Asymptotic Analysis and Synthesis in Mechanics of Solids and Nonlinear Dynamics

Details Asymptotic Analysis and Synthesis in Mechanics of Solids and Nonlinear Dynamics Asymptotic Analysis and Synthesis in Mechanics of Solids and Nonlinear Dynamics

2011-06-09

arxiv.org/abs/1106.1783v1

Physics

Mathematical Physics

Scientific paper

In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation appears: the existence of asymptotics for $\ve\rightarrow 0$ implies an existence of the asymptotics for $\ve\rightarrow\infty$. Therefore, the idea to construct one function valid for the whole parameter interval for $\ve$ is very attractive. The construction of asymptotically equivalent functions possessing a known asymptotic behaviour for $\ve\rightarrow 0$ and $\ve\rightarrow \infty$ will be discussed. Using summation and interpolation procedures we focus on continuous models derived from a discrete micro-structure. Various continualization procedures that take the non-local interaction between variables of the discrete media into account are analysed.

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