A Fast and Accurate Step-by-step Solution Procedure for Direct Integration

Very small time steps are usually needed in numerical computation as conventional time integration methods are used to compute the response of a structure subjected to a dynamic loading with rapid changes or load discontinuity. To overcome this drawback, this study proposed a fast, fourth-order accurate step-by-step time integration (FASSTI) algorithm that is unconditionally stable and allows larger time steps for linear dynamic problems. From the stability and accuracy analysis, it is shown that the FASSTI algorithm retains the features of unconditional stability, accuracy, and fast convergence than the Newmark method. As a first test, a closed-form solution of an excited single degree of freedom (SDOF) system is derived and used to verify the reliability of the present algorithm in solving linear dynamic problems. In the numerical examples, the accuracy and efficiency of the proposed method is demonstrated in the solution of the dynamic response of an SDOF system under a series of impulse-type forces.