Comparative Study of Non-Dissipative Structure-Dependent Integration Methods

• Main Authors: Yen-Rong Chen, 陳彥蓉
• Other Authors: 張順益
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/gtbbk7

碩士 === 國立臺北科技大學 === 土木工程系土木與防災碩士班 === 106 === Four structure-dependent integration methods are explored and compared in this work. These integration methods are different from conventional integration methods since their coefficients of the difference equations are not scalar constants but can be functions of the product of the initial structural properties and step size. Either favorable or adverse numerical properties of each structure-dependent integration method are thoroughly explored. For comparison purpose, numerical properties of the commonly used Newmark family method are also investigated. The favorable properties include unconditional stability, second-order accuracy, explicit formulation and no overshoot in both transient and steady-state responses. Whereas, the adverse properties that might be experienced for structure-dependent integration methods are conditional stability for stiffness hardening systems, a high frequency overshoot in steady-state responses, a poor capability of capturing structural nonlinearity and a weak instability. All the four structure-dependent integration methods can only have conditional stability for stiffness hardening systems. Hence, a stability amplification factor can be applied to enlarge the unconditional stability interval. As a result, an unconditional stability can be achieved for certain stiffness systems after using an appropriate stability amplification factor except for TLM. In addition, these integration methods also show a high frequency overshoot in steady-state responses. However, they can be eliminated by introducing a load-dependent term into the displacement difference equation. It is very important to find that CRM and TLM have a weak instability property, which may lead to an inaccurate solution or even numerical instability. Although CEM and CFM2 generally have no weak instability, they exhibit a poor capability for seizing structural nonlinearity. Notice that CRM is a special member of CFM2 and is the only member that exhibits a weak instability for CFM2. In general, CFM1 can have all the desired numerical properties while it does not show any above-mentioned adverse properties. Consequently, it is strongly recommended for practical applications.