An unconditionally stable time-stepping procedure with algorithmic damping: a weighted integral approach using two general weight functions

✍ Scribed by Golley, Bruce W.; Amer, Muhammad

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 121 KB
• Volume: 28
• Category: Article
• ISSN: 0098-8847
• DOI: 10.1002/(sici)1096-9845(199911)28:11<1345::aid-eqe870>3.0.co;2-o

✦ Synopsis

An accurate algorithm for the integration of the equations of motion arising in structural dynamics is presented. The algorithm is an unconditionally stable single-step implicit algorithm incorporating algorithmic damping. The displacement for a Single-Degree-of-Freedom system is approximated within a time step by a function which is cubic in time. The four coe$cients of the cubic are chosen to satisfy the two initial conditions and two weighted integral equations. By considering general weight functions, eight additional coe$cients arise. These coe$cients are selected to (i) minimize the di!erence between exact and approximate solutions for small time steps, (ii) incorporate speci"ed algorithmic damping for large time steps, (iii) ensure unconditional stability and (iv) minimize numerical operations in forming the ampli"cation matrix. The accuracy of the procedure is discussed, and the solution time is compared with a widely used algorithm.