Two analogies in solid continuum mechanics

✍ Scribed by S.F. Borg

• Publisher: Elsevier Science
• Year: 1961
• Tongue: English
• Weight: 451 KB
• Volume: 272
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(61)90560-9

✦ Synopsis

This paper shows that the equations governing the behavior of moment and torque loaded thin plates which have small deflections are analogous to the equations of the two-dimensional linearized mathematical theory of isotropic elasticity. Because of the analogy, all solutions of two-dimensional plane-strain or plane-stress problems may be taken as solutions of a particular thin plate problem and vice versa.

A three-dimensional generalization of the above is also developed. In this form the theory draws an analogy between solutions in three-dimensional elasticity and those of thin plates subjected to lateral and shear loads as well as moments and torques.

The latter development is based on a tensoral generalization of the two-dimensional result to three dimensions. Because of this analogy all the known solutions for thin plates subjected to lateral loads represent possible solutions in a threedimensional elastic structure, 3 and vice versa.

Examples of both analogies are given.