Sophisticated computational techniques for damage mechanics with mixed uncertain input fields

该研究项目的目标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高效的计算技术。对于认识的不确定性，即未知的输入随机场参数的治疗，一个Dempster-Shafer p盒的方法将被利用和实施到一个自适应嵌套采样策略。系统的研究pboxes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）将进行调查。自适应多级蒙特-卡罗方案将用于结构响应面的有效采样。该方案已被扩展为嵌套的认识-偶然抽样定义一些复杂的错误标准。重点是敏感性或可靠性分析，将生成感兴趣的数量（即剩余承载能力）的响应面。在这里，一个自适应广义多项式混沌（GPC）计划将实施，其中的认知参数空间上elementwise GPC的新发展出现了一个有吸引力的选择。系统的研究可能元素的正交多项式的有效和准确的建设必须进行。将研究我们自己的3维基准问题上的混凝土梁进行4点弯曲荷载的适用性的计算方法。该示例用于整个计算方法的参数研究。

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.