双模量悬臂梁在分布荷载作用下的Kantorovich解

双模量悬臂梁在均布载荷作用下发生弯曲变形时,会形成各向同性的拉伸区和压缩区.在此种情况下,把双模量悬臂梁看成2种各向同性材料组成的层合梁,采用弹性理论建立了双模量悬臂梁在均布载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量悬臂梁的中性面位置.在此基础上,利用Kantorovich法研究了分布载荷作用下双模量悬臂梁的平面应力问题,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,分布载荷作用下双模量悬臂梁的平面应力问题,不宜采用相同弹性模量弹性理论,而应该采用双模量弹性理论.

The Kantorovich solution for bimodulous cantilever under distributed loads

Bimodulous cantilever formed isotropic compression and tensile area under distributed load.Bimodulous cantilever was regarded as laminated beam composited of two kind of otropic material.Static equilibrium equation of bimodulous cantilever under distributed load was established by using elastic mechanics theory.The location of neutral plane in bimodulous cantilever was determined by the utilization of static equilibrium equation.Then it was studied that plane stress problem of bimodulous cantilever under distributed loads by Kantorovich method,meanwhile the stress formula was derived.The calculation results were compared with that obtained by finite element method,the reliability of this method was verified.The analysis of examples indicated that the plane stress problem of bimodulous cantilever under distributed loads may as well not apply classical elastic theory with same elastic modulus,and should use bimodulous elastic theory.