caa a22 4500 469084782 CHVBK 20180323133002.0 cr unu---uuuuu 170328e19920601xx s 000 0 eng 10.1007/BF00042522 doi (NATIONALLICENCE)springer-10.1007/BF00042522 Gregory R. Department of Mathematics, University of Manchester, M13 9PL, Manchester, England aut The general form of the three-dimensional elastic field inside an isotropic plate with free faces [Elektronische Daten] [R. Gregory] 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 % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabes8a0naaBaaaleaacaWGPbGaamOAaaqabaaaaa!3FFD!\[\tau _{ij} \] which can be generated in the plate can be decomposed in the form % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabes8a0naaBaaaleaacaWGPbGaamOAaiabg2da9aqabaGccqaH% epaDdaqhaaWcbaGaamyAaiaadQgaaeaacaWGqbGaam4uaaaakiabgU% caRiabes8a0naaDaaaleaacaWGPbGaamOAaaqaaiaadofaaaGccqGH% RaWkcqaHepaDdaqhaaWcbaGaamyAaiaadQgaaeaacaWGqbGaamOraa% aaaaa!5277!\[\tau _{ij = } \tau _{ij}^{PS} + \tau _{ij}^S + \tau _{ij}^{PF} \] where (i) % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabes8a0naaDaaaleaacaWGPbGaamOAaaqaaiaadcfacaWGtbaa% aaaa!41AB!\[\tau _{ij}^{PS} \] is an (exact) plane stress state, (ii) % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabes8a0naaDaaaleaacaWGPbGaamOAaaqaaiaadofaaaaaaa!40D6!\[\tau _{ij}^S \] is a shear state, and (iii) % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabes8a0naaDaaaleaacaWGPbGaamOAaaqaaiaadcfacaWGgbaa% aaaa!419E!\[\tau _{ij}^{PF} \] is a 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, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabes8a0naaDaaaleaacaWGPbGaamOAaaqaaiaadofaaaaaaa!40D6!\[\tau _{ij}^S \] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabes8a0naaDaaaleaacaWGPbGaamOAaaqaaiaadcfacaWGgbaa% aaaa!419E!\[\tau _{ij}^{PF} \] 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. Kluwer Academic Publishers, 1992 Journal of Elasticity Kluwer Academic Publishers 28/1(1992-06-01), 1-28 0374-3535 28:1<1 1992 28 10659 https://doi.org/10.1007/BF00042522 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00042522 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gregory R. Department of Mathematics, University of Manchester, M13 9PL, Manchester, England aut NATIONALLICENCE 773 0- Journal of Elasticity Kluwer Academic Publishers 28/1(1992-06-01), 1-28 0374-3535 28:1<1 1992 28 10659 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer