Abstract
This paper reports on the improvement of Craig-Bampton (CB) method for transient analysis of structures with large-scale plastic deformation. As is known, the CB method is effective and accurate in reduced order modeling for linear system. In contrast to this, an improved CB method using tangent modes for nonlinear dynamic analysis has been developed. To do this, the incremental governing equations of nonlinear system are linearized in each time step by using tangent stiffness matrix, and the corresponding tangent modes are proved to be orthogonal with respect to mass matrix as well as with respect to tangent stiffness matrix by incorporating the elastic-plastic material behavior. Thus, the tangent modes can be used to assemble the transformation matrix of CB method in nonlinear dynamic analysis. Using the proposed method, two elastic-plastic beams loaded impulsively are examined. Simulation results show that the improved CB method is valid and accurate for transient analysis of structures with large-scale plastic deformation and has lower computational cost compared with full order model.
Highlights
The elastic-plastic dynamic analysis of structure is typically performed using finite element method (FEM), and has been remarked as a complicated and time-consuming work [1]
It can be concluded that by the responses and comparison study, the fixed beam has gone through large-scale plastic deformation under the pulsing load, the improved CB method is valid for this problem, and the responses obtained from proposed method have the same accuracy as that obtained from full order model
Unlike the original CB method, the transformation matrix of the improved CB method is constructed with a type of nonlinear modes of structure
Summary
The elastic-plastic dynamic analysis of structure is typically performed using finite element method (FEM), and has been remarked as a complicated and time-consuming work [1]. Another commonly used reduction method in linear system is component mode synthesis (CMS) technique, which is originally developed for modal analysis of large or complex structure With this method, first the entire structure is partitioned into a number of substructures, a set of structure modes (e.g. exact eigenmodes, static modes, interface modes, etc.) called component modes were set up to represent the motion of substructures. With the help of this idea, the nonlinear frequency spectrum is used to generate the reduced modal space, and the original CB method is improved to be able to reduce the transient analysis of structure with large-scale plastic deformation. The process of this work can be summarized as follows: First, the incremental governing equations of elastic-plastic dynamic problem are linearized over a small time interval by using tangent stiffness matrix.
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