Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (2): 472-477.doi: 10.13229/j.cnki.jdxbgxb20191183

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First and second⁃order sensitivity method of structure static displacement

Kai MA1(),Bang-hui LI1,Kun YANG2(),Qiao-ling LIU1   

  1. 1.College of Mechanical and Aerospace Engineering，Jilin University，Changchun 130022，China
    2.Basic Education College of Aviation University of Air Force，Changchun 130022，China
  • Received:2019-12-24 Online:2021-03-01 Published:2021-02-09
  • Contact: Kun YANG E-mail:makai@jlu.edu.cn;Yangkuncust@163.com

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Abstract:

Based on Epsilon algorithm and improved Neumann series， an approximate method for calculating the first and second order sensitivity of structural static displacement is proposed. First， the Epsilon algorithm is combined with the improved Neumann series to form a new fast approximate calculation method of static displacement， and a fast approximate calculation method of the first-order sensitivity of static displacement is derived. Then， the second-order sensitivity approximate calculation method of static displacement is further derived by combining the difference method with the first-order sensitivity method. The sensitivity calculation results of truss model and beam model show the engineering application value of the two sensitivity methods.

Key words: improved Newman series, Epsilon algorithm, sensitivity analysis, structural reanalysis

CLC Number: 

  • O342

Fig.1

Epsilon algorithm calculation flow chart"

Fig.2

Results of ignoring of odd rows"

Fig.3

Planar truss structure"

Fig.4

First order sensitivity calculation results"

Fig.5

Second-order sensitivity calculation resoult"

Table 1

First-order displacement sensitivity(example 1)"

节点编号 及位移方向精确解近似解误差/%
1-x-1.5E-05-1.50E-050.00E+00
1-y-5.739E-05-5.74E-05-0.005 74
2-x07.74E-507.74E-48
2-y05.04E-365.04E-34
3-x0.000 114 7750.000 114 7770.011 478
3-y0.000 554 1930.000 554 1940.055 419
4-x-0.001 123 375-0.001 123 378-0.112 34
4-y0.000 683 9620.000 683 9610.068 396
5-x01.11E-481.11E-46
5-y0-5.04E-36-5E-34
6-x-1.5E-05-1.50E-05-0.001 5
6-y5.739E-055.74E-050.005 74

Table 2

Second-order displacement sensitivity(example 1)"

节点编号 及位移方向精确解近似解误差/%
1-x5.812 5E-095.79E-09-0.310 2
1-y2.218 12E-082.22E-080.011 0
2-x0-2.37E-530
2-y-1.946 9E-39-1.95E-390.003 4
3-x-4.434 4E-08-4.44E-080.053 3
3-y-2.141 9E-07-2.14E-070.014 44
4-x4.341 88E-074.34E-070.012 97
4-y-2.643 5E-07-2.64E-070.012 94
5-x0-6.60E-510
5-y1.946 88E-391.95E-390.003 37
6-x5.812 5E-095.79E-09-0.310 3
6-y-2.218 1E-08-2.22E-080.011 0

Fig.6

Hexagonal tower structure with a beam section radius of 5 mm"

Fig.7

First-order sensitivity calculation result"

Table 3

First-order displacement sensitivity(example 2)"

节点编号及位移方向精确解近似解误差/%
190-x0.065 30.065 278 871-0.032
191-x0.061 50.061 475 388-0.04
94-x0.057 70.057 671 711-0.049
3-x0.053 90.053 897 051-0.005 5
4-x0.050 20.050 211 74-0.023 4

Table 4

Second-order displacement sensitivity(example 2)"

节点编号及位移方向精确解近似解误差/%
190-x-0.026 35-0.026 5-0.502 8
191-x-0.024 8-0.024 90.563
94-x-0.023 3-0.023 40.415
3-x-0.021 8-0.021 90.300 7
4-x-0.020 3-0.020 40.348 3

Fig.8

Second-order sensitivity calculation result"

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