Conference Agenda

During the last decade, additive manufacturing techniques have gained extensive attention. Especially extrusion-based techniques utilizing plastic, metal or even cement-based materials are widely used. Numerical simulation of additive manufacturing processes can be used to gain a more fundamental understanding of the relations between the process and material parameters on one hand and the properties of the printed product on the other hand.

Hence, the dependencies of the final structural properties on different influencing factors can be identified. Additionally, the uncertain nature of process and material parameters can be taken into account to reliably control and finally optimize the printing process. Therefore, numerical models of printing processes demand geometric flexibility while being computationally efficient.

An efficient numerical simulation of an extrusion-based printing process of concrete, applying a voxel-based finite element method is used in this study. Along with the progressing printing process, a previously generated FE mesh is activated step-by-step using a pseudo-density approach. Additionally, all material parameters vary spatially and temporally due to the time dependency of the curing process. In order to estimate material and process parameters realistically a polymorphic uncertainty approach is chosen incorporating interval-probability based random processes and fields.

By having a numerical model – at least at some level of abstraction – and an extensive description and possibility to consider uncertainties, the probabilities of the occurrence of the failure mechanisms (strength-based stability, geometric deviations, layer interface, and buckling) can be estimated. In an optimal steering of the process, failures should be minimized. However, reducing the failure probabilities of one mechanism may increase the ones of the other mechanisms, e.g., shape stability and layer interface might be in conflict.

In this study, process steering is rationalized using a reliability-based optimization approach taking into account the uncertain nature of the system’s material and process parameters. In the light of polymorphic uncertainty, tailored surrogate model strategies are investigated to boost efficiency for this numerically demanding task.

The combination of both types of uncertainty – aleatoric and epistemic – in polymorphic uncertainty models is common as fundamental step for a realistic description of system parameters (geometric definitions, loads, boundary conditions and material properties) in structural safety assessment. Such polymorphic uncertainty models are defined by combination of basic uncertainty models, such as random variates, interval sets, fuzzy sets etc., where the two types of uncertainty are accounted for in different basic models. As combined models, p-boxes, fuzzy probability based random variates etc. are documented.

In addition to the consideration of the two types of uncertainty, functional dependencies of uncertain quantities are observed in real world problems. Functional dependencies are due to temporal variation, referred to as uncertain process, or due to spatial variation, referred to as uncertain field.

This contribution focuses on temporally dependent polymorphic uncertainty in safety assessment of – in this application case, structural – systems. Therefore, uncertainty quantification is required, which means estimating the uncertain system responses (uncertain output) of a structural analysis (basic solution), based on the uncertain structural parameters (uncertain input). When considering polymorphic uncertain processes, a key challenge arises from the coupling and propagation of the temporal dependency in the uncertain input and in the basic solution. For this propagation, two concepts are presented.

The first concept is propagation of temporal dependency by the uncertainty analysis. Therefore, each single basic solution is not necessarily time dependent. Contrarily, the time dependency is reached by sampling from a time dependent uncertain input parameter in the uncertain analysis and each sample is applied for a single computation of the basic solution. Finally, the chaining of such basic solutions and the interdependence between them leads to time-dependent output of the total uncertainty quantification.

The second concept is propagation of time dependency in the basic solution. Therefore, each sample of the uncertainty analysis is a full realization of a time dependent function, in particular a full deterministic process. The basic solution in this concept is required to be time-dependent and the realization of the process is the deterministic input defining the function of the parameter in time.

In this contribution, both concepts are presented, and the challenges and advantages in their implementations are outlined. Moreover, general problems of polymorphic uncertainty models are pointed out based on the shown concepts and solutions for their unbiased modeling and re-sampling are introduced. As numerical examples, application cases in the simulation of the life-cycle (production process and structural operation) of compressed wood components are shown, where both concepts are applied in multiple simulation phases.

The development of new materials allows to increase the span length of footbridges constructed as lightweight structures. However, slender footbridges are more sensitive to vibrations caused by human-induced vibrations. This can reduce the comfort for pedestrians significantly. In addition, eigenfrequencies of slender footbridges are often in the range of the step frequency. A resonance case has to be avoided to ensure the structural safety. The gait of a pedestrian and thus the step frequency is very difficult to quantify in a dynamic load model. It depends on many factors, e.g., body height and weight, gender, age, psychological aspects and even the economic and social status of a human have an influence. There are many parameters with a lack of knowledge to quantify these factors in a load model. Therefore, pedestrian load models are very simplified in current design guidelines. An adequate quantification of aleatoric and epistemic uncertainties is not yet sufficiently addressed in the modeling of human-induced vibrations of footbridges.

In this contribution, uncertain parameters for a pedestrian load model are quantified with polymorphic uncertainty models based on available data. Then, dynamic structural analyses are performed with human-induced vibrations, which are approximated by surrogate models. The results are fuzzy stochastic processes of the structural accelerations, velocities and displacements. In current design codes, the comfort levels are defined with respect to acceptable accelerations. Due to the subjective perception of structural accelerations, the comfort levels are also defined with uncertainty models. Associated results are presented for a real-world footbridge using a 3D finite element model.

In the present landscape, researchers quantify the natural variability or lack of knowledge of a system to counteract its effects. What if, instead of trying to reduce this uncertainty, we try to exploit it during the development? In this work we propose how to use the knowledge on the said uncertainty to increase the design flexibility of the sub-systems of a new product. Imagine the development process being supported by the solution space method and its corridors on the performance of each sub-system. From a certain point of view, these corridors quantify an interval epistemic uncertainty of the development process. The method, however, allows to change the intervals while maintaining the same overall target performance. We exploit the flexibility of the method to find on which parts of the new product is worth investing to reduce the variability and which ones to allow a larger interval. A larger interval yields a bigger flexibility in the design, hence less development effort. The method we propose balances in the development process between reducing the variability of certain sub-systems and increasing the flexibility on the design of other sub-systems.