## Finite strain analysis in elastic theory

 dc.contributor.author Rock, Donald dc.contributor.department Mathematics dc.date 2018-08-23T18:40:05.000 dc.date.accessioned 2020-06-30T07:24:43Z dc.date.available 2020-06-30T07:24:43Z dc.date.copyright Sun Jan 01 00:00:00 UTC 1939 dc.date.issued 1939 dc.description.abstract

The stability of the clamped circular thin plate is investigated beginning with v. Karman's non linear differential equations for large strains. This non-linear system is developed into two linear sequences of equations ordered in powers of a parameter. The first approximation is found to yield the elementary solution of the problem. The second approximation of the radial membrane stress is shown to decrease the compressive stress in the center of the plate and increase it at the edge. The method of removing the indeterminacy of the second approximation to the slope function is outlined but not carried out because the explicit form of the particular integral free of integrals was not obtained;A parameter expansion, due to Garabedian, is employed to order the three-dimensional equilibrium equations and surface traction conditions for the moderately thick circular plate. From these equations the differential equations for the deflection and the stretching of the middle plane of the plate are derived for large strains. A method of successive approximations is then used to solve the non-linear differential equation for the case of the clamped plate with uniform loading. The correction to the elementary solution for the deflection is found to be significant only for extremely large values of the loading. The solution for the stretching of the middle plane of the plate, using the elementary value of the deflection, is found to be possible only under the assumption that rigid clamping of the edge of the plate against lateral displacements is impossible.

dc.format.mimetype application/pdf dc.identifier archive/lib.dr.iastate.edu/rtd/12911/ dc.identifier.articleid 13910 dc.identifier.contextkey 6866480 dc.identifier.doi https://doi.org/10.31274/rtd-180813-14175 dc.identifier.s3bucket isulib-bepress-aws-west dc.identifier.submissionpath rtd/12911 dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/66332 dc.language.iso en dc.source.bitstream archive/lib.dr.iastate.edu/rtd/12911/r_DP11973.pdf|||Fri Jan 14 19:33:19 UTC 2022 dc.subject.disciplines Mathematics dc.subject.keywords Elastic plates and shells dc.subject.keywords Strains and stresses dc.subject.keywords Differential equations dc.subject.keywords Linear dc.title Finite strain analysis in elastic theory dc.type article dc.type.genre dissertation dspace.entity.type Publication relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 thesis.degree.level dissertation thesis.degree.name Doctor of Philosophy
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