| Summary: | 碩士 === 國立臺北科技大學 === 土木工程系土木與防災碩士班 === 106 === In structural dynamic, the step-by-step integration method is a universal and efficient integration method. The current development trend is to develop a step-by-step integration method that has unconditional stability and explicit formulation. A semi-explicit structure-dependent integration method has been successfully developed for time integration, where the displacement difference equation is explicit while the velocity difference equation is implicit. This implies that an iteration procedure might be still involved for velocity-dependent problems, such as that many types of viscous and viscoelastic dampers have been added into buildings to dissipate energy. A novel family of fully explicit structure-dependent integration methods is proposed for time integration. This family of integration methods can combine unconditional stability and fully explicit formulation together. Thus, it will involve no nonlinear iterations for each time step for either solving a displacement-dependent and/or velocity-dependent problems. As a result, it is very computationally efficient for solving general structural dynamics problems, where the total response is dominated by low frequency modes while high frequency responses are of no interest. In general, this family method can only have unconditional stability for linear elastic and stiffness softening systems while it will become conditionally stable for stiffness hardening systems. To overcome this difficulty, a stability amplification factor is introduced into the structure-dependent coefficients. Hence, unconditional stability for stiffness hardening systems can be also achieved. Some numerical examples are applied to confirm the numerical properties.
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