Solution to boundary value problems on linear elastic confocal elliptic domain based on collocation technique. (English) Zbl 1533.74004
Summary: Domains with elliptic boundaries are regularly pursued in Elasticity to elucidate the role of circular asymmetry and are associated with many classical closed form solutions. The work under consideration presents a unified semi-analytical approach to solve for stress and displacement field while being subjected to all kinds of plausible boundary conditions on any variant of elliptic geometry i.e. elliptic cylinder to confocal elliptic annulus to elliptic hole in an infinite plane. The generalized representation of Airy stress function in elliptical co-ordinates truncated to finite terms is considered and the associated coefficients are deduced to ensure boundary conditions using collocation technique. The correctness and effectiveness of the method is demonstrated through solution to a variety of problems and its validation via an independent finite element simulation.
MSC:
| 74B05 | Classical linear elasticity |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
| 74S99 | Numerical and other methods in solid mechanics |
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