摘要
在本文中首先提出各向异性薄壳张量形式的变分原理,其中包括势能原理和混杂变分原理。当前立交桥和高速公路发展迅速,亟需圆曲线桥的有效和精确的计算方法。为此目的,作为特例,列出平面极坐标情况的变分原理。 在梁、板式桥梁中常将梁、板看成各向异性的板。本文第二部分,对两个方向的刚度张量和柔度张量进行了推导,并分别考虑了直角坐标和平面极坐标两种情况。 混杂元法是求解平板问题的良好方法。根据文中提出的混杂变分原理,本文推导了四边扇形混杂单元的性质矩阵和折算荷载。最后,用以上混杂有限元法作了曲线桥的计算实例。为了便于了解曲线桥的变位和受力情况,在算例中绘制了变位和弯(扭)矩的影响场。
In this paper, the variational principle of orthotropic shell in tensor form,including the potential principle and the hybrid variational principle, is pro-posed. Since multi-structure interchange and expressway are developed rapidlynowadays, it is urgently needed to have an effective and accurate computationalmethod for circular curved bridge design.For this purpose, the variationalprinciple in plane polar coordinates is particularly presented. In beam-slab bridge, the beam-slab is usually regarded as an orthotropicplate. In the second part of this paper, the rigidity tensors and flexibility ten-sors for two directions are derived, and both cases of Cartesian coordinatesand plane polar coordinates are considered respectively. The hybrid finite element method is a fine method for solving plate problems.According to the hybrid variational principle proposed in this paper, the behavi-our matrix and reduced loads of the fan -shaped hybrid element are derived.Finally,a numerical example by use of the above finite element method is given.For finding the deflections and stresses of the curved bridge in this example,the influence fields of deflection and bending (torque ) moment are drawnup.
出处
《土木工程学报》
EI
CSCD
北大核心
1989年第3期23-38,共16页
China Civil Engineering Journal
