弹性地基上梁式基础的一种修正分析法

摘要

采用变分原理,对弹性模量随深度呈指数变化的修正Vlasov双参数地基上的梁式基础进行分析.基于最小势能原理,建立梁式基础的变形控制微分方程,并得到与地基弹性模量相关的可用简化迭代确定的形状参数.结合边界条件,导出梁式基础及地基的位移解.通过算例分析,探讨了形状参数对竖向位移衰减函数及地基梁式基础内力和变形的影响,以及各参数间的相互关系,并与有限元所得数值法结果进行对比.分析结果表明,考虑地基土弹性模量呈非线性变化,较符合工程实际,在同等条件下具有更好的经济效益.%An exact closed-form solution for beam founfation resting on the modified Vlasov elastic ground that the modulus of foundation soil exponentially increases with the increase of thickness was developed.The governing differential equation of the beam foundation was derived by using variational principle,and a dimensionless parameter that could be refined by iteration was introduced as a function of the modulus of the beam.Then,the deformation and the shear force and bending moments of the beam were determined by solving the boundary value problem.Finally,interaction among the parameters was discussed in the practical analysis example,and the results were compared with more sophisticated finite element solutions.The analytic results illustrate the method has a better economic benefit in the same conditions and correspond to actual project for engineering practice to consider nonlinear modulus of the foundation soil.