Combined shape and cross-section optimisation of composite structures based on the singular value decomposition of sensitivity matrices

设计具有非线性结构行为（包括稳定性现象）的复合材料是一个与实际高度相关的优化问题，其首要目标是开发一种算法，通过目标函数和约束函数自动确定对结构行为（包括稳定性方面）最相关的影响。将考虑对髋臼杯几何形状和复合材料进行修改。将使用主成分分析（PCA）的线性和非线性方法，例如奇异值分解（SVD），对计算出的灵敏度进行增强分析。结果将用于指导自动非线性规划算法以及工程师的直观解释。第二个目标是优化方法的扩展，以解决组合问题，包括优化壳体的几何形状，将域细分为具有相同复合材料的子域，以及在这些子区域内的最佳层合板参数。该方法将在几个工业应用中应用和测试。

Desigining composites with non-linear structural behaviour including stability phenomena is a demanding optimisation problem highly related to practice.The first goal is to develop an algorithm to automatically determine quantitativelyof the most relevant influences on the structural behaviour including stability aspects via objective and constraints functions. Modifications of the shell geometry and of the composite material will be considered. The enhanced analysis of the computed sensitivities will be performed using linear and non-linear methods of principal component analysis (PCA), e.g. the singular value decomposition (SVD). The results will be used to guide the automatic nonlinear programming algorithm as well as the intuitive interpretation of engineers.The second goal is the extension of the optimisation methods to solve combined problems consisting of optimising the geometry of the shell, the sub-division of the domain into sub-domains with identical composite material, and the optimal laminate parameters within these sub-domains.The method will be applied and tested on several industrial applications.