A Finite Element Code for Structural Collapse Analyses of Framed Structures under Impact Loads


This study aims to develop an efficient analysis code for impact analyses of framed structures. If the model to be analyzed is a large structure, it is desirable, from the point of calculation costs, to use a small number of elements per member. However, this tends to lower the accuracy and reliability of the result and so it is very important to have a numerical scheme that ensures accuracy even when the number of elements per member is small. Toi and Isobe developed the Adaptively Shifted Integration (ASI) technique for the linear Timoshenko beam element. In comparison to the conventional finite element method, the ASI technique normally gives a comparatively more precise solution. However, compared to the converged solution, it still lacks accuracy in elastic deformation when used with two elements per member. In this study, the ASI technique is modified into the ASI-Gauss technique by placing the numerical integration points of the two consecutive elements forming a member in such a way that stresses and strains are evaluated at the Gaussian integration points of the two-element member. On comparison with the ASI technique, the ASI-Gauss technique proved its high accuracy and efficiency in elastic range.
Generally, it is difficult to determine the impact loads resulted in a structure due to a collision. Moreover, applying impact loads to an analytical model in the form of nodal forces may not well simulate the impact phenomenon. This study tries to simulate the impact phenomenon by means of contacts between the elements involved. Contact determination is done by examining the following two factors: (1) the distance between the approaching element and the another one, (2) the condition under which all four nodal points of the two elements lie on the same plane. Elemental contact is simulated by temporarily binding the two elements in contact with a total of four gap elements, whose stiffness and resultant forces are set to zero after a certain period of time. This elemental contact algorithm was verified from the point of conservation of energy and the results showed its high reliability. Furthermore, impact analyses are performed using a high-rise framed structure and a small aircraft. From the results, we could observe propagation phenomena of impact loads and shock waves. Different parameters of the aircraft produced proper difference in impact damage. Moreover, soon after impact, tensile stresses were observed in the columns that had been compressed by gravity loads before impact.

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