A Method to Estimate Dynamic Buckling Response of an Unstiffened Plate Elastically Restrained Along all Edges Under In-Plane Impact

Unstiffened plates in structures are usually welded or fastened to supporting members, providing rotational restraint stiffness to the plate. Previous studies have shown that neglect of rotational restraint stiffness at the edges of a plate in a structure can introduce deviations in the analysis of dynamic elastic buckling. In this study, the in-plane impact-induced dynamic elastic buckling responses of isotropic imperfect unstiffened plates with four elastically restrained edges are analytically investigated, based on the large-deflection theory of thin plate. The evolution of the peak deflection predicted by the proposed analytical method is found to be consistent with the responses available from the literature. Then the method is further used to estimate the deformation map of an unstiffened plate with four elastically restrained edges, and the effects of rotational restraint stiffness, initial geometric imperfection and shock duration on the dynamic buckling response of the plate are examined. The results show that the critical dynamic buckling load and the maximum deflection response of the plates are significantly influenced by the rotational restraint stiffness as well as the first-order initial geometric imperfection, and thus cannot be neglected in the analysis of dynamic buckling.

Application of Chebyshev tau method for bending analysis of elastically restrained edge functionally graded nano/micro-scaled sandwich beams, under non-uniform normal and shear loads

In this study, for the first time, an approximate solution procedure based on the Chebyshev tau method (CTM) is developed for bending analysis of functionally graded nano/micro-scaled sandwich beams. The proposed approach has the advantage of decreasing the problem to the solution of a system of algebraic equations, which may then be solved by any numerical method. In the CTM, the solution is approximated via a truncated Chebyshev series expansion and the Chebyshev polynomials are used as the test function. Based on the proposed technique, sandwich beams with elastically restrained edges under arbitrary non-uniform distributed normal and shear loads can be analyzed. The effectiveness of the CTM is illustrated by comparison of the obtained results for various end supports with those extracted from the ABAQUS software. In each considered cases, the numerical results indicate that the proposed scheme is of high accuracy and is efficient for solving the ordinary differential equations and systems of them.

Development of Rotational Fixity Factors for Vibration Design of Cross-Laminated Timber Floors

As an emerging building solution, cross-laminated timber (CLT) floors have been increasingly used in mass timber construction. The current vibration design of CLT floors is conservative due to the assumption of simple support conditions in the floor-to-wall connections. It is noted that end fixity occurs as a result of clamping action at the ends, arising from the gravity load applied by the structure above the floor and by the mechanical fasteners. In this paper, the semi-rigid floor-to-wall connections are treated as elastically restrained edges against rotations to account for the effect of partial constraint. A rotational end-fixity factor was first defined to reflect the relative bending stiffness between CLT floors and elastic restraints at the edges. Then, for the design of vibration serviceability of CLT floors as per the Canadian Standard for Engineering Design in Wood (CSA O86), restraint coefficients were defined and their analytical expressions were derived for natural frequencies and the mid-span deflection under a concentrated load, respectively. In particular, a simplified formula of the restraint coefficient for the fundamental frequency was developed to assist engineers in practical design. At last, by comparing with reported experimental data, the proposed design formula showed excellent agreement with test results. In the end, the proposed end fixity factor with their corresponding restraint coefficients is recommended as an effective mechanics-based approach to account for the effect of end support conditions of CLT floors.