A high‐order accurate explicit time integration method based on cubic b‐spline interpolation and weighted residual technique for structural dynamics
Weibin Wen, Shanyao Deng, Shengyu Duan, Daining Fang
Abstract
Abstract A novel explicit time integration method is proposed on the basis of cubic b‐spline interpolation and weighted residual method. Its calculation formulation and procedure are presented. Accuracy, algorithmic damping, and period elongation are theoretically and numerically solved. The influence of two algorithmic parameters on basic properties of the proposed method is studied to obtain optimal parameters values for dynamic problems. Various linear and nonlinear dynamic problems are tested to demonstrate high efficiency of the proposed method.
Topics & Concepts
Spline interpolationResidualMethod of mean weighted residualsSpline (mechanical)Applied mathematicsInterpolation (computer graphics)Nonlinear systemMathematicsMonotone cubic interpolationAlgorithmBasis (linear algebra)Basis functionMathematical optimizationB-splineComputer scienceBicubic interpolationMathematical analysisGeometryBilinear interpolationStructural engineeringGalerkin methodEngineeringAnimationQuantum mechanicsStatisticsComputer graphics (images)PhysicsNumerical methods for differential equationsFractional Differential Equations SolutionsNumerical methods in engineering