横截面为直角梯形的圆孔凹模板刚度理论

RIGIDITY OF A CONCAVE TEMPLATE OF RIGHT ANGLE TRAPEZOID CROSS SECTION WITH A CIRCULAR APERTURE

采用线弹性平板理论,对均匀、连续、各向同性材料制成的变横截面为直角梯形的圆孔凹模板刚度计算理论进行了研究.首先建立力学和数学计算模型,其次,针对承受垂直冲裁力的圆形孔凹模板,建立了用挠度表示的三阶变系数常微分方程,并给出了新的边界条件,然后采用半逆解法求解,进行弯曲问题的挠度计算,进而确定刚度计算理论,最后进行实例分析.

Based on the linear elastic plate theory,the rigidity of a concave template of a right angle trapezoid cross section made of homogeneous,continuous and isotropic material with a circular hole is calculated.At first,a mechanical and mathematical calculation model is built.Secondly,the third order variable coefficient differential equation expressed in deflection is obtained with boundary conditions.And then,the deflection is obtained,as well as the rigidity.Finally,an application example is given.