SGER: Stochastic and Convex Finite Element Methods Asociated with Micromechanics

9910195针对随机结构，即那些包含随机弹性和/或几何特性，并承受随机或未知但有界荷载的结构，发展了一种新的有限元方法。该方法基于微观力学。现有文献很好地涵盖了所涉及的随机参数的变异系数、场的函数很小以及随机场是现象学定义的情况。实验证据表明，对于中等或较大变异系数的情况，有必要推广现有技术。目前解决这些问题的唯一方法是蒙特卡罗方法。在这里，将开发一些不需要使用蒙特卡罗方法的有效数值方法。建立了新的变分原理来处理剪力梁、梁板弯曲和壳的变形。所开发的技术结合微观力学，对随机参数的小、中、大变化都是有用和有效的数值技术。此外，第一次，凸有限元将发展为问题的概率信息是不可用的。

9910195Novel finite element method is developed for stochastic structures, i.e. those involving random elastic and/or geometric properties and subjected to random or unknown-but-bounded loads. The method is based on micromechanics. Existing literature covers well the cases when the coefficient of variation of involved random parameters, functions of fields are small, as well when the stochastic fields are defined phenomenologically. The experimental evidence necessitates for generalization of existing techniques for the case of moderate or large coefficients of variation. The only procedure existing today to tackle these problems is the Monte Carlo Method. Here, some effective numerical methods will be developed that do not necessitate the use of the Monte Carlo Method. Novel variational principles are established to deal with shear beams, bending of beams and plates, deformation of shells. The developed techniques constitute useful and efficient numerical techniques for both small, moderate or large variation of stochastic parameters, in conjunction with them being based on micro-mechanics. In addition, for the first time, the convex finite elements will be developed for problems where probabilistic information is unavailable.