Remarks on variational principles in elastodynamics

✍ Scribed by Yu Chen

• Publisher: Elsevier Science
• Year: 1964
• Tongue: English
• Weight: 256 KB
• Volume: 278
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(64)90352-7

✦ Synopsis

Two principles are basic in the variational formulations of elasticity. Green's "variation for displacements" leads to the principle of minimum potential energy, whereas Castigliano's "variation for stresses" leads to the principle of minimum complementary energy. In the small vibration of elastic bodies, the result of Green's approach coincides with Hamilton's principle of dynamics. Toupin (3) and Crandall (4) both established complementary extremum principles for dynamics. Reissner (1) has derived a complementary extremum principle for steady-state vibration of elastic bodies. The present paper derives the extremum principle for small vibration of elastic bodies in general.