In this paper, a novel generalized structure-dependent semi-explicit method is presented for solving dynamical problems. Some existing algorithms with the same displacement and velocity update formulas are included as the special cases, such as three Chang algorithms. In general, the proposed method is shown to be second-order accurate and unconditionally stable for linear elastic and stiffness softening systems. The comprehensive stability and accuracy analysis, including numerical dispersion, energy dissipation, and the overshoot behavior, are carried out in order to gain insight into the numerical characteristics of the proposed method. Some numerical examples are presented to show the suitable capability and efficiency of the proposed method by comparing with other existing algorithms, including three Chang algorithms and Newmark explicit method (NEM). The unconditional stability and second-order accuracy make the novel methods take a larger time-step, and the explicitness of displacement at each time-step succeeds in avoiding nonlinear iterations for solving nonlinear stiffness systems.

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