Static response analysis of structures with interval parameters using the second-order Taylor series expansion and the DCA for QB

2015 ◽  
Vol 31 (6) ◽  
pp. 845-854 ◽  
Author(s):  
Qi Li ◽  
Zhiping Qiu ◽  
Xudong Zhang
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Second Order ◽  
Response Analysis ◽  
Static Response ◽  
Interval Parameters

The second-order theory of conformal solutions

1957 ◽  
Vol 240 (1223) ◽  
pp. 561-580 ◽  
Keyword(s):  
Thermodynamic Properties ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Order Theory ◽  
Second Order ◽  
Intermolecular Potential ◽  
Cell Theory ◽  
Reference Solution ◽  
Random Mixing

This paper describes a theoretical contribution to the statistical thermodynamics of mixtures of spherical molecules. The second-order perturbation free energy of a conformal solution is obtained by a rigorous Taylor-series expansion of the configuration integral in powers of the differences between intermolecular energy and size parameters, about an ideal unperturbed reference solution. Unlike the first-order terms, those of the second order contain statistical functions of the reference solution which cannot, in general, be related to its thermodynamic properties. All but one of these functions are concerned with departures from a random molecular distribution, and have been called molecular fluctuation integrals ; the remaining function can be related exactly to thermodynamic properties for the Lennard-Jones form of the intermolecular potential. The expressions for the molecular fluctuation integrals implied by the full random mixing approximation and by the semi-random mixing approximation of the cell theory, are derived and compared with the correct expressions given by the cell theory. The role of the Taylor series expansion as a critique of solution theories is discussed.

Static Response Analysis of Uncertain Structures With Large-Scale Unknown-But-Bounded Parameters

2021 ◽  
Vol 13 (01) ◽  
pp. 2150004
Author(s):  
Tonghui Wei ◽  
Feng Li ◽  
Guangwei Meng ◽  
Wenjie Zuo
Keyword(s):  
Large Scale ◽  
Taylor Series Expansion ◽  
Upper And Lower Bounds ◽  
Response Analysis ◽  
Original Structure ◽  
Uncertain Parameters ◽  
Static Response ◽  
Interval Parameters ◽  
Structural Problems ◽  
Function Decomposition

This paper proposes an interval finite element method based on function decomposition for structural static response problems with large-scale unknown-but-bounded parameters. When there is a large number of uncertain parameters, it will lead to the curse of dimensionality. The existing Taylor expansion-based methods, which is often employed to deal with large-scale uncertainty problems, need the sensitivity information of response function to uncertain parameters. However, the gradient information may be difficult to obtain for some complicated structural problems. To overcome this drawback, univariate decomposition expression (UDE) and bivariate decomposition expression (BDE) are deduced by the higher-order Taylor series expansion. The original structure function with [Formula: see text]-dimensional interval parameters is decomposed into the sum of several low-dimensional response functions by UDE or BDE, each of which has only one or two interval parameters while the other interval parameters are replaced by their midpoint values. Therefore, solving the upper and lower bounds of the [Formula: see text]-dimensional function can be converted into solving those of the one- or two-dimensional functions, which savethe calculation costs and can be easily implemented. The accuracy and efficiency of the new method are verified by three numerical examples.

scholarly journals Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaowang Li ◽  
Zhongmin Deng
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Time History ◽  
Taylor Series Expansion ◽  
Second Order ◽  
New Method ◽  
Dynamic Loads ◽  
Discrete Equation ◽  
System Response ◽  
Structural Dynamic

A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white noise excitation are applied on a cantilever beam, respectively, to illustrate the effectiveness of this algorithm. One also makes a comparison between the new method and conventional state space method. The results show that the proposed method can obtain a more accurate identified force time history whether the responses are polluted by noise or not.

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