Seismic Response Analysis Method of Damping Structures Based on the Inter-history Iteration and Secondary Development of ABAQUS - JIA Chuanguo; QUAN Ziyu; CHEN Xi; LI Yutao (工程科学与技术)
ObjectiveTwo typical approaches for assessing the seismic response of a structure equipped with viscous dampers are direct integration methods and equivalent linear methods. Although direct integration methods provide precise results, their extensive computational cost and susceptibility to numerical instability stemming from the integration step hinder their practical use in most engineering applications. The equivalent linearization method provides a more tractable alternative by linearizing the system and incorporating stiffness and damping proportional to the response level. However, the equivalent linearization method is based on a single-degree-of-freedom structure, and the seismic response of the structure is assumed to be a sine function. For this reason, practical engineering applications of the equivalent linear method can also introduce errors. Therefore, proposing a simple yet highly precise analysis method to calculate the seismic response of a structure equipped with viscous dampers is of great significance.MethodThis study introduces an alternative method for seismic response analysis of structures incorporating viscous dampers. Based on the equivalent linear method, the Maxwell model is used as the assumed restoring force model to account for dampers. The analysis is based on an inter-history iteration approach to simulate the response over time. In this approach, an extra equivalent linear damper replaces all dampers on each floor, and its supplementary equivalent damping coefficient is computed and updated based on the velocity response of the structure during an earthquake. Then, the velocity response of the structure is recalculated using the updated additional equivalent damping coefficient. This iterative process continues until the additional equivalent damping coefficient meets the specified criteria. The increasing adoption of finite element analysis (FEA) platforms in civil engineering enables high-precision simulation of structural dynamic behaviors through advanced numerical modeling techniques. Among the various finite element software options, ABAQUS stands out for providing several user-subroutine interfaces. These interfaces empower users to expand the functionality of the main program by writing specific function codes designed to their requirements. It becomes practical and meaningful to develop a seismic response analysis method by integrating the concept and approach of inter-history iteration and using the capabilities of ABAQUS software. This method aims to avoid complicated calculations and achieve rapid convergence, which is of great significance to the seismic design of structures equipped with viscous dampers in practical engineering.Result and DiscussionThis study introduces the Maxwell viscous damper model at the beginning. After the brief introduction, the inter-history iteration method, grounded in the equivalent linear method, is presented. This method is used for the seismic response analysis of structures equipped with viscous dampers. ABAQUS is utilized to model and analyze a seven-story frame structure. Simultaneously, the seven-story frame structure is also modeled in MATLAB, which calculates the structural response using the direct integration method. The outcomes obtained through the direct integration method in MATLAB are used as the standard of comparison to the modeling and analysis in ABAQUS. The error of the first five modes is small, with the error of the first and second modes being less than 0.1%, demonstrating that the two modeling approaches are very close. The comparison and error of the first five modes in the two software verify the correctness of the model in ABAQUS. Python is further utilized to perform the secondary development of ABAQUS to realize the automatic iteration of the inter-history iteration method, thus obtaining a method that efficiently calculates the additional equivalent damping coefficient. Finally, a comparative analysis is conducted between the results obtained from the automated inter-history iteration method developed in ABAQUS and those from the direct integration method. The results demonstrated that, in the case of a seven-story frame structure, the inter-history iteration method exhibits strong convergence. In addition, it aligns well with the top displacement response curve calculated using the direct integration method. The error in the results meets engineering accuracy requirements, confirming that the automatic inter-history iteration calculation method provides high calculation accuracy and reliability while enhancing analysis efficiency. The error rate between the two calculation methods remains within 5%, indicating high accuracy. Simultaneously, compared to the direct integration method, the inter-history iterative method produces a smaller calculation result. This discrepancy arises because, in the calculation formula of the additional equivalent damping coefficient, the hysteresis curve corresponding to a larger response amplitude is fuller, while the curve for a smaller response amplitude is flatter. Therefore, the calculated additional equivalent damping coefficient is larger, leading to a smaller result in the inter-history iteration method. The automatic inter-history iteration calculation method, developed through the secondary development of ABAQUS, reduces manual data processing complexity and minimizes operational errors, significantly simplifying the calculation process of the inter-history iterative method. Based on the analysis above, the inter-history iterative method demonstrates the potential for broader application in engineering practice.ConclusionThe inter-history iterative method presented in this study provides several advantages: 1) Utilization of ABAQUS. The seismic response analysis of damped structures is performed using ABAQUS, eliminating the need for a complex numerical integration method. 2) Efficiency of the iterative process. Unlike the extensive computational steps required by the numerical integration method, the inter-history iterative method achieves strong convergence with only a few iterations. 3) Nonlinear problem avoidance. The model employs an equivalent linear damper, allowing for the avoidance of nonlinear challenges.