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The objective of this study is to develop and validate similitude requirements and scaling laws for studying the real characteristics of structures easily and economically, especially for large structures. The generalized similitude requirements and the scaling law of orthogonally stiffened cylindrical panels and shells for buckling and free vibration are derived by applying the similitude transformation to the total energy of the structural system directly. In practice, due to either the difficulty of satisfying all of the similitude requirements simultaneously or to save experimental cost and time, distorted models with partial similarity are necessarily employed and approximate scaling laws are proposed. The partial similitude is mainly investigated first by using specific formulas of stiffness parameters and corresponding scaling laws are given. Also discussed herein are particular models with relaxations in the material properties of stiffeners, the materials of both the skin and the stiffeners and the material properties and geometry. The obtained results indicate that the distorted models are able to accurately predict the behavior of the prototype. [ABSTRACT FROM AUTHOR]

This paper presents the Hencky bar-chain model (HBM) for buckling and vibration analyses of Euler-Bernoulli beams with elastic end restraints. The Hencky bar-chain comprises rigid beam segments (of length a = L/n where L is the total length of beam and n the number of beam segments) connected by frictionless hinges with elastic rotational springs of stiffness EI/a where EI is the flexural rigidity of the beam. The elasticity and the mass of the beam are concentrated at the hinges with rotational springs. The key contribution of this paper lies in the modeling of the elastic end restraints of the Hencky bar-chain that will simulate the same buckling and vibration results as that furnished by the first-order central finite difference beam model (FDM) which was earlier shown to be analogous to the HBM. The establishment of such a physical discrete beam model allows one to obtain solutions for beam-like structure with repetitive cells (or elements) as well as to calibrate the Eringen's coefficient e0 in the nonlocal beam theory that captures the small length scale effect. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the transverse vibration of a circular plate loaded by uniform pressure along its edge. The plate is supported by an elastic ring support being coaxial with the plate. At its edge the plate is clamped but the radial displacement is allowed. Apart from this problem, the heated plate clamped at its edge, but without the possibility of radial displacement, is also analyzed. The analytical solution of governing equation is obtained in the form of Bessel's functions. Using the analytical solution, the frequencies of transverse vibrations depending on loads, elastic ring stiffness and the location of ring are obtained. The results show that the lowest frequencies vibrations can be either symmetric or asymmetric having one or two nodal diameters. It is also shown that multiple vibration frequencies can occur for special values of load and ring stiffness. [ABSTRACT FROM AUTHOR]