Structural Similitude and Scaling Laws of Anti-Symmetric Cross-Ply Laminated Cylindrical Shells for Buckling and Vibration Experiments

Abstract

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 lengthto-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.

A Review of Similitude Methods for Structural Engineering

“…As was done for composite plates, STAGE is applied to composite cylinders in Refs. [78][79][80][81]87], and [153][154][155]. The conditions for complete similitude are those already obtained for plates, plus the conservation of the curvature parameter (squared length over the product between thickness and radius).…”

Dynamic characteristics and seismic response of frame–core tube structures, considering soil–structure interactions

“…The similitude proportionality coefficients, length ( S l ), elastic modulus ( S E ), and acceleration ( S a ), were chosen as the main control coefficients. The remaining coefficients were deduced based on the Buckingham π theorem . The similitude proportionality coefficients are listed in Table .…”

High-Order Vibrations’ Dynamic Scaling Laws of Distorted Scaled Models of Thin-Walled Short Cylindrical Shells

“…In their studies, scaling laws of different material properties, plies' numbers and geometric sizes were derived by solving the governing equations of laminated plate and shell. Ungbhakorn and Singhatanadgid (2003); Ungbhakorn and Wattanasakulpong (2007) derived the scaling laws of symmetric and antisymmetric cross-ply laminated circular cylindrical shell by a directly use of the governing equations. Both complete and incomplete similarity cases are investigated in predicting the vibration and buckling problems.…”