構造体解析方法および構造体解析装置

專利類型

發明

專利國別 (專利申請國家)

日本

專利申請案號

特願 2019-211068

專利證號

特許 6830521

專利獲證名稱

構造体解析方法および構造体解析装置

專利所屬機關 (申請機關)

國立中央大學

獲證日期

2021/01/28

技術說明

傳統結構動力分析採用隱式直接積分法進行非線性歷時分析之主要缺點為結構特性矩陣之反矩陣計算，非常耗時，本隱式結構動力有限元素計算程序提出等效節點割線勁度與阻尼係數之概念，使結構勁度矩陣與勁度阻尼矩陣對角化，並採集中質量方式建立質量矩陣，使運動方程式為非耦合，再採用任何隱式直接積分法，配合增量-迭代程序，使每一步幅均達到收斂條件。當採用無條件隱定之隱式直接積分法時，可採取較大之時間步幅，大幅提高計算效率。因配合迭代計算，在求得同等精度解時，本法計算效率遠高於顯式直接積分法。經由數值驗證，本法之收斂速度(convergence rate) 等同於傳統quasi-Newton迭代程序之收斂速度，數值解的穩定性(stability)與正確性(accuracy) 等同於傳統隱式直接積分法之穩定性與正確性。由於不需建立結構勁度矩陣與阻尼矩陣，且僅需計算元素之節點內力與阻尼力，任何形式之有限元素與阻尼元件均可直接加入本分析程序中，故本法可廣泛用於分析各種非線性與不連續之問題，更可運用於結構物耐震設計檢核，驗證並確認所設計結構物在不同地震等級下，是否達到所設定之性能目標。 Conventional implicit methods used to analyze nonlinear dynamic systems must simultaneously solve the coupled equilibrium equations with factorization of a coefficient matrix. Therefore, implicit methods generally require a much greater amount of computational effort even though they allow larger time steps to be used. The concept of equivalent nodal secant stiffness and damping coefficient is adopted to diagonalize the conventional stiffness matrix and stiffness-proportional damping matrix, respectively. With the lumped-mass idealization, the decoupled equilibrium equations of the structure are then solved by any implicit method. Additionally, an incremental-iterative procedure is performed to ensure that the equilibrium conditions are satisfied at the end of each time step. The proposed analysis procedure has the advantages of both the conventional explicit and implicit integration procedures, but with their disadvantages removed. Through several numerical simulations performed using various analysis procedures, the results demonstrate that the stability and accuracy of the proposed analysis procedure are analogous to those of the traditional implicit procedure. Likewise, the convergence rate of the proposed analysis procedure is analogous to that of the traditional quasi-Newton iteration procedure. An important attribute is that any kind of FE can be included in the analysis procedure as long as the element internal and damping nodal forces can be exactly evaluated. Thus, the procedure is feasible and powerful for dealing with a vast variety of nonlinear and discontinuous problems with different types of damping force and hysteretic model. The simple implicit nonlinear dynamic analysis method is a promising computation tool for efficiently predict the seismic responses of structures under extreme ground motions due to its high computational efficiency, stability, accuracy, and robustness. Once the seismic response of a structure is reasonably predicted, the designers can estimate whether this structure is capable of achieving the prescribed performance objectives associated with earthquake hazard levels.

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