Correlation Between Discretization Error of Dynamic Loading and Amplitude Distortion for Time Integration

• Main Authors: Shang-Ru Yang, 楊尚儒
• Other Authors: Shuenn-Yih Chang
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/ba8pz3

碩士 === 國立臺北科技大學 === 土木工程系土木與防災碩士班（碩士在職專班） === 103 === In the step-by-step integration procedure, it is important to choose an appropriate time step to obtain a reliable solution. The three basic requirements, stability, accuracy and convergence, must be satisfied. Period distortion is often found in time integration. Hence, a reliable solution can be obtained only if the period distortion is controlled to be relatively small based on accuracy consideration. Period distortion may arise from the difference equations for displacement and velocity, linearization errors and the inaccurate representation of dynamic loading. Although it is well recognized that a step size must be small enough to capture the rapid variation of dynamic loading to yield an accurate solution, there is no criterion to determine an appropriate step size to conduct time integration. In this work, an asymptotic ratio of the relative amplitude error over the discretiztion loading error as the step size approaching zero is considered as an index number for the capability of an integration method to capture the rapid variation of dynamic loading. At first, the discretization error for each dynamic loading of sine loading, cosine loading and linear loading will be analytically evaluated. Next, the response to the abovementioned dynamic loading will be analytically obtained by using an integration method. This response will be compared to the exact response to estimate the response error. As a result, the asymptotic ratio for each dynamic loading for each integration method can be calculated. It seems that the asymptotic ratio is a simple number and a small number implies a less amplitude error.