摘要
挠度与转角独立插值的Timoshenko梁在板架及高腹板梁的计算中具有很大优势,但传统的采用Lagrange插值的Timoshenko梁单元计算误差较大,且在细长梁情况下易发生剪切锁死。本文从Timoshenko梁理论出发,采用假设剪切应变法,将假设剪切应变的插值函数分别用三角函数、二次多项式及指数函数表示,得到3种两节点四自由度梁单元。这些单元不会发生剪切锁死,且在无论是细长梁还是高腹板梁的计算中均具有不错的精度,特别是在高腹板梁情况下计算结果尤其准确。同时该新型单元表达格式简单,计算效率较高,易于运用。
The Timoshenko beam use independent deflection and rotation interpolating shape function,and it is very effective in the calculation of grillage structure and high web beam. However,the traditional Timoshenko beam element which used Lagrange interpolating function is not accurate enough,and shear locked phenomena will happen in the slender beam calculation. This article base on the Timoshenko beam theory and assumed shear strains theory,using the trigonometric function,quadratic polynomial and exponential function as the assumed shear strains interpolating function. Three 2- nodes 4-freedoms beam elements are deduced. These elements can avoid the shear locked phenomena. Calculation results show that these elements are accuracy in both slender beam and high web beam calculation,and the result is especially precise in the high web beam calculation. These elements have relatively simple formulation,better computational efficiency and easy to use.
出处
《舰船科学技术》
北大核心
2015年第S1期35-40,共6页
Ship Science and Technology
