Since the explicit weight function and polynomial local approximation functions are used in the high order numerical manifold method (HONMM) with triangular mathematical covers (MCs), the simplex method is a convenient way for the integration in this method. However, this method cannot be used when the integrand function is non-polynomial. So, in the current paper by examining some of the existing Gaussian Legendre methods over the triangular region and modifying them to avoid the crowding of quadrature points, an alternative proposal for integration in HONMM is provided. To investigate the problems with the non-polynomial integrand function, the three-node complex Fourier shape function is used as the weight function in HONMM. Also, to survey the complicated geometry in the integration process the non-conform MCs are used. Five examples for testing integration methods, including three tests for elastostatic and two tests for elastodynamic problems are simulated by HONMM. Also, an example of 1/r^αsingularity that occurs during crack propagation modeling in the singular patch is evaluated. The results show that the composite integration method is a suitable alternative method for problems where the simplex integration is limited.

由于显式权重函数和多项式局部逼近函数用于具有三角形数学覆盖（MCs）的高阶数值流形法（HONMM），单纯形法是该方法中集成的一种方便方式。但是，当被积函数是非多项式时，不能使用此方法。因此，在当前的论文中，通过在三角形区域上检查一些现有的高斯勒让德方法并对其进行修改以避免正交点的拥挤，提供了一种在 HONMM 中集成的替代建议。为了研究非多项式被积函数的问题，在 HONMM 中使用三节点复数傅里叶形状函数作为权重函数。此外，为了调查集成过程中的复杂几何形状，使用了不合格的 MC。HONMM模拟了五个测试集成方法的例子，包括三个弹性测试和两个弹性动力学问题测试。另外，一个例子 1/评估了在奇异补丁中的裂纹扩展建模过程中出现的r ^{α奇异性。}结果表明，复合积分法是解决单纯形积分受限问题的一种合适的替代方法。