用Kantorovich及Galerkin联合法研究双模量板的弯曲

Kantorovich and galerkin solution to the bending of bimodulous plate

双模量矩形板在外载荷作用下,会形成各向同性的拉伸区和压缩区,因此可把双模量矩形板看成两种各向同性材料组成的层合板,采用弹性力学理论建立了双模量矩形板在外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矩形板的中性面位置.在此基础上,采用Kantorovich及Galerkin联合法研究了双模量矩形板的弯曲问题.把该方法计算结果与有限元计算结果进行了比较分析,验证了此方法计算精度比较高.算例分析表明,当双模量矩形板材料的拉压弹性模量相差较大时,其弯曲计算不宜采用相同弹性模量经典薄板理论,而应该采用双模量弹性理论.

Bimodulous rectangular plate could form isotropic compression and tensile area under uniform load. Bimodulous rectangular plate was regarded as laminated plate composed of two kind of otropic material. Static equilibrium equation of bimodulous plate under uniform load was established by using elastic mechanics theory. The location of neutral plane in bimodulous rectangular plate was determined by the utilization of static equilibrium equation. Then the bending deforma- tion of bimodulous rectangular plate under uniform load was studied with Kantorovich and Galerkin variational method. And the calculation results were compared with that obtained by finite element, and it shows that Kantorovich and Galer- kin variational method is reliable. The main conclusions are as follows., the deflection calculation of bimodulous rectangular plate which has larger difference between tensile elastic modulus and compressive elastic modulus may as well not apply classical plate-shell theory with the same elastic modulus, and should use bimodulous elastic theory.