弹性地基上Euler-Bernoulli梁的临界荷载计算

Critical Load Calculation of Euler-Bernoulli Beam on Elastic Foundation

研究运用微分求积法(DQM)求解了弹性地基上功能梯度Euler-Bernoulli梁的屈曲临界荷载。首先基于Euler-Bernoulli梁理论,将弹性地基上功能梯度Euler-Bernoulli梁临界荷载的计算转化为一组变系数常微分方程的特征值问题,由微分求积法可以一次性地计算出Euler-Bernoulli梁的临界荷载。梁上离散节点采用非均匀等比数列和切比雪夫多项式的根两种布点方式,根据微分求积法计算梁的屈曲临界荷载时,二者的计算精度等价,且计算值与已有文献结果完全吻合,证明了微分求积法求解弹性地基上Euler-Bernoulli梁临界荷载的可行性和精确性。

The differential quadrature method(DQM)is used to solve the buckling critical load of functionally graded Euler Bernoulli beams on elastic foundation.Based on the theory of Euler Bernoulli beam,the calculation of critical load of Euler Bernoulli beam with functional gradient on elastic foundation is transformed into the eigenvalue problem of a set of ordinary differential equations with variable coefficients.The critical load of Euler Bernoulli beam can be calculated by differential quadrature method.The discrete nodes on the beam are arranged in two ways:non-uniform proportional sequence and the root of Chebyshev polynomial.When the critical buckling load of the beam is calculated by the differential quadrature method(DQM),the calculation accuracy of the two methods is equivalent,and the calculation results are completely consistent with the results of the existing literature.It is proved that the differential quadrature method(DQM)is feasible and accurate for solving the critical buckling load of Euler Bernoulli beam on elastic foundation.