Solving fuzzy static structural problems using symmetric group method. (English) Zbl 1458.74144
Chakraverty, Snehashish (ed.) et al., Recent advances in applications of computational and fuzzy mathematics. Singapore: Springer. 95-107 (2018).
Summary: In general, static problems of structures follow ordinary differential equations. Usual models of these problems include the parameters in the differential equation as exact or crisp. However, in actual practice these parameters may not be crisp but maybe with some uncertainty, viz. in term of fuzzy. As such our goal is here to solve the static problems that are encountered in civil, mechanical, and aerospace structures with fuzzy parameters which convert the problem into fuzzy differential equations. These equations are often nonlinear too and solving them requires efficient and suitable methods. As regards, the properties of symmetries provide a unique tool for solving such crisp differential equations. Till date no work is available to use this method in solving fuzzy differential equations in particular to structural problems. Accordingly, the target of this chapter will be to use symmetry to solve fuzzy differential equations. Simple example of civil, mechanical, and aerospace structures
has been solved for showing the powerfulness and reliability of the method. The obtained solutions are compared with crisp solutions in special cases.
For the entire collection see [Zbl 1408.93002].
For the entire collection see [Zbl 1408.93002].
MSC:
| 74S99 | Numerical and other methods in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
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