特高拱坝有限元网格尺寸与离散误差分析

ANALYSIS ON FINITE ELEMENT MESH SIZE AND DISCRETIZATION ERROR FOR SUPER-HIGH ARCH DAM

与世界上200米级高度以上的特高拱坝相比,我国已建和在建的6座特高拱坝具有顶底宽度比、顶底厚度比和弧高比均大的特殊体型和齐顶总水压力大的特点.论文在推导了形状和受力均与特高拱坝相近的空心球体热-结构耦合计算公式、并进行理论解和有限元解误差对比分析的基础上,以我国某特高拱坝为例,按照拱冠梁底部厚度作为划分坝体单元尺寸指标,采用易于剖分特殊体型的普通四面体二次耦合单元,方便快捷地实践了该种单元对某特高拱坝的网格划分,探讨了不同有限元网格密度的误差和收敛情况,分析了拱坝的特殊受力状况,并提出了在普通微机上采用该种单元和强耦合方法操作计算特高拱坝力学行为时,从计算精度、方便操作和计算成本等方面均可接受的坝体单元尺寸.研究表明,只要坝体单元尺寸取为0.25倍坝底厚度左右时,除应力奇异和集中区外,其余大部分区域的计算结果误差均很小,坝体能量误差泛数小于10%,计算成本也仅是几分钟.由于我国特高拱坝的形状都较为相近,此结论具有一定的广延性.

Compared with the world super-high arch dams with height more than 200 meters,the six super-high arch dams already built or under construction in China share the same special body shapes with higher ratios for both top/bottom width and thickness,and for top arch length with dam height.Also all of them are subjected to higher top-level water pressures.In the paper,the computational formulation of thermal-structure coupled hollow sphere similar to arch dam in shape and load-subjected is derived first and analysis of errors from the finite element method compared with the analytic solution is made.Then,a typical super-high arch dam is taken as the example of structure analysis including dam body mesh division,stress distribution,error estimation and so on.Employing quadrilateral Coupled-field tetrahedral element with size decided by the bottom thickness multiple of arch crown beam,performance of mesh division and analysis for complex model is done conveniently and fast.Also,the paper investigates the error and convergence of results with different mesh density,discusses the special stress states of arch dam,and proposals acceptable dam body element size from calculation accuracy,convenient operation and elapsed time when performance is carried on with strong coupling on conmen personal computers.The research work indicates that errors of analysis results in most part of area are very small excepting those for the local singularity and concentration part when the dam body element size is decreased to 0.25 multiple of bottom thickness of arch crown beam,with dam body energy error norm less than 10%and consuming a couple of elapsed time.The conclusion should be common for the arch dams in China as they have similar shapes.