侧向均布剪应力作用下双模量悬臂梁的弹性解

利用弹性理论研究了双模量悬臂梁在侧向均布剪应力分布载荷作用下的平面应力问题,推导出了悬臂梁的应力公式.并把该应力公式的计算结果与有限元法的计算结果进行了比较,验证了双模量悬臂梁的应力公式是可靠的.算例分析表明:双模量悬臂梁的拉压区的弯曲应力随着双模量悬臂梁的长高比的增大而增大;采用相同弹性模量弹性理论研究双模量悬臂梁平面应力问题时,得到的弯曲应力公式与材料的弹性模量无关;采用双模量弹性模量弹性理论研究双模量悬臂梁平面应力问题时,得到的弯曲应力公式与材料的弹性模量有关.双模量悬臂梁材料的拉压弹性模量相差较大时,平面应力问题计算应采用双模量弹性理论.

The elastic solution for bimodulous cantilever beam under lateral uniform shear stress loads

It was studied that the plane stress problem of bimodulous cantilever beam under lateral uniform shear stress loads, meanwhile the stress formula were derived. And the calculation results were compared with that obtained by finite element, also the reliability of the stress formula for bimodulous cantilever beam was verified. The analysis of examples indicated that with the increase of length and height ratio of bimodulous cantilever beam, the bending stress of bimodulous cantilever beam increase accordingly, and the bending stress formula for bimodulous cantilever beam was independent of elastic modulus as using the same elastic modulus elastic theory to study the plane stress problem of bimodulous cantilever beam, however, which was related to elastic modulus as using the bimodulous elastic theory. Therefore, the elastic theory of difference elastic modulus in tension and compression should be used when the difference between tensile modulus and compression modulus is large.