统一化的微分–积分求积法
A Unified Differential-Integral Quadrature Method
摘要:
传统微分求积法和势能原理相结合有助于解决具有局域特殊性的力学问题，因此，求解这类问题时不仅涉及微分计算，还涉及积分计算。为简化计算流程，提高计算效率，本文基于微分/积分求积法的思想，提出了统一化的微分/积分求积的权系数计算方法，从而形成统一化的微分–积分求积法，并将此计算方法得到的结果与解析解进行比较，验证了该方法在收敛速度、求解精度、稳定性、应用范围方面的优势。
Abstract:
The combination of the differential quadrature method and potential energy principle is greatly helpful to solve mechanical problems with local particularity. This kind of solutions is not only related to differential calculation, but also to integral calculation. In order to simplify such kind of calculation process and improve the computational efficiency, this paper presents an unified differential-integral quadrature method (D-IQM), based on the original concepts of differential/ integral quadrature method, to calculate weight coefficients of differential/integral quadrature in an unified format of mathematics. The results from D-IQM were compared with the analytical solutions, demonstrating the advantages of this method in convergency, accuracy and stability, and robusticity on application.
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