An improved quartic B-spline based explicit time integration algorithm for structural dynamics

In this study, an improved explicit time integration method based on quartic B-spline interpolation is generalized for linear and nonlinear dynamics. The accuracy order of the proposed method is analytically obtained as well as its spectral radius, period elongation, and algorithmic damping. The analysis shows the proposed method achieves third-order and at least second-order accuracy for displacement and velocity, respectively. With one algorithmic parameter, the proposed method can adjust numerical dissipation and accuracy. Linear dynamic examples demonstrate that the effectiveness of the proposed method as well as its high-order accuracy. Nonlinear dynamic problems show the proposed method can provide desirable solutions. Numerical results demonstrate the proposed method can provide more stable and accurate solutions than other classical explicit methods.

Automated summary

The study presented an improved explicit time integration method based on quartic B-spline interpolation for linear and nonlinear dynamics, achieving high accuracy with the ability to adjust numerical dissipation and precision. Results demonstrated its effectiveness in linear and nonlinear dynamic problems, providing stable and accurate solutions compared to classical explicit methods.