Plates and Shells: Asymptotic Expansions and Hierarchic Models

Chapter 8 Plates and Shells: Asymptotic Expansions and Hierarchic Models

Plates and shells: Asymptotic expansions and hierarchical models

Concerning thin structures such as plates and shells, the idea of reducing the equations of elasticity to twodimensional models defined on the mid-surface seems relevant. Such a reduction was first performed thanks to kinematical hypotheses about the transformation of normal lines to the mid-surface. As nowadays, the asymptotic expansion of the displacement solution of the three-dimensional lin...

Second Order Moment Asymptotic Expansions for a Randomly Stopped and Standardized Sum

This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright}‎ where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of ran...

Research Article Asymptotic Solution of the Theory of Shells Boundary Value Problem

This paper provides a state-of-the-art review of asymptotic methods in the theory of plates and shells. Asymptotic methods of solving problems related to theory of plates and shells have been developed by many authors. The main features of our paper are: (i) it is devoted to the fundamental principles of asymptotic approaches, and (ii) it deals with both traditional approaches, and less widely ...

Free Vibration Analysis of Bidirectional Functionally Graded Conical/Cylindrical Shells and Annular Plates on Nonlinear Elastic Foundations, Based on a Unified Differential Transform Analytical Formulation

In the present research, a unified formulation for free vibration analysis of the bidirectional functionally graded conical and cylindrical shells and annular plates on elastic foundations is developed. To cover more individual cases and optimally tailored material properties, the material properties are assumed to vary in both the meridian/radial and transverse directions. The shell/plate is a...