A Novel Approach in Formulation of Special Finite Elements

特殊有限元公式化的新方法

• 批准号: 8709558
• 负责人: Nesrin Sarigul-Klijn
• 金额: $ 1.2万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-10-01 至 1989-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8709558&HistoricalAwards=false
• 关键词: Novel; Approach; Formulation; Special; Finite

The research includes a new approach to develop more accurate and efficient techniques for solution of three dimensional problems with discontinuities and local nonlinearities. The finite element method owes its significance to its potentiality for the treatment of rather arbitrary geometry, and different material properties. One may build a special finite element that contains the discontinuity in the element formulation, and couple the special element to the mesh that models the rest of the system. The special element formulation, unlike others, will incorporate already existing classical solutions into the element formulations. The displacement function, for structural problems for example, used in approximations will exactly satisfy the analytical results wherever available. This will be achieved by invoking the classical solutions as constraints in the derivation of element stiffness coefficients. This research will bring about a new technique to handle discontinuities, local geometric-material nonlinearities at local level without requiring mesh refinements. For numerical comparison purposes a computer program will be developed.

该研究为开发具有不连续和局部非线性的三维问题的更精确和有效的求解技术提供了新的途径。有限元法的意义在于它可以处理相当任意的几何形状和不同的材料性质。人们可以建立一个特殊的有限元，它包含了单元公式中的不连续，并将特殊的单元耦合到对系统其余部分建模的网格上。特殊的元素公式，不像其他的，将已经存在的经典解决方案纳入元素公式。例如，对于结构问题，在近似中使用的位移函数将完全满足可用的分析结果。这将通过调用经典解作为推导单元刚度系数的约束来实现。本研究将提供一种新的技术来处理局部不连续性，局部几何材料非线性，而不需要网格的细化。为了进行数值比较，将开发一个计算机程序。