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We shall define localic Krull dimension for topological spaces. In particular, a space X has the localic Krull dimension n if n is the greatest number such that X can be mapped, via a continuous and open map, onto the n‐chain seen as an Alexandroff space. We shall discuss the applications of this concept in obtaining topological completeness results in modal logic. We shall also show how the localic...
We present recent results on the deepening connection between proof theory and formal language theory. To each first‐order proof with prenex cuts of complexity at most Πn/Σn, we associate a typed (non‐deterministic) tree grammar of order n (equivalently, an order n recursion scheme) that abstracts the computation of Herbrand sets obtained through Gentzen‐style cut elimination. Apart from offering...
A fundamental question in mathematical logic asks: What are the minimal assumptions and deduction principles required to prove a particular theorem? Now consider the special case of a theorem that can be established by checking a finite number of decidable cases — think of a single instance of the finite Ramsey theorem. In this particular situation the answer to our question is trivial: The theorem...
In design of reinforced concrete structures, a ductile design is needed, because the brittle fracture is sudden. Also, the energy absorbed by the structure is effective for ductile structures during earthquake excitations. In design regulations, especially for vertical supporters such as columns, the shear force and axial force capacity is limited, although the strength of the members is not at the...
In context of design optimisation, the treatment of inelastic, path‐dependent materials is a topic of interest. As opposed to purely elastic materials, it is necessary to store and analyse the deformation history in order to appropriately describe inelastic material behaviour. For design optimisation of structures sensitivities of all quantities of influence have to be computed so as to use gradient...
At the application of the plastic analysis and design methods the control of the plastic behaviour of the structures is an important requirement. Since the plastic limit analysis provides no information about the magnitude of the plastic deformations and residual displacements accumulated before the adaptation of the structure, therefore complementary strain energy of the residual forces could be...
The determination of the global optimized (GO) shapes of flying configurations leads to extended variational problems with free boundaries. The author has developed special optimization strategies called optimum optimorum and iterative optimum optimorum strategies and have used them for the design of GO shapes of three models, which are of minimum drag at three different supersonic cruising Mach numbers...
A homogenization framework for the stochastic average meso‐scale tread‐road interaction with emphasis on macro‐scale rolling resistance calculations is presented in this contribution. This framework accounts for large scale, high‐frequency penetration of tread rubber by the highest asperities as well as for the nonlinear thermo‐viscoelastic material behavior of this tread rubber in the regime of finite...
Many processes contain phenomena on different time scales, leading to model equations with fast and small parts. There are several approaches to solve these equations, like additive Runge Kutta methods or multirate infinitesimal steps methods (MIS). Both methods make use of the additive splitting of the ODE in fast and small parts. The multiple infinitesimal step method integrates the slow part with...
The transition from simulation software to optimization software is often quite cumbersome and error prone. With Algorithmic Differentiation(AD) a semi automatic transition can be achieved, but most of the times the performance characteristics of the modified software are not clear in advance. Therefore the performance model from Griewank is tested against real world examples and an automated measurement...
In this work, a kinetic energy preserving DG scheme in one space dimension using Gauss‐Legendre nodes is presented. Stability problems will be demonstrated when using interface terms that are derived from the Lobatto nodes within the Gauss‐Legendre skew‐symmetric DG formulation. However, combined with correct interface terms, the skew‐symmetric DG scheme constructed on Gauss‐Legendre nodes is expected...
We extend the multirate GARK approach by Günther and Sandu [1, 2] to the case of non‐constant micro steps per macro step to be able to cover time adaptivity, arriving at our so‐called TAMGARK scheme and derive order conditions for arbitrary non‐constant micro step sizes. The TAMGARK scheme is applied to the classical piston problem [3] to study the interaction between the piston and inviscid fluid...
Numerical simulations of structures using higher‐order finite elements is still a challenging task, in particular for domains with curved boundaries. A new higher‐order accurate approach is proposed, combining the advantages of the classical p‐FEM with embedded domain methods. Boundaries and/or interfaces are described implicitly using the level set method. In the elements cut by the zero level set,...
Hydrogels have gained importance during the last years due to their wide range of synthetically fabricable elastic properties as well their increasing meaning in biomedical applications. Future exploitation of the vast prospects of hydrogels is however only feasible by establishing reliable material models that precisely capture their behavior in different environments. To this end, we propose a consistent variational framework...
Depending on the process parameters, the directional solidification (DS) of eutectic alloys leads to a fibrous or lamellar microstructure. A physically motivated creep model which was evaluated for a DS‐eutectic with a fibrous microstructure is applied to a DS‐eutectic with a lamellar microstructure. Creep curves are simulated and compared to experimentally measured ones. It is shown, that the simulation...
An schlanken, geneigten Zylinderstrukturen wie Kabeln von Schrägkabelbrücken und Hängebrücken, Hängern von Bogenbrücken oder an Abspannseilen kann bei gleichzeitigem Auftreten von Regen und Wind das hydroaeroelastische Phänomen der Regen‐Wind induzierten Schwingungen beobachtet werden. Die komplexen Strömungsvorgänge des Phänomens bedingen die Entwicklung eines hybriden Modells. Diese halbanalytischen/halbnumerischen...
The finite cell method is based on a fictitious domain approach, providing a simple and fast mesh generation of structures with complex geometries. However, this simplification leads to intersected cells where the standard Gauss quadrature does not perform well. To perform the numerical integration of these cells, we use the moment fitting approach that generates an individual quadrature rule for...
In this contribution a new specimen, which enables high precision tension‐compression testing, is presented. Due to a special mounting geometry, tests from a compression strain of −45 % up to a tension strain of 400 % can be performed with a nearly homogeneous deformation field within the measuring zone. Consequently, the mechanical behavior of rubber, which exhibits phenomena like Mullins effect,...
This paper investigates the uncertainty of a hyper‐elastic model by random material parameters as stochastic variables. For its stochastic discretization a polynomial chaos (PC) is used to expand the coefficients into deterministic and stochastic parts. Then, from experimental data in combination with artificial data for elastomers the distribution of the force‐displacement curves are known. In the...
We study the coupled behavior in soft active microstructured materials undergoing large deformations in the presence of an external electric or magnetic field. We focus on the role of the microstructures on the coupled behavior, and examine the phenomenon in the composites with (a) periodic composites with rectangular and hexagonal periodic unit cells, and (b) in composites with the random distributions...
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