Structural Optimization and Parallel Computation

结构优化与并行计算

• 批准号: 9108787
• 负责人: Thomas Coleman
• 金额: $ 4万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9108787&HistoricalAwards=false
• 关键词: Structural; Optimization; Parallel; Computation

The proposed research will exploit parallelism in unconstrained structural optimization problems involving Finite Element Analysis (FEA). Typical engineering problems involve large finite element models and optimization algorithms take several hundred iterations. Parallel finite element analysis and optimization cannot be decoupled because calculation of gradients is closely tied with the function evaluation (FEA), requiring proper distribution of data such as global stiffness matrix and displacement solution across processors. Since the total computational cost is dominated by the cost of function evaluation, methods that result in fewer function evaluations at the expense of more linear algebraic operations per iteration might be preferred. This might require the calculation of second derivatives in order to obtain a better quadratic model. The parallelization of linear elastic finite element analysis and parallel calculation of first and/or second derivatives will be considered. In the area of biomechanics, researchers are using optimization methods to predict the distribution of material properties in the human femur due to the presence of artificial implants. Several theoretical models have been proposed. A typical model would formulate bone remodeling as an optimization problem where the objective function is strain energy and the independent variables are the material properties in each finite element. Parallel structural optimization will be used to solve some problems in this field.

拟议的研究将利用并行 有限长无约束结构优化问题 有限元分析。 典型的工程问题包括 大型有限元模型和优化算法 几百次迭代。 并行有限元分析与 优化无法解耦，因为梯度计算 与功能评估（FEA）密切相关，需要 适当的数据分布，如整体刚度矩阵和 跨处理器的位移解决方案。 由于总 计算成本主要由函数成本决定 评估，导致更少功能评估的方法， 每次迭代的更多线性代数运算的代价 可能会更喜欢。 这可能需要计算秒 为了获得更好的二次模型，需要对导数进行修正。 的 线弹性有限元分析的并行化 一阶和/或二阶导数的并行计算将是 考虑了 在生物力学领域，研究人员正在使用 优化方法来预测材料的分布 由于存在人工的， 植入物. 已经提出了几种理论模型。 一 典型的模型将骨重建公式化为优化 问题的目标函数是应变能和 独立变量是每个有限单元中的材料属性， 元素 并行结构优化将用于解决 这一领域的一些问题。