Abstract
A simple unified set of displacement and velocity approximations is presented to express various two-stage composite time integration schemes. Based on the unified approximations, two novel sets of optimized parameters are newly proposed for the implicit composite schemes to enhance the capability of conserving total energy. Two special cases of the unified approximations are also considered to overcome some shortcomings of the existing schemes. Besides, the newly proposed unified set of approximations can include many of the existing composite time integration schemes. To be specific, both implicit and explicit composite schemes can be expressed by using the unified set of approximations. Thus, both implicit and explicit types of composite schemes can be selected from the unified set by simply changing algorithmic parameters. To demonstrate advantageous features of the proposed unified set of approximations, various numerical examples are solved, and results are analyzed.
Highlights
Direct time integration schemes have been widely used for the effective analysis of linear and nonlinear structural dynamics [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
Two novel sets of optimized parameters are presented for the implicit schemes to enhance the total energy conserving capability
The unified set of time approximations presented in this article can include many of the existing composite schemes, and some novel implicit composite schemes can be newly developed base on it
Summary
Direct time integration schemes have been widely used for the effective analysis of linear and nonlinear structural dynamics [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. The concept of subdividing a complete time step (or time interval) into two sub-steps is frequently employed for the development of direct time integration schemes with enhanced numerical performances. Time integration schemes developed based on this strategy are often called the composite time integration scheme They are called the two-stage time integration scheme. Implicit and explicit schemes of this type are known to possess improved numerical performances when compared with the conventional single-stage time integration schemes [8, 12, 13, 14, 15, 16, 17, 18, 19]. Even though various composite schemes are designed to solve the equation of structural dynamics numerically, they have never been expressed in a unified form
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