通用截面特性计算软件开发研究

Research on the Development of Common Calculation Software for Section Property

为找到一种适用于任意截面形式的截面特性计算方法,开发通用高效的计算软件,通过对截面特性中面积、静矩、惯性矩和惯性积的数学表达式进行深入研究,运用格林公式将截面特性的数学表达式中对面积的二重积分转换为对截面边界曲线的积分,代入曲线参数方程将边界曲线的二元积分转换为一元积分,利用牛顿-莱布尼兹公式精确求解截面特性,进而采用面向对象方法开发通用截面特性计算软件。软件使用灵活方便,适用于实体或空心,整体或分离,单一或组合材料的任意组合截面形式。通过在大量工程设计项目的应用表明:本方法计算结果精确,计算效率高,实用意义突出。

In order to find a section property calculation method for arbitrary cross sections and develop the common efficient software,the mathematical expressions of area,static moment,moment of inertia and product of inertia are studies deeply. The area double integral boundary curve integral in the section property mathematical expressions is transformed to boundary curve integral with Green formula. The boundary curve integral from tow parameter is converted to one parameter by curve parameter equation.The section properties are calculated by Newton Leibniz formula,and then,the common section property calculation software is developed by means of object-oriented method. The software is proved to be flexible and convenient,and suitable for arbitrary composite sections. The application in a large number of engineering design projects shows that the method is accurate and efficient with prominent practical significance.