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Digital twins are seen as one of the key technologies of Industry 4.0. Although many research groups focus on digital twins and create meaningful outputs, the technology has not yet reached a broad application in the industry. The main reasons for this imbalance are the complexity of the topic, the lack of specialists, and the unawareness of the twin opportunities. The project "Digital Twin Academy" aims to overcome these barriers by focusing on three actions: Building a digital twin community for discussion and exchange, offering multi-stage training for various knowledge levels, and implementing realworld use cases for deeper insights and guidance. In this work, we focus on creating a flexible learning platform that allows the user to select a training path adjusted to personal knowledge and needs. Therefore, a mix of basic and advanced modules is created and expanded by individual feedback options. The usage of personas supports the selection of the appropriate modules.
We study the possibility to fabricate an arbitrary phase mask in a one-step laser-writing process inside the volume of an optical glass substrate. We derive the phase mask from a Gerchberg–Saxton-type algorithm as an array and create each individual phase shift using a refractive index modification of variable axial length. We realize the variable axial length by superimposing refractive index modifications induced by an ultra-short pulsed laser at different focusing depth. Each single modification is created by applying 1000 pulses with 15 μJ pulse energy at 100 kHz to a fixed spot of 25 μm diameter and the focus is then shifted axially in steps of 10 μm. With several proof-of-principle examples, we show the feasibility of our method. In particular, we identify the induced refractive index change to about a value of Δn=1.5⋅10−3. We also determine our current limitations by calculating the overlap in the form of a scalar product and we discuss possible future improvements.
Abstracts of the ACHEMA 2000 - International Meeting on Chemical Engineering, Environmental Protection and Biotechnology, May 22 - 27, 2000. Frankfurt am Main. Achema 2000 : special edition / Linde. [Ed.: Linde AG. Red.: Volker R. Leski]. - Wiesbaden : Linde AG, 2000. - 56 p. : Ill., . - pp: 79 - 81
The structural reliability with respect to plastic collapse or to inadaptation is formulated on the basis of the lower bound limit and shakedown theorems. A direct definition of the limit state function is achieved which permits the use of the highly effective first order reliability methods (FORM) is achieved. The theorems are implemented into a general purpose FEM program in a way capable of large-scale analysis. The limit state function and its gradient are obtained from a mathematical optimization problem. This direct approach reduces considerably the necessary knowledge of uncertain technological input data, the computing time, and the numerical error, leading to highly effective and precise reliability analyses.
In the new European standard for unfired pressure vessels, EN 13445-3, there are two approaches for carrying out a Design-by-Analysis that cover both the stress categorization method (Annex C) and the direct route method (Annex B) for a check against global plastic deformation and against progressive plastic deformation. This paper presents the direct route in the language of limit and shakedown analysis. This approach leads to an optimization problem. Its solution with Finite Element Analysis is demonstrated for mechanical and thermal actions. One observation from the examples is that the so-called 3f (3Sm) criterion fails to be a reliable check against progressive plastic deformation. Precise conditions are given, which greatly restrict the applicability of the 3f criterion.
We propose a stochastic programming method to analyse limit and shakedown of structures under random strength with lognormal distribution. In this investigation a dual chance constrained programming algorithm is developed to calculate simultaneously both the upper and lower bounds of the plastic collapse limit or the shakedown limit. The edge-based smoothed finite element method (ES-FEM) using three-node linear triangular elements is used.
We propose the so-called chance constrained programming model of stochastic programming theory to analyze limit and shakedown loads of structures under random strength with a lognormal distribution. A dual chance constrained programming algorithm is developed to calculate simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit. The edge-based smoothed finite element method (ES-FEM) is used with three-node linear triangular elements.
Safety and reliability of structures may be assessed indirectly by stress distributions. Limit and shakedown theorems are simplified but exact methods of plasticity that provide safety factors directly in the loading space. These theorems may be used for a direct definition of the limit state function for failure by plastic collapse or by inadaptation. In a FEM formulation the limit state function is obtained from a nonlinear optimization problem. This direct approach reduces considerably the necessary knowledge of uncertain technological input data, the computing time, and the numerical error. Moreover, the direct way leads to highly effective and precise reliability analyses. The theorems are implemented into a general purpose FEM program in a way capable of large-scale analysis.
The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress–strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress–strain curves of the fissured sandstone specimens.