Discussion on the pedagogy of concept of limit , definite integral and double integral 二重积分概念教法之探讨
The volume integrals can be transformed to surface integrals using gauss ' s theorem . two cases are studied , one is floating upright and another is free floating in 3d space 运用gauss定理,关于空间封闭区域的三重积分可以转化为沿封闭边界曲摘要面的二重积分。
In computation of stiffness matrix , the calculation of double singular integration is needed . the exactly integral formula is used in the inner integral expression , and the numerical integral formula is used in the outer integral expression 在计算单元刚度矩阵时,对二重积分的第一重使用精确积分,第二重使用数值积分,从而有效的克服了奇异积分的计算。
Generalize the integral characters of the odd and even functions of the unary definite integral in the symmetrical interval about the origin are generalized to the double integral of binary symmetrical functions in the symmetrical region , where similar characters are obtained 摘要导出了把一元定积分中奇、偶函数在关于原点的对称区间上的积分性质推广到在对称区域上的二元对称函数的二重积分的情形。
And the thickness of the overlay is achieved . the target of this paper is to set up connection between ndt and the methods . if flexibility of the overlay is measured , the thickness of it is gotten straightly through this connection 然后将解析解的表达式经过一系列恒等变换,得到二维有限区域上二重积分的形式;进行二维fourier反变换,利用高斯积分编制计算程序,求出数值解,并以此为基础通过目标优化得到加铺层厚度。