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Existence of solutions of plane traction problems for ideal composites

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dc.contributor.authorPipkin, Allen C.
dc.contributor.authorSánchez de los Reyes, Víctor Manuel
dc.date.accessioned2023-06-21T02:06:49Z
dc.date.available2023-06-21T02:06:49Z
dc.date.issued1974-01
dc.description.abstractThe theory of plane deformations of ideal fiber-reinforced composites involves hyperbolic equations, but boundary data are specified as in elliptic problems. When the surface tractions are given at every boundary point of a plane region, and thus given at two points on each characteristic, it is not obvious that the problem is well-set. We show that under the usual global equilibrium conditions on prescribed tractions, a solution does exist. This is done by reducing the problem to an integral equation whose kernel depends on the shape of the region, locating the spectrum of eigenvalues, and then invoking standard results of the Hilbert-Schmidt theory
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/22954
dc.identifier.doi10.1137/0126018
dc.identifier.issn0036-1399
dc.identifier.officialurlhttp://www.jstor.org/stable/2099667
dc.identifier.relatedurlhttp://www.jstor.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/64882
dc.issue.number1
dc.journal.titleSIAM Journal on applied mathematics
dc.language.isoeng
dc.page.final220
dc.page.initial213
dc.publisherSociety for Industrial and Applied Mathematics
dc.rights.accessRightsopen access
dc.subject.cdu52
dc.subject.ucmAstronomía (Física)
dc.titleExistence of solutions of plane traction problems for ideal composites
dc.typejournal article
dc.volume.number26
dcterms.referencesA. C. PIPKIN AND T. G. ROGERS, Plane deformations of incompressible fiber-reinforced materials, J. Appl. Mech., 38 (1971), pp. 634-640. A. C. PIPKIN AND T. G. ROGERS, A mixed boundary value problem for fiber-reinforced materials, Quart. Appl. Math., 29 (1971), pp. 151-155. T. G. ROGERS AND A. C. PIPKIN, Small deflections offiber-reinforced beams or slabs, J. Appl. Mech., 38 (1971), pp. 1047-1048. G. C. EVERSTINE AND T. G. ROGERS, A theory of machining offiber-reinforced materials, J. Comp. Mat., 5 (1971), pp. 94-106. T. G. ROGERS AND A. C. PIPKIN, Finite lateral compression of a fiber-reinforced tube, Quart. J. Mech. Appl. Math., 24 (1971), pp. 311-330. G. C. EVERSTINE AND A. C. PIPKIN, Stress channelling in transversely isotropic elastic composites, ZAMP, 22 (1971), pp. 825-834. B. C. KAO AND A. C. PIPKIN, Finite buckling offiber-reinforced columns, Acta Mech., 13 (1972), pp. 265-280. A. J. M. SPENCER, Plane strain bending of laminatedfiber-reinforced plates, Quart. J. Mech. Appl. Math., to appear. A. J. M. SPENCER, Deformations of Fibre-Reinforced Materials, Oxford University Press, London, 1972. A. C. PIPKIN, Finite deformations of idealfiber-reinforced .composites, Micromechanics, G. P. Sendeckyi, ed., Academic Press, New York, 1973. A. H. ENGLAND, The stress boundary value problem for an idealfibre-reinforced material, J. Inst. Math. Appl., 9 (1972), pp. 310-322. A. H. ENGLAND AND T. G. ROGERS, Plane crack problemsfor idealfibre-reinforced materials. R. COURANT AND D. HILBERT, Methods of Mathematical Physics, vol. I, Interscience, New York, 1953.
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