Two-dimensional biharmonic analysis and some applications
Brown, I. C. (1973). Two-dimensional biharmonic analysis and some applications. (Unpublished Doctoral thesis, The City University)
Abstract
This thesis lies within the subject area of the mathematical theory of elasticity and plasticity. Integral equation methods are applied to three problems lying broadly within the field of applied biharmonic analysis. The first concerns the deflection of a thin clamped elliptic plate subject to a concentrated transverse load. The second is that of determining the elastic stress field in the neighbourhood of a cavity of elliptic cross-section within an infinite medium. Finally, the previous problem is extended to the analysis of the plastic zone that develops near the tips of the cavity. This problem has relevance to the analysis of crack growth, and an approximation for the equilibrium elasto-plastic boundary is obtained.
This work is analytical and computational. Numerical solutions are obtained on a digital computer. Extensive use is made of numerical analysis and some
developments in the field of techniques have been achieved.
| Publication Type: | Thesis (Doctoral) |
|---|---|
| Subjects: | Q Science Q Science > QA Mathematics |
| Departments: | School of Science & Technology > Department of Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses |
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