Design of scaled down models for stability of laminated plates

Abstract

This study investigates problems associated with design of scaled down models. Similitude theory is employed to develop the necessary similarity conditions. Scaling laws provide the relationship between a full-scale structure and its scale models and can be used to extrapolate the experimental data of a small, inexpensive, and easily tested model into design information for the large prototype. Both complete and partial similarity are discussed. Particular emphasis is placed on the cases of buckling of rectangular symmetric angle-ply laminated plates under uniaxial compressive and shear loads. This analytical study indicates that distorted models with a different number of layers, material properties, and geometries than those of the prototype can predict the behavior of the prototype with good accuracy. A scaled-down (by a large factor) model, scale model, which can predict the structural behavior of the full-scale system, prototype, can prove to be an extremely beneficial tool. This possible develop- ment must be based on the existence of certain structural parameters that control the behavior of the structural system when acted upon by static and/or dynamic loads. If such structural parameters exist, a scaled-down replica can be built, which will duplicate the response of the full-scale system. The two systems are then said to be struc- turally similar. The term, then, that best describes this similarity is structural similitude. Similitude theory is employed to develop the necessary similarity conditions (scaling laws). Scaling laws provide the relationship be- tween a full-scale structure and its scale models and can be used to extrapolate the experimental data of a small, inexpensive, and eas- ily tested model into design information for a large prototype. The difficulty of making completely similar scale models often leads to accept certain type of distortion from exact duplication of the prototype (partial similarity). Both complete and partial similarity are discussed. A parametric investigation of problems associated with designing small-scale models for cross-ply laminated wide beams1 and plates2 has been presented. The procedure consists of systematically observing the effect of each parameter and corre- sponding scaling laws. Then acceptable intervals and limitations for these parameters and scaling laws are discussed. In each case, a set of valid scaling factors and corresponding response scaling laws which accurately predict the response of prototypes from ex- perimental models is introduced. Particular emphasis is placed on the cases of buckling of rectangular angle-ply laminated plates un- der uniaxial compressive and shear loads. This analytical study also indicates that distorted models with a different number of layers, material properties, and geometries than those of the prototype can predict the behavior of the prototype with good accuracy. The objectives of the investigation described herein are twofold. The first is to derive the necessary similarity conditions in order to design a distorted model that accurately predicts prototype behav- ior including distortion in stacking sequence and number of plies (N) and ply-level and sublaminate-level scaling; distortion in ma- terial properties, E/;, v/y, and p and distortion in fiber orientation angle 0. The second is to evaluate the derived similarity conditions analytically. In all of our work in this area we will restrict ourselves to linearly elastic material behavior. Therefore, scale effects are not present. Furthermore, it is assumed that all laminas have equal thickness f, and the laminates are free of damage (delaminations, matrix crack- ing, fiber breaks, etc.).