Space-Time Reduced Element for Adaptive Finite Element Analysis of Forced Vibration of Elastic String in Maximum Norm
Source abstract
Abstract
This paper presents, by taking the elastic string vibration problem as the model problem, the space–time reduced element and the corresponding adaptive analysis algorithm. The solution of the space–time reduced element is extracted from the standard two-dimensional (spatial and temporal dimensions) polynomial element of the Galerkin-type by omitting the highest-degree terms, which serve as a built-in pointwise error estimator for the reduced solution. Taking the reduced solution as the final solution, the proposed adaptivity algorithm can produce solutions from the reduced element that satisfy the user-preset error tolerances in the maximum norm. Theoretical analysis and formulation are presented. Representative numerical examples, including forced vibrations with damping on an elastic foundation and moving load problems, validate the feasibility, effectiveness, and reliability of the proposed method.
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Research context
OpenAlex topics: Numerical methods for differential equations · Dynamics and Control of Mechanical Systems · Composite Structure Analysis and Optimization
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Affiliations
Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil Engineering, Tsinghua University, Beijing 100084, China
Funding
National Natural Science Foundation of China
References (24)
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