{"data":{"id":"10.13016/m2sm68","type":"dois","attributes":{"doi":"10.13016/m2sm68","prefix":"10.13016","suffix":"m2sm68","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Stepanov, Alexey","nameType":"Personal","givenName":"Alexey","familyName":"Stepanov","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"ANALYSIS OF STEADY-STATE AND DYNAMICAL RADIALLY-SYMMETRIC PROBLEMS OF NONLINEAR VISCOELASTICITY"}],"publisher":"Digital Repository at the University of Maryland","container":{},"publicationYear":2015,"subjects":[{"subject":"Mathematics","subjectScheme":"pqcontrolled"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Mechanical engineering","subjectScheme":"pqcontrolled"},{"subject":"FOS: Mechanical engineering","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Materials Science","subjectScheme":"pqcontrolled"},{"subject":"blowup","subjectScheme":"pquncontrolled"},{"subject":"elasticity","subjectScheme":"pquncontrolled"},{"subject":"existence","subjectScheme":"pquncontrolled"},{"subject":"live load","subjectScheme":"pquncontrolled"},{"subject":"material","subjectScheme":"pquncontrolled"},{"subject":"viscoelasticity","subjectScheme":"pquncontrolled"}],"contributors":[],"dates":[{"date":"2015","dateType":"Issued"}],"language":"en","types":{"ris":"THES","bibtex":"phdthesis","citeproc":"thesis","schemaOrg":"Thesis","resourceType":"Dissertation","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"description":"This thesis treats radially symmetric steady states and  radially symmetric motions of nonlinearly elastic and viscoelastic plates and shells subject  to dead-load and hydrostatic pressures on their boundaries and with the plate subject to centrifugal force. The plates and shells are described by specializations of the exact (nonlinear) equations of three-dimensional continuum mechanics.  The treatment in every case is very general and encompasses large classes of constitutive functions (characterizing the material response). \n\nWe first treat the  radially symmetric steady states of plates and shells and the radially symmetric steady rotations of plates. We show that the existence, multiplicity, and qualitative behavior of solutions for  problems accounting for the live loads due to hydrostatic pressure and centrifugal force depend  critically on the material properties of the bodies, physically reasonable  refined descriptions of which are given  and examined here with great care, and on the nature of boundary conditions.The treatment here, giving new and sharp  results, employs several  different mathematical tools, ranging from  phase-plane analysis to the mathematically more sophisticated  direct methods of the Calculus of Variations, fixed-point theorems, and global continuation methods, each of which has different strengths and weaknesses for handling intrinsic difficulties in the mechanics. \n\nWe then treat the initial-boundary-value problems for the radially symmetric motions of annular plates and spherical shells that consist of a nonlinearly viscoelastic material of strain-rate type. We discuss a range of physically natural constitutive equations. We first show that when the material is strong in a suitable sense relative to externally applied loads, solutions exist for all time, depend continuously on the data, and consequently are unique. We study the role of the constitutive restrictions and that of the regularity of the data in ensuring the preclusion of a total compression and of an infinite extension for finite time. We then show that when the material is not sufficiently strong then under certain conditions on the (hydrostatic) pressure terms there are globally defined unbounded solutions and there are solutions that blow up in finite time. \n\nThe practical importance of these results is that for each problem involving live loads they furnish thresholds in material response delimiting materials for which solutions are ill behaved. A mathematical or numerical study limited to a particular class of materials may dangerously indicate well-behaved solutions when there are other realistic materials for which solutions are ill behaved. Moreover this work furnishes so-called trivial solutions for the subsequent study (not given here) of bifurcation of stable equilibrium configurations from these trivial solutions.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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