【作者】 王帅； 胡兆鑫； 张向东；

【Author】 WANG Shuai;HU Zhao-xin;ZHANG Xiang-dong;School of Civil Engineering,Liaoning Technical University;

【机构】 辽宁工程技术大学土木工程学院；

【摘要】 经典弹性理论方法计算地基附加应力,受被积函数是否可积的限制,只能计算规则形状、规则分布基底压力下的地基附加应力。由于实际工程中的均布荷载是一种简单粗糙的平均化,是一种权宜的处理方式,这是传统计算方法、包括纽马克应力感应图法的一个缺陷。传统方法用得最多和最广泛的是矩形域和圆形域应力分布,难以满足现阶段特种建筑形式和要求艺术美感的特殊建筑形式的要求。采用有限元方法的位移插值函数,只能实现与插值次数相等的代数精度,提高插值次数后,龙格现象显著,数值计算失稳。对于大规模计算,有限单元法通常的解决手段是尽可能多地采用低阶次的单元,以避免网格畸变和数值失稳,这样会使单元数量大大增加,计算成本高,计算效率低。针对传统计算方法和数值模拟方法的上述缺陷,利用高斯求积公式与被积函数的具体形式无关的特性,将数值积分方法应用于地基附加应力的计算,推导出了基于弹性理论的地基附加应力数值计算公式。有限元法n个插值节点,只能达到n次代数精度。高斯求积公式的插值节点选择为正交多项式的n个零点,可以达到2n+1次的高代数精度,并且求积公式中节点的权值均为正值,具有高度的数值稳定性。本文方法不局限于规则荷载下规则形状的附加应力计算,对于非均布荷载、非规则域的一般情况,可以得到计算附加应力的显式代数公式,具体手段是:利用显式的辛普森公式将非矩形域的附加应力计算公式中隐式的二重积分显化去积分号,转化为显式的累次积分,即可类似矩形域情形得到求解附加应力近似值的显式解析代数式。工程应用中,只须向现场的工程技术人员提供高斯-勒让德公式插值结点的位置和插值的权值系数,以及辛普森公式的具体形式,即可手算得到附加应力计算结果,这是传统计算方法和有限元数值模拟方法难以达到的。如果从学术严谨和理论完备的角度考虑,还可以结合计算机程序的循环算法使用复化高斯求积公式,这时在标准情况下,本文方法已经与经典弹性理论的计算结果高度一致。更多还原

【Abstract】 We can calculate the flexible foundation subsidence under the uniform foundation pressure with classical elastic theory method.But it is a hard promotion to get the settlement with foundation pressure because it is uncertain whether the integrand is integral.With independent features between Gaussian quadrature formula and the integrand form,the numerical integration method is used in the calculation of soft foundation settlement.We deduced the numerical formula of flexible foundation settlement based on the theory of elasticity.We used the numerical simulation software Adina to build the finite element model of foundation settlement under non-uniformly distributed loading.We also compared the simulation results and the proposed settlement calculation method.Compared with calculation results of the classical method under uniform load,it shows the correctness of the quadrature formula.When the Gaussian quadrature formula is higher than 3th quadrature,it is highly consistent with the classical elastic theory calculation result.Numerical Simulation Result is compared with the situ test data of Dongrong mine shaft tower foundation.It shows that the settlement calculation method can calculate the settlement of flexible foundation under non-uniform load correctly.This method is not only used to the settlement calculation of rectangular flexible foundation,but also used to non-rectangular foundation.As long as the double integral of the settlement calculation formula is changed into iterated integral,It can be similar to the rectangular domain to get the settlement approximation.So there is universal significance and application value of the method.更多还原