摘要
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 for non-linear analysis of foundation beam was presented.Firstly,a piecewise linear function was used to fit the nonlinear p-s curve and a unified relationship between pressure and settlement under foundation beam was set up with an introduced control variable.The energy functional dealing with the deformation of foundation beam was then derived.Combined with the complementarities which drawn from the piecewise linear function,a standard linear complementary model was formed by using parametric variational principle.This model can be solved by a mature programming algorithm known as planning algorithm.Consequently,the non-linear analysis of foundation beam was transformed into computing a standard mathematical model.After the rationality of the proposed method was validated,a detailed solution process for non-linear analysis of foundation beam under concentrated load was presented.On the basis,the difference between linear and non-linear analyses and factors that affect the non-linear calculation results were investigated.It shows that the uneven settlement and the internal bending moment of foundation beam increases when the non-linear effects are considered.Increasing the nonlinearity level of the p-s curve or decreasing the pressure threshold into non-linear section,the non-linear effects become more obvious.Both the load intensity and the relative stiffness of beam to foundation affect the distribution form of displacement in the non-linear analysis of foundation beam.
出处
《建筑结构学报》
EI
CAS
CSCD
北大核心
2012年第4期142-149,共8页
Journal of Building Structures
关键词
地基梁
P-S曲线
分段线性模型
非线性分析
参变量变分原理
位移
foundation beam
p-s curve
piecewise linear model
non-linear analysis
parametric variational principle
deformation
