Experimental and computational analysis of plates under air blast loading
Introduction
In recent years, the explosive loads have received considerable attention by different events, accidental or intentional, over important structures all over the world. In consequence, in the last decade there was an important activity in the research of explosive loads. Initially, these works were mostly empirical, but, in the last few years, important researches have begun to develop.
The detonation of an explosive generates the violent expansion of hot gases originating a pressure wave, moving outward at high velocity from its source. When the front of the shock wave arrives at the observation point the pressure rises very sharply, followed by a quasi exponential decay back to ambient pressure po and a negative phase in which the pressure is less than ambient. The peak values of the underpressure are usually small compared with the peak positive overpressure. When the shock wave arrives at a point of interest it originates a dynamic pressure that is proportional to the square of the wind velocity and the density of the air behind the shock front. Finally, when the incident blast wave from an explosion in air strikes a more dense medium (earth, water, wall), it is reflected. The peak value of the reflected pressure depends on the peak of the incident wave, the angle at which it strikes the surface and the nature of the surface.
Generally, simplifying assumptions must be made in order to solve specific problems. Until now, most practical problems have been solved through empirical approaches. Years of industrial and military experience have been condensed in charts or equations [1], [2]. In connection with structural analysis there are several simple methods in the classical books of structural dynamics by Biggs [3] and Clough and Penzien [4]. For a more rigorous analysis, the structure model as a system of multiple degree of freedom and the equilibrium equation solves using modal superposition or direct integration methods. If the difference exists between the stiffness of the component parts of the structure (resistant structure and panels), then it is possible to separate them. In this case, the parts can be analyzed in separate ways [5].
The dynamic loads originated by explosions are impulsive and result in strain rates in the material about 10−1–103 seg−1. These extreme loads produce a special behavior in the material that is characterized, among other effects, by overstrength and increased stiffness, in comparison with normal, static properties. Galiev [6] and Krauthammer et al. [7] describe the metal behavior under impulsive load.
In the analysis, it is sometimes necessary to consider the effects of geometric and material nonlinearities. Louca et al. [8] propose a method based on Lagrange equation to realize an elastic analysis considering large displacement. Theoretical analysis considers only simple boundary conditions, while modeling of other boundary conditions is possible using springs. Ellis and Tsui [9] indicate a method to determine the stiffness of spring. Many papers using the plastic hinged model were proposed by Jones [10]. In the paper of Nonaka [11], attention is focused on the failure mode of a steel brace in New York World Trade Center.
In connection with tests it is usual to refer the weight of used explosives to an equivalent weight of TNT. The results presented by Formby and Wharton [12] are very useful to understand and to obtain the TNT equivalence of various commercial explosives.
The objectives of this paper are, first, the comparison between testing and numerical responses in order to obtain guides to the numerical modeling and analysis of this phenomenon and, in the second place, to provide data that could be used for checking the accuracy of a variety of calculation methods. According to these objectives, a set of four tests at natural scale was performed on two unstiffened metallic steel plates with different boundary conditions (one clamped in the soil and another clamped in the four edges), subjected to the action of pressure waves originated by the detonation of explosive loads. The time history of the acceleration in different points of both plates and the pressure waves in selected points, are recorded. On the other hand, a numerical analysis using the finite element program ABAQUS/Standard [13] was carried out. At first, a linear dynamic analysis considering small displacements was performed and afterwards a nonlinear dynamic analysis considering large displacements was executed. Related with this research, Ellis et al. [9] present experimental results of reinforced concrete panels subjected to explosive loading; Rudrapatna et al. [14] present numerical results for clamped, square stiffened steel plates subjected to blast loading and Louca et al. [8] describe numerical results of nonlinear analysis on both stiffened and unstiffened plates. On the other hand, Shen and Jones [15] analyse the nonlinear dynamic response and failure of clamped circular plates.
The results presented in this paper could be used in order to obtain design guidelines of offshore topsides and steel bridge plated construction. In connection with this, Pan and Louca [16] said that while there has been interest in blast resistance of plates and panels over the past few years, there is very little data available on their response characteristics. Moreover, some aspects are useful for the verification of vehicle barrier systems used to prevent the intrusion of malevolent vehicles with explosives in nuclear power plants (NUREG/CR-6190 [17]). These barriers are designed to resist the kinetic energy of the vehicle and can be verified to the subsequent explosion.
Section snippets
Experimental setup and instrumentation
The analyzed structures in this paper are two unstiffened steel plates subject to impulsive loads originated by detonation of explosives. The explosive used was Gelamon VF80 theoretically equivalent in mass to 80% TNT. This explosive is similar to Special Gelatine 80 (Formby and Wharton [12]). Four tests with different amounts of explosives were carried out (Fig. 1). In order to measure the overpressure generated by the shock waves, four pressure sensors Honeywell 180PC were used (Fig. 2). On
Numerical analysis
The numerical analysis was carried out using the finite element program ABAQUS/Standard 5.7. The plates were modeled using shell elements. In both cases, the boundary conditions were considered as perfectly clamped. The adopted material properties were Young modulus E=180 GPa (experimental value), Poisson's coefficient ν=0.3 and density ρ=7850 kg/m3. The dynamic analysis was performed using the modal superposition method and integration direct method. The integration was carried out step by step
Comparison and discussion
In view of the objectives of the paper, a comparison between the computational and the experimental results of the time-history of the accelerations is carried out at this point. For the purpose of comparison, Model 2 (refined) was used in all the cases.
Conclusions
A set of experimental results of unstiffened steel plates subjected to blast load is presented. Moreover, for comparison purposes, a numerical analysis was carried out. On the basis of the results obtained, the following conclusions may be drawn:
- 1.
According to Fig. 11 and Table 4, it is extremely important that the number of vibration modes be considered in the analysis because, in general, this type of loads excites the high frequencies. Then, for predicting numerical analysis, it is necessary
Acknowledgements
The authors wishes to thank the collaboration of Eng. Sergio Salomón the owner of the test field and the help received from technical staff, Mr. Eduardo Batalla and Mr. Daniel Torielli, during the development and preparation of the tests. Moreover, the financial support of the CONICET and the Universidad Nacional de Tucumán is also gratefully acknowledged. Special acknowledgements are extended to one of the reviewers of the first version of the paper, since his useful suggestions led to many
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