A high order single step β algorithm, a new direct integration algorithm is proposed for solution of equations of motion. Whenβ=0.5, the accuracy of displacement, velocity and acceleration is of forth order (a trunc...A high order single step β algorithm, a new direct integration algorithm is proposed for solution of equations of motion. Whenβ=0.5, the accuracy of displacement, velocity and acceleration is of forth order (a truncation error of Δ t 5), and the algorithm is unconditionally stable and has no arithmetic damping and no overshooting. When >0.5, and an arithmetic damping is adopted, the algorithm is again unconditionally stable with a third order accuracy (a truncation error of Δ t 4). The analyses run with typical examples show that the algorithm proposed has higher speed, higher precision and better properties than other direct integration methods, such as Wilson θ method and Newmark β method in analysing linear elastic responses and nonlinear earthquake responses.展开更多
文摘A high order single step β algorithm, a new direct integration algorithm is proposed for solution of equations of motion. Whenβ=0.5, the accuracy of displacement, velocity and acceleration is of forth order (a truncation error of Δ t 5), and the algorithm is unconditionally stable and has no arithmetic damping and no overshooting. When >0.5, and an arithmetic damping is adopted, the algorithm is again unconditionally stable with a third order accuracy (a truncation error of Δ t 4). The analyses run with typical examples show that the algorithm proposed has higher speed, higher precision and better properties than other direct integration methods, such as Wilson θ method and Newmark β method in analysing linear elastic responses and nonlinear earthquake responses.
