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The nodal line in a plate strip corresponds to several section knots with four degrees of freedom (u, v, w, θ) at each knot along the nodal line.
The deformation of the plate strip is classified as flexural (w, θ) and membrane (u, v) displacements based on Kirchhoff's thin plate theory and plane stress condition, respectively. For both flexural and membrane deformation, cubic splines are used for interpolating displacements in the longitudinal direction with different spline amendment schemes for end conditions. In the transverse direction of the plate, flexural displacements are interpolated using cubic Hermitian functions and membrane displacements using the Lagrangian interpolation function.
This and the next 2 images are FROM:
S.S. Ajeesh (1) and S. Arul Jayachandran (2)
(1) School of Civil Engineering, Vellore Institute of Technology, Vellore, India
(2) Department of Civil Engineering, Indian Institute of Technology, Madras, India
“Spline finite strip analysis of thin-walled flexural members subjected to general loading with intermediate restraints”, Thin-Walled Structures, Article 107171, Vol. 158, January 2021, https://doi.org/10.1016/j.tws.2020.107171
ABSTRACT: The design of cold-formed steel flexural members using the Direct Strength Method (DSM), use signature curves of cross-sections with the assumption of equal end moments and uniform stresses in the longitudinal direction. However, for beams subjected to general transverse loads, the assumption of longitudinal uniform stress is conservative. In calculating elastic critical loads of thin-walled flexural members, to incorporate a non-uniform variation of longitudinal stresses, this paper presents a spline finite strip computational procedure, which can also be used for beams with intermediate restraints. To the authors’ knowledge, such a procedure using spline finite strip is presented for the first time in the literature. The present formulation is comprehensive in its generality compared with similar works published. The membrane and shear stresses due to transverse loads on the beam are determined in the local direction of the plate at section knots of the spline strip. These stresses are incorporated in the geometric stiffness matrix, and buckling analysis is performed for calculating the elastic buckling load. Restraint matrices are incorporated in buckling analysis for the decomposition of buckling modes and for calculating mode participation. The proposed formulation is compared with generalized beam theory (GBT) for lipped channel cross-section with variation in span, general loading, and intermediate restraints. This method is demonstrated to be good for calculating elastic buckling stresses for the practical design of thin-walled flexural members.
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