A time-domain spectral element method with C1 continuity for static and dynamic analysis of frame structures

This paper presents a new C-1-type beam spectral element method, which aims to ensure the continuity of the deflection and its first derivative at the junction of the adjacent spectral elements. The proposed method is based on the Euler-Bernoulli beam theory. The main novelty of the method is that two different sets of interpolation functions are adopted for the axial displacement and deflection in order to meet the C-1 continuous requirement. By removing the rotational degrees of freedom of the internal nodes, a lumped mass matrix can be formed in this spectral element method. Static and dynamic analysis of various beams and frame structures are performed to examine the validity of the proposed spectral beam element model. The numerical results show that the proposed method is accurate and effective. A single element for each component of the structure is able to provide good results.