Geodesic
The finite element method use for large displacements calculations of plane linear-elastic structures
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 5 (2011), pp. 83-91

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A proposed version of the finite element method can find large displacements of a plane linearelastic structure with given nodal loads, and conversely, nodal loads at the given displacements. A calculation model includes geometrical, static and physical relations (Hooke's law). The calculation showed that several different deformed positions of the structure may correspond to the same loads. To verify the proposed model, the pure bending of a beam was calculated with large displacements taken into account. Analysis of the results showed the adequacy of the proposed model. At that the results differ markedly from the ANSYS solution.
Keywords: geometric nonlinearity, large displacements, finite deformations, pure bending, plane stress-strain state. 
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     author = {A. O. Scherbakova},
     title = {The finite element method use for large displacements calculations of plane linear-elastic structures},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {83--91},
     publisher = {mathdoc},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2011_5_a11/}
}
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A. O. Scherbakova. The finite element method use for large displacements calculations of plane linear-elastic structures. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 5 (2011), pp. 83-91. http://geodesic.mathdoc.fr/item/VYURM_2011_5_a11/