圆孔变厚度凹模板刚度和强度理论的研究  

RESEARCH CONCAVE CIRCULAR HOLE TEMPLATE LINEAR VARIABLE THICKNESS STIFFNESS AND STRENGTH THEORIES

作　　者：李韶杰[1] 

机构地区：[1]陕西科技大学理学院,西安710021

出　　处：《机械强度》2015年第5期940-946,共7页Journal of Mechanical Strength

基　　金：陕西省教育厅自然科学基金项目(2013JK0636)资助~~

摘　　要：研究圆孔线性变厚度凹模板的刚度和强度计算理论。首先建立物理力学模型:凹模板为圆形,外周界固定;中心有圆孔,内周界自由,承受均布垂直外载荷作用。其次,建立数学计算模型:推导凹模板在轴对称条件下,弹性曲面的变系数常微分方程,并给出边界条件数学表达式。再次,针对微分方程的边值问题,按位移法和Matlab算法求解,得出凹模板的挠度函数,并建立凹模板的刚度计算条件。然后,推算出凹模板所承受的弯矩、最大弯矩和应力,从而建立凹模板的强度计算条件。最后算例给出了问题的函数解,以变参数λ控制凹模板截面的变化规律。这样不仅凸显了各量之间的相互依赖关系,还有利于优化,便于讨论和应用。该结果适用于均匀、连续、各向同性材料制成的构件。由于在推算和数据处理过程中带有误差,所以得到的算式是近似的。This paper studies linear variable thickness circular aperture concave template theory of stiffness and strength calculation. First, set up mechanical model ： Template for circular concave, outside the perimeter fixed ; center has a round hole, inside the perimeter free, outside under uniformly distributed vertical load. Secondly, the establishment of mathematical model ： Derivation of concave template in the axisymmetric condition, ordinary differential equation with variable coefficients of elastic curved surface, and gives the mathematical expressions of boundary conditions. Again, in view of the differential equation boundary value problem, the displacement method and the Matlab algorithm, it is concluded that the deflection of concave template function, and establish the stiffness calculation condition of concave template. Then, determine the concave template on the bending moment and the maximum bending moment and stress, so as to establish a concave template strength calculation conditions. Finally, numerical examples. This paper presents the function solutions, to change law of control concave template section variable parameters. In this way, not only highlight the interdependent relationship between the quantity of each, and optimization, and discussion and application. The result is suitable for uniform, continuous, isotropic material artifacts. Because in the process of calculation and data processing with error, so the formula is similar.

关 键 词：线性变厚度 圆孔凹模板 刚度计算 强度计算 

分 类 号：TH213[机械工程—机械制造及自动化]