Nonlinear Dynamic Analysis of Frames and Axisymmetric Shell Structures

Abstract

New beam bending element was proposed in Ref. 1) including the effect of shearing deformation, which was composed of two rigid bars connected by two different types of springs. In case of uniform division this discrete element derived by physical consideration is equivalent to the beam element in the conventional finite element method, which was introduced in Ref. 2) by employing linear displacement and rotation functions in conjunction with one-point integration based on the penalty method. Almost the same situation holds for the conical frustum element used for the discrete analysis of axisymmetric shell structures.These discrete elements give accurate linear elastic solutions in spite of their simplicity and they can be effectively used in the limit load analysis because they can construct the plastic collapse mechanisms.In this paper the application of these discrete elements is treated to the nonlinear dynamic analysis of frames and axisymmetric shell structures. As numerical examples nonlinear behavior is analyzed of plane and space frames, circular plates, circular cylindrical shells, and spherical shells loaded impulsively. The obtained results are compared with theoretical solutions, other numerical ones, and experimental results in order to justify the validity of the present method.