Mathematical Sciences: Theoretical and Computational Methods in Optimal Design of Elastic Structures

小行星9625129 本文提出了一个弹性和非弹性结构优化的研究方案， 结合了现代变分技术的导体， 均匀化和新的计算方法。 由于结构 优化问题通常是不适定的，如所述，效率和 这些问题的数值算法的稳定性取决于 一个适定问题的理论公式。预期结果 包括非凸变分问题松弛方面的进展， 发现具有极端特性的新微观结构， 高度敏感问题的有效算法。述应用程序包括 实时设计实用的优化结构，如转子，圆柱形， 壳，轮，圆顶等。各种效率泛函，如 总刚度、主本征频率、加权挠度等， 考察 还将系统地选择次优项目， 考虑了 这项研究涉及改进和整合最好的电流 系统设计的理论和计算方法 具有最佳性能特征的结构。这允许 降低材料的总成本及其重量， 影响航空航天和类似应用中的最终成本。 的 理论方面涉及理解最优的 微观结构，而计算方面涉及分布和 对这些复合材料进行改性以最好地适应实际工作条件。 设计方法和设计本身的效率 应证明在工业应用中是有利的。

9625129 Cherkaev A program of research is proposed for structural optimization of elastic and conducting bodies which combines modern variational techniques, homogenization, and new computational methods. Since structural optimization problems are typically ill-posed as stated, the efficiency and stability of numerical algorithms for these problems depends upon theoretical formulation of a well-posed problem. The expected results include advances in relaxation of non-convex variational problems, discovery of new microstructures with extremal properties, and developing effective algorithms for highly sensitive problems. The applications include real-time design of practical optimal structures, such as rotors, cylindrical shells, wheels, domes, etc. Various efficiency functionals such as the overall stiffness, principal eigenfrequency, weighted deflection, etc. will be examined. Systematic selection of suboptimal projects will also be considered. The research involves improving upon and integrating the best current theoretical and computational methods for systematically designing structures with optimal performance characteristics. This permits the reduction of the overall cost of materials, and their weight, which greatly influences the ultimate cost in aerospace and similar applications. The theoretical aspect involves understanding the nature of optimal microstruatures, while the computational aspect involves distributing and modifying these composites to best adapt to practical working conditions. The efficiency of both the design methods and the designs themselves should prove advantageous in industrial applications.