Solution of problems of the theory of plates and shells with spline functions (survey)
- National Academy of Sciences of Ukraine, Kiev (Russian Federation)
The study of the stress-strain state of plates and shells subjected to various types of loads with different support conditions entails the formulation of boundary-value problems that generally involve systems of partial differential equations with variable coefficients. The complexity of solving these problems stems not only from the high order of the system and the variability of the coefficients, but also from the need to exactly satisfy prescribed boundary conditions. The use of a given method to obtains a solution with a satisfactorily high degree of accuracy depends to a significant extent on the geometric and mechanical parameters characterizing certain aspects of the problem and the type of boundary conditions. These factors sometimes limit the possibilities of solving problems in the important (in a practical sense) cases in which the stiffness of the shell or plate supports is also variable. In addition, problems of the shell theory entail local and edge effects, which imposes certain stiffness conditions on boundary-value problems related to the phenomenon of instability in the computation. Spline functions have recently come into wide use to solve such problems in the areas of computational mathematics, mathematical physics, and mechanics. The popularity of this approach stems from the advantages offered by spline functions compared to other methods. Among these advantages: the stability of splines in relation to local perturbations, i.e. the behavior of the spline in the neighborhood of a point has no effect on the behavior of the spline as a whole (which is not the case in a polynomial approximation); good convergence of a spline-interpolation, in contrast to a polynomial interpolation; simplicity and ease of use of algorithms that construct and calculate splines on computers. 65 refs., 5 figs., 7 tabs.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 245124
- Journal Information:
- International Applied Mechanics, Journal Name: International Applied Mechanics Journal Issue: 6 Vol. 31; ISSN IAMEEU; ISSN 1063-7095
- Country of Publication:
- United States
- Language:
- English
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