拟梁等参单元和坝内垫层钢管的应力分析

Beam-imitative isoparametric element and Beam—imitative isoparametric element and Stres analysis for penstock with cushion layer

坝内垫层钢管的应力分析,由于钢管和垫层的厚度相对很小,垫层端部应力梯度较大,使用常规有限单元很难得出满意的结果,特别不能正确求出垫层端部的局部应力。作者提出一种拟梁等参单元,这种单元描述位移和应力变化的能力在一个方向很强,而在与之正交的方向相对较弱。它很适合用于坝内垫层钢管的应力分析。本文采用拟梁等参单元对三峡工程坝内钢管的设计比较方案等进行了计算,计算结果与试验结果吻合较好。计算结果表明:钢管应力,有垫层段远大于无垫层段,在垫层端部存在较大的局部应力;垫层弹模值的大小对钢管应力影响较大。垫层弹模值越小,传递到混凝土的荷载也越小,越靠近垫层端部这种影响越显著。三峡工程的钢管,当管壁厚度为4.6cm时,垫层弹模值以略大1.0MPa为宜。

For the stress analysis of the penstock with cushion layer embedded in the concrete dam, due to the relatively small thicknesses of the penstock and cushion layer and the relatively high stress gradients around the ends of the cushion layer, it is difficult to solve by means of the conventional finite elements, especially for the local stresses around both ends of the cushion layer. A kind of isoparametric element is developed in this paper by imitating beam deformation and thus called beam—imitative isoparametric elements. The ability of the elements in expressing the displacement or the stress gradient is rather high in one direction while relatively low in the normal direction. This just fits the case of the stress analysis of the embedded penstock with cushion layer. An element of the kind is used in the stress analysis for the embedded penstocks of the Three Gorges Project. The computational results are in accord with their corresponding experimental results. The result also shows that the stress of the penstock is much bigger in the cushion layer section than elsewhere, that rather large local stresses exist at the ends of the cushion layer, and that the modulus of elasticity of the cushion layer will greatly affect the penstock stresses, i. e. the lower the modulus, the smaller will be the load transmitted to the concrete, and the effect is more obvious near the ends of the cushion layer. For the Three Gorges Project, if the thickness of the penstock is 4. 6 cm, a value of such modulus of a little bigger than 1. 0 MPa will be feasible.