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梯形重力坝的应力函数解及其有限元验证

STRESS FUNCTION SOLUTION FOR TRAPEZOIDAL GRAVITY DAM AND ITS FINITE ELEMENT VERIFICATION
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摘要 弹性力学教材中通过取三次多项式应力函数给出三角形横截面的重力坝应力场,但工程中重力坝的横截面几乎均为梯形,其坝顶并非三角形尖顶。将应力函数的半逆解法与锲形体的应力函数相结合,寻找出适用于梯形重力坝的应力函数,根据梯形重力坝力的边界条件,并利用圣维南原理,给出了梯形重力坝的应力场解析式。用有限元计算给出了梯形重力坝应力场的数值仿真结果。应力场解析式与有限元仿真结果非常吻合,说明了梯形重力坝应力场解析式的正确性。梯形重力坝应力场解析式对水利工程中重力坝的结构强度及设计具有重要的理论指导意义和应用价值。 In the textbook of elasticity mechanics, the stress field of gravity dam with triangular cross-section is given by taking cubic polynomial stress function. However, the cross-section of engineering gravity dam is generally trapezoid, and its dam crest is not triangular cusp. Combining the semi-inverse method of stress function with the stress function of the tiny body, the stress function applicable to trapezoidal gravity dam is found out. Based on the boundary conditions of trapezoidal gravity dam force and using the Saint-Venant principle, the analytical formula of the stress field of trapezoidal gravity dam is given. Numerical simulation results of the stress field of trapezoidal gravity dam are given by finite element calculation. The analytical formula of the stress field is in good agreement with the finite element simulation result, which shows the correctness of the analytical formula of the stress field of trapezoidal gravity dam. The analytical formula of the stress field of trapezoidal gravity dam has important theoretical guiding significance and application value for structural strength and design of a gravity dam in hydraulic engineering.
作者 肖先志 肖奉英 黄模佳 XIAO Xianzhi;XIAO Fengying;HUANG Mojia(Institute of Engineering Mechanics,Nanchang University,Nanchang 330031,China)
出处 《力学与实践》 北大核心 2023年第1期113-118,共6页 Mechanics in Engineering
基金 江西省学位与研究生教育教学改革研究项目资助(JXYJG-2021-057)。
关键词 梯形重力坝应力场 应力函数求解 有限元仿真比较 stress field of trapezoidal gravity dam stress function solution finite element simulation comparison
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