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为提高裂纹结构静力和动力分析问题的收敛速度和分析精度,将基于Legendre正交多项式的p型自适应有限元方法与断裂力学方法相结合,给出了p型自适应梁单元刚度矩阵和质量矩阵的显式积分表达式,同时建立了裂纹单元的刚度方程。数值仿真和实验案例表明,该方法与细化网格的h型有限元方法相比,在自由度减少的同时能够有效地提高计算精度。考虑到裂纹识别问题一般采用有限元方法建立精确辨识模型,该文提出的方法在降低识别复杂度和提高识别精度方面具有一定的工程实用价值。
In order to improve the convergence speed and accuracy of the static and dynamic analysis of cracked structures, the p-type adaptive finite element method based on the Legendre orthogonal polynomial is combined with the fracture mechanics method, and the p-type adaptive beam element stiffness matrix and Mass matrix explicit integral expression, at the same time establish the crack cell stiffness equation. The numerical simulation and experimental results show that compared with the h-type finite element method of the refined mesh, this method can effectively improve the calculation accuracy while reducing the degree of freedom. Considering that the problem of crack identification generally uses the finite element method to establish the accurate identification model, the method proposed in this paper has certain engineering practical value in reducing the identification complexity and improving the recognition accuracy.