The general form of the three-dimensional elastic field inside an isotropic plate with free faces

✍ Scribed by R. D. Gregory

• Publisher: Springer Netherlands
• Year: 1992
• Tongue: English
• Weight: 909 KB
• Volume: 28
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00042522

✦ Synopsis

A homogeneous, isotropic plate has free faces and is "stretched" by tractions around its edge which are symmetrical about the mid-plane, but are otherwise generally distributed. We give a rigorous proof that the most general state of stress z~j which can be generated in the plate can be decomposed in the form

es is an (exact) plane stress state, (ii) z~ is a shear state, and (iii) z~ r is a where (i) ziy Papkovich-Fadle state, which is a 3-dimensional generalisation of the Papkovich-Fadle eigenfunctions for the elastic strip. Furthermore, we prove that, as the plate thickness h ~0, z~ and z~e are exponentially small at points inside the plate and represent edge effects of thickness O(h).

Corresponding results are also given for the case of plate "bending", in which the applied tractions around the plate edge are anti-symmetrical about the mid-plane.