Simplified Methods for Dynamic Analysis of Structures under Blast Loading

Abstract

The increasing threat of extremely severe loading conditions caused by a number of explosive sources made engineers and scientists developing, during the last half century, several methods of analysis and design of blast–resistant structures. Simple, intermediate, and advanced computational approaches have been adopted, requiring increasing computational resources. These efforts led to the publication of several manuals and guidelines for the analysis and design of blast–resistant reinforced concrete and steel structures, mostly based on simple considerations derived from Single Degree of Freedom (SDOF) models. Although the development of future guidelines based on advanced numerical techniques is desirable, typical design activities cannot be effectively carried out by applying complex methods, because of their large demand of resources. Therefore the necessity to develop simplified, low time consuming, methods of analysis, capable of supporting a daily design activity and, at the same time, takeing into account issues usually neglected, such as a strong non linear material behavior and the influence of the strain rate caused by a blast load on the structural response. The development of such design tools is the object of this study. The first part of this thesis deals with the influence of the blast load shape on the dynamic response of an undamped linear elastic oscillator. Response spectrum and pressure–impulse diagrams are shown for several shape parameters, and a sensitivity analysis of the results with respect to the computational parameters is also presented. A method validation is carried out via genetic algorithms, through a careful calibration of all the genetic parameters, such as crossover fraction and number of elite elements. Non linear material modeling and strain rate dependent constitutive laws are objects of the second part of this dissertation. A non linear oscillator made of displacement, velocity, and acceleration dependent springs and dampers, under an arbitrary dynamic load, is proposed. Spring and damper constitutive laws have no restrictions as well as the load–time function, and the dynamic analysis is accomplished by a piecewise linear approximation of any input function. Numerical problems are dealt with by applying the Newton–Raphson method, in such a way that enables the error range to be estabiv lished “a priori”. Any possible drawback of this method is carefully avoided, and a quadratic speed of convergence is always ensured. Since the model provides velocity dependent springs, strain rate effects of blast loads on the structural response are taken into account by including strain rate dependent constitutive laws within the problem definition.