Development of a direct time integration method based on Bezier curve and 5th-order Bernstein basis function

- Proposing an implicit unconditionally stable time integration method.
- Using 5th-order Bernstein basis function.
- Good accuracy compared to the methods in the literature.
- Lower numerical amplitude dissipation and period dispersion can be achieved.

In this study, a robust unconditionally stable method for linear analysis of structures based on Bezier curves and Bernstein polynomials is proposed. The Bezier curve is used as interpolation function and Bernstein basis functions are applied for interpolation. The spectral radius, period elongation and amplitude decay are investigated for stability analysis, numerical dispersion and dissipation of proposed method, and results are compared with other methods that are the best in these properties. It is also shown that the behavior of the proposed method in analysis of finite element system is effective and reliable. To show the robustness and features of proposed method, a challenging problem with a very stiff and flexible response, a Howe truss under impact load, a frame under harmonic loading and a rectangular domain in plane strain condition are considered, and derived results are compared with references solutions and other results reported in the literature.