Mathematical Sciences: Computation, Control, Optimization and Vibration Analysis of Shell Equations

数学科学：壳方程的计算、控制、优化和振动分析

• 批准号: 9404380
• 负责人: Goong Chen
• 金额: $ 9.9万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9404380&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Computation; Control; Optimization

9404380 Chen/Zhou This research will focus on (1) the formulation of boundary integral equations and development of boundary element schemes and software for dynamic shell equations; (2) the analysis of vibration eigenfrequencies and damping rates of dynamic shell equations; (3) the study of qualitative stability properties of shells when damping is present; (4) structural shape control and optimization, for several thin or shallow circular cylindrical, conical, and spherical shell models. Shells are known to have advantageous structural properties. Under suitable design, even very thin shells can support large loads. They are therefore widely used in aircraft and ship structures where light weight is essential. In other cases, such as pressure-vessels, roofs and domes, the combined strength and enclosing properties of shells are utilized. Mathematically, shells are described by coupled systems of partial differential equations of higher order. This research is directed towards (1) computing the deformation and stress distribution of shells in aerospace, civil and maritime structures (in particular, with efficiency greatly surpassing the traditional finite element method); (2) providing feedback designs of control systems that can stabilize dynamic shell motion; (3) analyzing and simulating ``smart structure control'' of shells such as the automatic tuning of the radius of curvature of a spherical shell in a deformable mirror.

9404380陈/周 本文的主要研究内容包括：（1）动力壳方程的边界积分方程的建立、边界元格式和软件的开发;（2）动力壳方程的振动本征频率和阻尼率的分析;（3）动力壳方程的定性稳定性研究;（4）动力壳方程的边界元格式和软件的开发;（5）动力壳方程的振动本征频率和阻尼率的分析;（6）动力壳方程的定性稳定性研究。（4）结构形状控制与优化，针对几种薄或浅圆柱壳、圆锥壳和球壳模型。 已知壳体具有有利的结构特性。 在适当的设计下，即使是非常薄的壳体也可以承受很大的载荷。 因此，它们被广泛用于飞机和船舶结构，其中重量轻是必不可少的。 在其他情况下，如压力容器，屋顶和圆顶，利用壳的综合强度和封闭性能。 在数学上，壳体由高阶偏微分方程的耦合系统描述。 本文的研究工作是：（1）计算壳体的变形和应力分布， 航空航天、民用和海洋结构（特别是其效率大大超过传统的有限元法）;（2）提供控制系统的反馈设计，使动态壳体运动稳定;（3）分析和模拟壳体的"智能结构控制“，如变形镜中球形壳体曲率半径的自动调节。