广义函数及其在力学中的应用述评

Comment on Generalized Functions and Their Application in Mechanics

简要介绍了广义函数的发展,给出了力学中常用的广义函数(即奇异函数)的定义及其微分、积分运算法则,分析了广义函数在力学各分支中的应用现状,通过用广义函数表示集中力作用下固支圆板的面分布集度来求解板弯曲挠度的实例,说明运用广义函数解决一些力学问题的优越性.

The development of the generalized functions, arid the definition of the commonly used generalized functions in mechanics （namely, singularity functions） and their operative principles are briefly introduced. Then the present status of generalized functions in all branches of mechanics is analyzed. The superiority of using the generalized functions to solve mechanic problems is illustrated by an example of the bending deflection of clamped circular plate under the concentrated force, using the generalized function to express the surface distribution density of the concenlrated force.