Development of Space-Time Finite Elements for Nonlinear Transient Response of Flexible Structures

柔性结构非线性瞬态响应时空有限元的发展

• 批准号: 8822003
• 负责人: Dewey Hodges
• 金额: $ 15.44万
• 依托单位: Georgia Tech Research Corporation - GA Tech Research Institute
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-11-15 至 1993-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8822003&HistoricalAwards=false
• 关键词: Development; Space; Time; Finite; Elements

This project focuses on the computational difficulties associated with steep gradients in the velocity and displacement fields in structures subjected to impulsive loadings. The conventional finite element approach would suggest creating a finer element mesh around the areas with large gradients, but since the gradients move through the structure, such a procedure is not efficient. This could be solved by increasing the number of finite elements throughout the structure, but it would be computationally impractical to do so. An alternative approach would call for formulation of the problem in terms of a modal analysis. The large number of modes thereby required to model the structure implies similar computational difficulties. A third alternative, finite differences in space and time is computationally inefficient for use in design oriented analysis. The approach adopted herein, finite elements formulated in the space time domain, offers the possibility of overcoming these computational problems. Three classes of physical systems will be analyzed including a string under constant tension, a string under nonuniform tension, and a linear Timoshenko beam. For the string models, initial value problems including those for which a wave travels down the string will be solved as well as those involving moving load and impulsive load problems. For the Timoshenko beam, moving loads and moving constraint problems will be considered. The project comprises three phases including: (1) determining shape functions and convergence criteria for finite elements that cut across space and time; (2) computing solutions for string problems and study of convergence properties, and set up of the general solution for a space time finite element formulation for Timoshenko beams; and (3) determining solutions for beam problems with moving loads and moving constraints. The impact of this research will be on the methods of analysis for systems with moving loads or constraints, deployment problems, and flexible manipulator arms.

这个项目的重点是相关的计算困难 在速度和位移场中具有陡峭的梯度， 承受冲击荷载的结构。 常规 有限元方法建议创建更精细的单元 网格周围的地区与大梯度，但由于 梯度通过结构移动，这样的过程不是 高效. 这可以通过增加 整个结构中的有限元，但它将是 这样做在计算上是不切实际的。 另一种方法 将要求用一种模式来表述这个问题， 分析. 大量的模式，从而需要建模 该结构意味着类似的计算困难。 一 第三种选择，空间和时间的有限差异， 在面向设计的分析中使用计算效率低。 本文采用的方法，有限元公式， 空间时间域，提供了克服这些的可能性 计算问题。 三类物理系统将 包括在恒定张力下的弦，弦 在非均匀张力下，和线性的Kroshenko梁。 为 弦模型，初始值问题，包括那些 波沿着弦传播的问题也将得到解决， 涉及移动载荷和冲击载荷问题。 为 将移动荷载和移动约束问题 被考虑。 该项目分为三个阶段，包括：（1） 有限差分法形函数的确定及收敛准则 跨越时空的元素;（2）计算解决方案 用于弦问题和收敛性质的研究，并设置 时空有限元的一般解 列式;（3）确定解 具有移动载荷和移动约束的梁问题。 的 这项研究的影响将是对分析方法， 具有移动负载或约束的系统，部署问题， 和柔性操纵臂。