The wavelet-based theory of spatial naturally curved and twisted linear beams

Abstract

The paper presents the wavelet-based discretization of the linearized finite-strain beam theory which assumes small displacements, rotations and strains but is capable of considering an arbitrary initial geometry and material behaviour. In the numerical solution algorithm, we base our derivations on the vector of strain measures as the only unknown functions in a finite element. In such a way the determination of the beam quantities does not require the differentiation. This is an important advantage which allows a wider range of shape functions. In the present paper, the classical polynomial interpolation is compared to scaling and wavelet function interpolations. The computational efficiency of the method is demonstrated by analyzing initially curved and twisted beams