结构动态应力计算方法研究
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摘要
复杂结构动态应力的准确计算是一个没有圆满解决的问题。本文以最小余能原理为基础 ,提出了计算结构动态应力的最小余能法。该方法采用二次分析思想 ,首先采用常规有限元对结构进行适当离散 ,计算输出结构所需应力区域的有限元结点位移和加速度动力时程反应 ,再应用最小余能法计算所求部位的动态应力值。这种方法的优点是它可以与现有的有限元程序有机结合 ,方便使用 ;动应力在区域内的分布规律可以由计算者根据具体情况而确定 ,一般情况下 ,可以选用二次曲线来逼近动应力在区域内的实际分布 ,避免了常规有限元法计算结构动应力时必须对单元形函数求导的做法 ,从而提高了动应力计算精度。计算结果表明 :本文方法计算结构动态应力结果较常规有限元法的计算结果有明显改进 ,特别是当结构变化剧烈时 ,改进效果更为明显
The accurate calculation of complex structure dynamic stress has not been fully solved in structure dynamics. In this paper, based on the variational principle of minimum complementary energy, the method of minimum complementary energy is put forward in calculating structure dynamic stress. With quadratic analysis thought used in this method. conventional finite element method is adopted to make a moderate discretion in the structure first. Next the finite element node displacement and the acceleration dynamic time history response are calculated and output for the stress area needed by the structure. Then the method of minimum complementary energy is used to calculate median dynamic stress value. The advantage of this method is that it can be closely combined with current finite element program and is easy to use. The distributing rule of dynamic stress in the region can be determined by calculating practical instances. For most instances conic can be selected to approach the actual distribution of dynamic stress in the region. So derivativing element shape function, which is necessary in calculating structure dynamic stress with regular method, can be bypassed. Consequently the precision of dynamic stress calculation is improved. The result of calculation using this method indicates that compared with that of conventional finite element calculation, there exists a distinct improvement in calculating structure dynamic stress. It is especially notable when the structure changes drastically.
The accurate calculation of complex structure dynamic stress has not been fully solved in structure dynamics. In this paper, based on the variational principle of minimum complementary energy, the method of minimum complementary energy is put forward in calculating structure dynamic stress. With quadratic analysis thought used in this method. conventional finite element method is adopted to make a moderate discretion in the structure first. Next the finite element node displacement and the acceleration dynamic time history response are calculated and output for the stress area needed by the structure. Then the method of minimum complementary energy is used to calculate median dynamic stress value. The advantage of this method is that it can be closely combined with current finite element program and is easy to use. The distributing rule of dynamic stress in the region can be determined by calculating practical instances. For most instances conic can be selected to approach the actual distribution of dynamic stress in the region. So derivativing element shape function, which is necessary in calculating structure dynamic stress with regular method, can be bypassed. Consequently the precision of dynamic stress calculation is improved. The result of calculation using this method indicates that compared with that of conventional finite element calculation, there exists a distinct improvement in calculating structure dynamic stress. It is especially notable when the structure changes drastically.
引文
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3 王博.大型渡槽结构地震反应分析理论与应用[D].上海:同济大学博士学位论文,2000
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2 陈淮.考虑剪切变形的框架结构动力分析的动态有限元法[J].地震工程与工程振动,1994,Vol.14,No.2:102～113
3 王博.大型渡槽结构地震反应分析理论与应用[D].上海:同济大学博士学位论文,2000
4 季文美,方同,陈松淇.机械 振动[M].北京:科学出版社,1985:375～382
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