用数值流形法分析温度场及温度应力

Thermal Field and Thermal Stress Analysis Based on Numerical Manifold Method

应用有限元法进行大体积混凝土结构的温度应力仿真分析时,为获得满意的计算精度,往往需要剖分比较密集的网格,计算工作量大。鉴于数值流形法具有自适应分析和网格剖分方便等优点,推导了基于高阶流形法的温度场及温度应力计算公式,公式中的被积函数均是多项式基底的乘积,可以直接采用单纯形积分法进行精确积分。在此基础上,开发了相应计算程序,为大体积混凝土结构的温度应力仿真计算开辟了新的途径。算例表明,在粗网格情况下,通过提高覆盖函数的阶数,数值流形法可迅速提高计算精度。

To obtain satisfied results with a high precision in the thermal stress analysis simulating construction process of mass concrete structures by using FEM, the refined finite element mesh is necessary and thus much computation is required. Being convenient in adaptive analysis and in mesh division, the numerical manifold method （NMM） is introduced to compute thermal field and thermal stresses and the formulae based on highorder NMM are derived. According to the derived formulae, in which all integrands are only the product of polynomial bases and convenient for implementation of the simplex integration, a program is developed and verified by examples, providing a new approach for the thermal stress analysis of mass concrete structures. Examples show that the NMM can rapidly improve the results by raising the order of cover function on a coarse mesh.