SGER: Stochastic and Convex Finite Element Methods Asociated with Micromechanics

SGER：与微观力学相关的随机和凸有限元方法

• 批准号: 9910195
• 负责人: Isaac Elishakoff
• 金额: $ 4万
• 依托单位: Florida Atlantic University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9910195&HistoricalAwards=false
• 关键词: SGER; Stochastic; Convex; Finite; Element

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.

9910195提出了一种用于随机结构的新的有限元方法，即涉及随机弹性和/或几何特性并承受随机或未知但有界载荷的结构。该方法是基于微观力学。现有的文献很好地涵盖了所涉及的随机参数，场函数的变异系数小的情况下，以及当随机场的定义是唯象的。实验证据需要推广现有的技术的情况下，中等或大的变异系数。目前解决这些问题的唯一方法是蒙特卡罗方法。在这里，将开发一些有效的数值方法，这些方法不需要使用蒙特卡罗方法。建立了新的变分原理来处理剪切梁、梁和板的弯曲、壳的变形。所开发的技术构成有用的和有效的数值技术的随机参数的小，中或大的变化，结合他们是基于微观力学。此外，第一次，凸有限元将开发的概率信息是不可用的问题。