Sophisticated computational techniques for damage mechanics with mixed uncertain input fields

本研究的目的是为具有不确定输入变量的详细损伤力学有限元模型提供有效的计算技术。对于认知不确定性的处理，即未知的输入随飞机参数，将使用Dempster-Shafer p-box方法并将其实现为自适应嵌套采样策略。系统研究pbox的离散化依赖于输入场建模方法，或者通过Karhunen-Loeve展开（KLE）或多项式混沌展开（PCE）进行研究。采用自适应多级蒙特卡罗格式对结构响应面进行有效采样。该方案必须扩展到嵌套的认知-随机抽样，定义了一些复杂的误差准则。重点是灵敏度或可靠性分析的响应面为感兴趣的数量，即剩余的承载能力，将产生。本文将实现一种自适应广义多项式混沌（gPC）方案，其中对于认知参数空间，基于元素的广义多项式混沌的新发展是一种有吸引力的选择。系统地研究如何有效而准确地构造可能的逐元正交多项式。所开发的计算方法的适用性将研究我们自己的三维基准问题上的混凝土梁受到四点弯曲荷载。这个例子用于整体计算方法的参数化研究。

Goal of this research project is to provide efficient computational techniques for detailed damage mechanics finite element models with uncertain input variables. For the treatment of epistemic uncertainties, i.e. unknown input random field parameters, a Dempster-Shafer p-box approach will be utilized and implemented into an adaptive nested sampling strategy. Systematic studies on the discretization of pboxesin dependency on the input field modeling approach, alternatively via Karhunen-Loeve expansion (KLE) or Polynomial Chaos expansion (PCE) will be investigated. An adaptive multi-level Monte-Carlo scheme will be applied for an efficient sampling of the structural response surfaces. This scheme has to be extended for the nested epistemic-aleatory sampling defining some sophisticated error criteria. With emphasis to sensitivity or reliability analysis response surfaces for the quantities of interest, i.e. remaining load bearing capacity, will be generated. Here an adaptive generalized Polynomial Chaos(gPC) scheme will be implemented, where for the epistemic parameter space newer developments on elementwise gPC appears an attractive option. Systematic studies on the efficient and accurate construction of possibly element-wise orthogonal polynomials have to be performed. The applicability of the developed computational approach will be studied on our own 3-dimensional bench-mark problem on a concrete beam subjected to 4 point bending loads. This example serves for parametric studies of the overall computational approach.