Response of structures to impact loads, using elastic and plastic analysis

The objective of this work is to study the response of structures to impact loads. Depending on the magnitude of impact the structural response may need elastic or plastic analysis. When the deformations are within the elastic region, normal mode analysis is used to find the response. Structures considered in this study are Beams and Rectangular Plates. The Rayleigh-Ritz method is used to obtain the natural frequency and mode shape coefficients. Different types of displacement shape functions are employed in the analysis in the past such as beam characteristic functions and beam characteristic orthogonal polynomials. An approximate plate function is arrived at by reduction of the plate partial differential equation and solving the resulting ordinary differential equation as in Kantarovich method, and then used in the Rayleigh-Ritz method. The same reduction procedure is also used along with successive iteration until convergence to obtain the natural frequencies and mode shape functions directly. This method takes much less time for response evaluation than that is required by using the Rayleigh-Ritz method. Structural response to impact loads is also carried out using rigid plastic analysis. A cantilever beam with impulsive load applied at the free end is considered with finite blade radius and varying centrifugal forces are considered in the investigation. Experimental simulation of impact loading is carried out in the laboratory using a mass falling from a known height onto the structure under investigation. The elastic response of a plate with two adjacent edges clamped and the other two free are observed, and a equivalent mathematical model formulated by using flexible edge support