resistivity Measurements ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Derivatives Of ◽  
Parameter Perturbation Method ◽  
Source Array ◽  
Auxiliary Source

Frechet derivatives provide the vital information for parametric resistivity inversion, but the calculation for a multidimensional problem is often computer intensive. This paper presents a new technique for fast calculation of the Frechet derivatives of resistivity measurements with respect to formation resistivity properties. The technique, referred to as the auxiliary source array method (ASAM), generalizes the reciprocity principle‐based methods in that for closely spaced receivers it may not be necessary to place a fictitious source at each receiver location. Rather, an auxiliary source array comprised of sparsely spaced fictitious sources can be constructed from which the field for any fictitious source location can be reconstructed. The ASAM was tested with a deviated‐well resistivity model for an array resistivity device that acquires 8 potential, 16 first potential difference, and 14 second potential difference data points at each depth level. The Frechet derivatives calculated by the ASAM agree well with those obtained through the parameter perturbation method. The tests showed that the calculation time of the ASAM has little dependence on the number of parameters for which the Frechet derivatives are to be calculated. The method can calculate the Frechet derivatives of 5 to 138 resistivity parameters with only 20% to 50% additional computer time. For the 138‐parameter model, the ASAM is about two orders of magnitude faster than the parameter perturbation method.

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