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提出一种分析地基梁非线性位移的新方法。首先采用分段线性函数对非线性的基底压力(p)-基底沉降(s)关系曲线进行拟合,通过引入控制变量,得到p-s曲线统一表达式。根据地基梁模型能量泛函,结合参变量变分原理和分段线性地基模型中的互补条件,导得一个标准的线性互补模型。该模型可用较为成熟的规划算法进行求解,使地基梁位移非线性求解问题转化为一个标准的数学问题。在对该法的合理性进行验证后,详细推导了集中荷载作用下地基梁位移的非线性求解方程,并对其进行求解。在此基础上,对线性与非线性计算的差异及影响非线性计算结果的因数进行分析,得到如下主要结论:考虑非线性影响时,地基梁位移曲线不均匀沉降增大,地基梁内力增大;随着p-s曲线非线性程度增加以及p-s曲线上进入非线性段临界压力值的减小,非线性影响越明显;荷载大小及梁与地基的相对刚度均会影响地基梁位移分布形式。
A new method to analyze the nonlinear displacement of foundation girder is proposed. First, the piecewise linear function is used to fit the non-linear substrate pressure (p) -substitution (s) curve, and the unified expression of p-s curve is obtained by introducing control variables. According to the energy functional of ground beam model, a standard linear complementary model is derived by combining the variational principle of parametric variables and the complementary conditions in the piecewise linear foundation model. The model can be solved by more mature planning algorithms, which can transform the problem of non-linear displacement of foundation beam into a standard mathematical problem. After verifying the rationality of this method, the nonlinear solving equation of ground beam displacements under concentrated load is derived in detail and solved. On this basis, the difference between linear and non-linear calculation and the factors affecting the nonlinear calculation results are analyzed. The main conclusions are as follows: When the nonlinear effect is considered, the uneven settlement of the displacement curve of foundation beam increases and the internal force of foundation beam increases The nonlinear effect is more obvious with the increase of the non-linearity of the ps curve and the decrease of the critical pressure of the non-linear section of the ps curve. The load distribution and the relative stiffness between the beam and the foundation all affect the displacement distribution of the foundation beam.