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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]

Sandwich panels have been developed to either produce lighter structures capable of carrying prescribed loads or increase the load-carrying capacity subject to limitations on weight. In these panels, facings carry bending and in-plane loads while the core functions similarly to the web of a beam, mostly resisting transverse shear. Improvements in the load-carrying capacity of sandwich panels can be achieved through modifications in their geometry, boundary conditions, and material distribution. One of the methods recently considered by the authors is based on using facings with a step-wise variable thickness that increases at the critical region of the structure.1 It was illustrated that the strength of a sandwich panel can be considerably enhanced using such stepped facings, without a detrimental increase of the weight. The present paper expands the study of the feasibility of the stepped-facing sandwich panel concept concentrating on three structural problems, i.e. a possible improvement in stability, changes in the natural frequencies, and forced dynamic response to the explosive blast. It is illustrated that the stepped-facing design can improve stability of the panel and its response to blast loading. However, fundamental frequencies of stepped-facing panels decrease compared to those in their conventional equal-weight counterparts. Such decrease is detrimental in the majority of engineering applications representing a limitation of stepped-facing panels. Nevertheless, the usefulness of the stepped-facing design is proven in the problems of bending, stability, and blast loading. Numerous examples presented in the paper validate our suggestion that the combination of a relatively simple manufacturing process and an improved structural response of sandwich panels with stepped facings may present the designer with an attractive alternative to conventional sandwich structures. [ABSTRACT FROM AUTHOR]

Developed herein are the scaling laws for physical modeling of anti-symmetric cross-ply laminated circular cylindrical shells for buckling and free vibration experiments. In the absence of experimental data, the validity of the scaling laws is verified by numerical experiments. This is accomplished by calculating theoretically the buckling loads and fundamental frequencies of the model and substituting into the scaling laws to obtain the corresponding values of the prototype. The predicted values of the prototype from the scaling laws are then compared with existing closed-form solutions. Examples for the complete similitude cases with various stacking sequences, number of plies, and length-to-radius ratios show exact agreement. The derived relationships between the model and prototype will greatly facilitate and reduce the need for costly experiments. In reality, either due to the complexity of the scaling laws or to economize experimental cost and time, it may not be feasible to construct the model to fulfil the scaling laws completely. Thus, several possible models of partial similitude are investigated numerically. These include models with distortion in laminated material properties, stacking sequences and number of plies. Model with distortion in material properties yields a high percentage of discrepancy and is not recommended. [ABSTRACT FROM AUTHOR]

The similitude invariants and scaling laws for the buckling and free vibration of antisymmetric angle-ply laminated circular cylindrical shells were derived by directly applying the similitude transformation to the governing differential equations of the problem considered. The scaling laws relate the buckling load and natural frequency of a model to those of a prototype when the similarity requirements between the two systems are fulfilled. In the absence of experimental data, the validity of the scaling laws was verified by calculating theoretically the buckling loads and fundamental frequencies of vibration of the model and substituting them into the scaling laws to yield values for the prototype, which were then compared with those directly computed for the prototype. The numerical studies show that for the case of complete similitude with various stacking sequence, number of plies, and radius ratio, the solutions predicted by the similitude theory agree exactly with those obtained directly from the theory. Some typical partial similitude cases were also investigated. It was demonstrated that the partial similitude model with distortion in stacking sequence is reliable for predicting the behavior of the prototype. On the other hand, models with distortion in material properties are not recommended because of the existence of large discrepancies in the predicted results. [ABSTRACT FROM AUTHOR]