A high‐order accurate explicit time integration method based on cubic b‐spline interpolation and weighted residual technique for structural dynamics

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.

A novel three sub‐step explicit time integration method for wave propagation and dynamic problems

“…With the identical strategy proposed by Wen et al, 17 the analytical truncation errors of the new method are, respectively, obtained as follows: $$$$ {e}_{u_{t+\Delta t}}={a}_1\cdot {u}_t^{(3)}\cdot {\left(\Delta t\right)}^3+O\left({\left(\Delta t\right)}^4\right),\kern21.2em $$$$ $$$$ {e}_{{\dot{u}}_{t+\Delta t}}={b}_1{u}_t^{(3)}\cdot {\left(\Delta t\right)}^2+\left({b}_2\cdot {u}_t^{(4)}+{b}_3\cdot \xi \omega {u}_t^{(3)}\right)\cdot {\left(\Delta t\right)}^3+O\left({\left(\Delta t\right)}^4\right),\kern8.5em $$$$ …”

“…A standard Van der Pol's equation described by $$$ \left(1+{u}^2\right){u}^{(2)}+\left(d+{u}^2\right){u}^{(1)}+u=0 $$$ is considered, 17 where d is the damping coefficient, and negative for this problem. We select $$$ c=-2.0 $$$ and the initial conditions, $$$ u(0)=-0.02 $$$ and $$$ {u}^{(1)}(0)=0 $$$.…”

Design of nonlinear control system for motion trajectory of industrial handling robot

“…The PSO simulates the foraging behavior of a flock of birds and performs stochastic optimization through the behavior of an intelligent population. 30 The advantages of the particle swarm algorithm are its strong global search capability, fast computational speed, and adaptation to global optimal solution search under multiple constraints. The idea of intelligent PSO is that individuals within the swarm adjust information parameters such as step size and speed by recording their own position and the position of the swarm during the search process, constantly updating their position state and eventually reaching the optimal solution or maximum number of iterations.…”

“…After determining the expression of the handling robot's trajectory in relation to time, the study investigates time‐optimal optimization control of trajectory planning by means of a PSO. The PSO simulates the foraging behavior of a flock of birds and performs stochastic optimization through the behavior of an intelligent population 30 . The advantages of the particle swarm algorithm are its strong global search capability, fast computational speed, and adaptation to global optimal solution search under multiple constraints.…”

A novel explicit three-sub-step time integration method for wave propagation problems

“…28, the NB method exhibits very good performance in the analysis of wave propagation problems. Besides, worth of mention are some efforts devoted to developing higher-order explicit methods [19,33,35] using two and more sub-steps. The improvement of the accuracy order, however, often leads to a reduction of the stability region.…”