中文摘要：

传统的结构优化方法需要预先给定受力条件,所得结构只保证在所给条件下最优,而在其他外力下可能较为脆弱.实际应用中物体可能受到各种外力,这时在单个受力条件下的优化方法无法保证结构的全局性能,一般通过加大材料的使用量来满足应用需求.文中提出的优化方法能够加强物体在各种可能受力条件下的全局强度,使物体的强度趋于各向同性以抵御各种不同的外力.该方法基于物体结构的模态分析检测结构中的脆弱区域,并通过刚度矩阵特征值的优化实现脆弱区域的加强;同时基于瑞利商的概念,提出一种高效可行的求解算法.实验结果表明,该方法可有效地提高物体的全局强度.

英文摘要：

Traditional structural optimization methods require predefined load conditions. The resulting structure is optimal under the given condition, but can be weak under different loads. Objects can suffer from various forc-es in practical applications. The overall performance of objects cannot be guaranteed and thus more material than actually needed is used. In this work we propose a novel approach to enhance the global strength of 3D objects under all possible load distribution, which make the strength of the object isotropic to resist different forces. The method is based on modal analysis. We first detect the weak region of the object and then reinforce it by optimiz-ing the eigenvalue of the stiffness matrix. Based on the concept of Rayleigh Quotient, an efficient algorithm is also presented. Experiments show that our method can effectively improve the global strength of 3D objects.