摘要
采用理想弹塑性模型,基于Euler梁的几何非线性理论,建立了梁在机械载荷作用下的弹塑性大挠度变形问题的控制方程.包括轴线位移、横截面转角、内力等6个未知函数.该数学模型能够分析弹塑性材料梁在弹性阶段以及塑性区扩展阶段的变形.作为算例,应用打靶法数值求解了水平悬臂梁在自由端受竖向集中力作用下的弯曲问题,绘出了不同载荷参数下的弹性和弹塑性挠度曲线,分析了载荷参数和梁自由端挠度之间的关系.结果表明,打靶法是解决弹塑性梁大挠度变形问题的有效方法.
Based on the geometrically nonlinear theory of Eulerian beam, governing equations of beam deformation with elastic-plastic large-deflection subjected to mechanical loads were established by using ideal elastic-plastic model. 6 unknown functions such as the displacements of central line, rotational angle, and internal resultant forces in the cross section were included in the equations. The deformation of elasticplastic beam in the elastic phase and extending phase of plastic region could be analyzed by using this mathematical model. As a numerical example, elastic-plastic bending of a cantilever beam subjected to a concentrated load at the free end was solved with shooting method. The equilibrium configurations of the deformed beam and the displacement of free end were given for different load parameters. The results showed that shooting method was effective to deal with the deformation of elastic-plastic beam with large-deflection.
出处
《兰州理工大学学报》
CAS
北大核心
2007年第1期170-172,共3页
Journal of Lanzhou University of Technology
基金
国家自然科学基金(10472039)
甘肃省教育厅科研基金(0503-10)
关键词
梁
弹塑性
大挠度
打靶法
beam
elasto-plasticity
large-deflection
shooting method
