A note on the stability of Newmark's algorithm in nonlinear structural dynamics

✍ Scribed by Thomas J. R. Hughes

• Publisher: John Wiley and Sons
• Year: 1977
• Tongue: English
• Weight: 198 KB
• Volume: 11
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620110212

✦ Synopsis

An integration formula for polynomial expressions in terms of the unit triangle co-ordinates is presented

Discussion

Eisenberg and Malvern' have derived relations for integrating products with non-integer exponents in terms of area co-ordinates. Other worker^^,^ often utilize two-dimensional elements mapped onto the unit triangle. In this system the (r, s) co-ordinates of the three corner nodes are (0, 0), (1,O) and (0, 1). By utilizing the derivation given by Eisenberg and Malvern one can formulate a similar expression for the unit triangle co-ordinates r and s : rpsqda = 2 ~r ( p + i ) r ( q + i ) / r ( p + q + 3 )