辅助空间高精度重分析快速计算方法研究

Personality is the trend of product design in the future. Therefore, the major challenge of the product design is to reduce the develop cycle under the premise of high quality of design. It is also an important factor to ensure competitiveness of enterprises. Therefore, the computational method becomes more and more important in product design. As an important method of computational methods, the main beautiful characteristic of reanalysis method is to avoid complete analysis when the original structure has been modified or redesigned locally. If the initial solution of original structure is obtained, the predicted solution can be easily achieved by determining the changed stiffness matrix. However, the most of popular reanalysis methods are limited to the simple structure or the simplified product design in practical engineering. In our opinion, the major bottlenecks might be the difficulty in determining the relationship between the mesh of before and after modification, the error due to the approximation and solving mode for nonlinear dynamical problems. Therefore, the main purpose of this project is to solve these three bottlenecks. The ultimate target is to build a new high accurate reanalysis method by integrating auxiliary space and block matrix method without any other complicated geometrical operations. Furthermore, we hope use this suggested method as a kernel to apply to nonlinear dynamical problems. Moreover, this kind of new reanalysis method can be extended for other high performance numerical methods. Then, it can be used for more disciplines in practice.

定制化是产品设计未来发展的趋势，如何在保证产品质量的同时大幅度缩短开发周期是保证企业竞争力的重要因素之一。因此，快速计算理论在优化设计中的地位为凸显重要。重分析作为一种重要的快速计算方法，其要意义在于：对于局部的结构修改，仅仅需要确定变刚度矩阵以及初始计算结果，就可以快速估计修改后的计算结果。然而，重分析方法目前的应用依然局限于结构较为单一，规模受限的实际工程问题或简化模型，难以在复杂产品设计中发挥作用。其主要原因在于：结构修改前后网格的对应关系的确定和获取，由于近似所产生的误差以及非线性动态问题的求解模式等。为此，项目拟围绕着这三个主要瓶颈，引进辅助空间，结合分块模式，在不增加额外几何操作的前提下，建立全新模式的高精度重分析方法。进而以该方法为核心，实现对非线性动态问题的快速求解。此外，希望将新型重分析计算体系向其他高效数值算法进行初步拓展，使重分析的应用领域更为宽广完备。

定制化是产品设计未来发展的趋势，如何在保证产品质量的同时大幅度缩短开发周期是保证企业竞争力的重要因素之一。因此，快速计算理论在优化设计中的地位为凸显重要。重分析作为一种重要的快速计算方法，其要意义在于：对于局部的结构修改，仅仅需要确定变刚度矩阵以及初始计算结果，就可以快速估计修改后的计算结果。然而，重分析方法目前的应用依然局限于结构较为单一，规模受限的实际工程问题或简化模型，难以在复杂产品设计中发挥作用。其主要原因在于：结构修改前后网格的对应关系的确定和获取，由于近似所产生的误差以及非线性动态问题的求解模式等。为此，项目拟围绕着这三个主要瓶颈，引进辅助空间，结合分块模式，在不增加额外几何操作的前提下，建立全新模式的高精度重分析方法。进而以该方法为核心，实现了对非线性动态问题的快速求解。此外，将新型重分析计算体系向其他高效数值算法进行初步拓展，使重分析的应用领域更为宽广完备。目前发表论文43篇，其中SCI论文37篇，发明专利5项，培养博士生3名，硕士生十余名。