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Axisymmetric static and dynamic buckling of orthotropic truncated shallow conical caps
Affiliation:1. South African National Biodiversity Institute, Kirstenbosch Research Centre, Private Bag X7, Newlands, Cape Town 7945, South Africa;2. Centre for Ecological Genomics and Wildlife Conservation, University of Johannesburg, Auckland Park, 2006 Johannesburg, South Africa;3. Department of Biodiversity and Conservation Biology, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa;4. Department of Zoology & Entomology, University of Pretoria, Pretoria 0001, South Africa;5. Department of Herpetology, National Museum, P.O. Box 266, Bloemfontein 9300, South Africa;6. Department of Zoology & Entomology, University of the Free State, P.O. Box 339, Bloemfontein 9300, South Africa;7. Port Elizabeth Museum, P.O. Box 13147, Humewood 6013, South Africa;8. School of Natural Resource Management, George Campus, Nelson Mandela University, George 6530, South Africa;9. CapeNature, Scientific Services, Private Bag X5014, Stellenbosch 7599, South Africa;10. Department of Botany and Zoology, Stellenbosch University, Private Bag X1, Matieland, 7602. Stellenbosch, South Africa;11. School of Animal, Plant and Environmental Sciences, University of the Witwatersrand, P.O. Wits, 2050 Johannesburg, South Africa;1. Universidade Federal Rural do Semiárido – UFERSA, Av. Francisco Mota, 572 - Costa e Silva, Mossoró, RN CEP: 59.625-900, Brazil;2. Universidade Federal de Campina Grande - UFCG, R. Aprígio Veloso, 882, Campina Grande, PB CEP: 58.429-140, Brazil
Abstract:This investigation deals with the axisymmetric static and dynamic buckling of a cylindricaliy orthotropic truncated shallow conical cap with clamped edge. The cases of conical caps with a free central circular hole and with a hole plugged by a rigid central mass have been considered. The governing equations are formulated in terms of normal displacement w and stress function Ψ. The orthogonal point collection method is used for spatial discretisation and the Newmark-β scheme is used for time-marching. Analysis has been carried out for a uniformly distributed conservative load normal to the undeformed surface and a central axial ring load at the hole. Dynamic load is taken as a step function load. The influence of orthotropic parameter β and annular ratio on the buckling loads has been investigated. New results for static and dynamic buckling loads have been presented for the isotropic and orthotropic truncated conical caps. Dynamic buckling loads obtained from static analysis have been found to agree well with the dynamic buckling loads based on transient response.
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