求解双参数层状地基模型的积分变换法

Integration Transform for Solving Two-Parameter Layer Foundation Model

计算弹性地基梁板时,大都采用文克尔地基模型。由于该模型过于简化,不能正确反映土的工程性质,为此本文提出了一种双参数层状地基模型。该模型由一系列的弹性层组成,并对每一层中应力应变分布做了假设。通过积分变换的方法可以求出每一层表面处位移与力之间的关系,进而形成层刚度矩阵。按照有限元法的原理,可把每一层的刚度矩阵凝聚成总体刚度矩阵进行求解。本文模型是Vlazov模型的延伸和发展。通过与Vlazov模型计算结果的比较,证明本文方法是正确的。并且本文得到了荷载作用于层状模型内部时的解答,为将双参数地基模型用于桩基分析打下了理论基础。

Winkler's model is widely used in designing beam and plate on foundation, but this model is too simple to reflect the characters of soil correctly. A new two-parameter layer model was presented in this paper. The model consists of a number of elastic layers, in which the distributions of stress and strain were assumed. The layer stiff matrix, which expresses the relation of force and displacement on surface of every layer,could be calculated to apply integral transformation. Thus, the layer system could be solved through compiling layer stiff matrixes to form total matrix under the principle of FEM. The model is viewed as an extension of Vlazov model, and proved to be correct comparing with the result gained from Vlazov model. The most important thing is that the result of load embedding in layer model is gained ,this means the method presented in this paper can be adapted to calculate pile foundation.