TY - JOUR
T1 - Conical shell edge disturbance
T2 - An engineer's derivation
AU - Blaauwendraad, J.
AU - Hoefakker, J. H.
PY - 2016
Y1 - 2016
N2 - Because a rigorous bending theory for thin shells of revolution is complicated, attempts have been made for reliable approximations of the edge disturbance problem under axisymmetric loading. A well-known one was published by Geckeler [1, 2], who obtained his approximation by mathematical considerations. He started from kinematic, constitutive and equilibrium equations for the rotationally symmetric thin shell without approximations. Herein he introduced mathematical simplifications. Each time when derivatives of a function of different orders appeared, he just kept the highest order derivative and neglected all lower ones. This is permitted if the function varies rapidly, as is the case for edge disturbances. Here we will present Geckeler's result in an alternate way, which illustrates the physical background of his mathematical approximation. Said in another way, we offer a derivation in the language of structural engineers.
AB - Because a rigorous bending theory for thin shells of revolution is complicated, attempts have been made for reliable approximations of the edge disturbance problem under axisymmetric loading. A well-known one was published by Geckeler [1, 2], who obtained his approximation by mathematical considerations. He started from kinematic, constitutive and equilibrium equations for the rotationally symmetric thin shell without approximations. Herein he introduced mathematical simplifications. Each time when derivatives of a function of different orders appeared, he just kept the highest order derivative and neglected all lower ones. This is permitted if the function varies rapidly, as is the case for edge disturbances. Here we will present Geckeler's result in an alternate way, which illustrates the physical background of his mathematical approximation. Said in another way, we offer a derivation in the language of structural engineers.
KW - Edge disturbance zone
KW - Engineer's approach
KW - Rotationally symmetric shell
UR - http://www.scopus.com/inward/record.url?scp=85018997009&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:6e75d8f5-04d2-4ce9-92de-331562df6a54
M3 - Article
AN - SCOPUS:85018997009
SN - 0046-7316
VL - 61
SP - 141
EP - 152
JO - Heron
JF - Heron
IS - 3
ER -