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对机械零件进行有限元分析时,为了更好逼近机械零件的边界,需要采用数值积分的曲面(线)单元。实际经验表明,在积分点上算得的应力精度最好,而结点上算得的应力精度最差,这是因为插值函数的精度在靠近插值区域的边缘通常是较差的,因而在单元内部取样的形函数的导数比在单元边界取样的准确。但是,通常工程上感兴趣的是边界上的应力或边界结点的应力。特别是在应力集中部位,由于应力梯度大,边界附近积分点的应力与边界上的应力值相差甚远,即使在结构相同、载荷相同的情况下,只要单元形状略有不同,积分点上的应力值也会有很大差异。因此,不能直接用积分点上的应力作为判别边界应力大小或用来计算应力集中的系数。
In the finite element analysis of mechanical parts, in order to better approximate the mechanical parts of the boundary, you need to use numerical integration of the surface (line) unit. Practical experience has shown that the stress accuracy at the integration point is the best and the stress at the junction is the worst because the accuracy of the interpolation function is usually poor near the edge of the interpolation region and therefore sampling inside the cell The derivative of the shape function is more accurate than sampling at the cell boundaries. However, what is usually of engineering interest is the stress on the boundary or the stress on the boundary node. Especially in the stress concentration area, due to the large stress gradient, the stress at the integral point near the boundary is far from the stress value at the boundary. Even in the case of the same structure and the same load, as long as the unit shapes are slightly different, Stress values can vary widely. Therefore, the stress at the integration point can not be directly used as a criterion to determine the boundary stress or to calculate the stress concentration factor.