Variational sensitivity analysis of physical reaction forces and application to multiscale problems

Nowadays profitability and efficiency of practical and industrial applications and therefore of material design is becoming a more important issue. Due to different well-known and established approaches for analysis and simulation of complex heterogeneous materials on multiple scales based on numerical homogenisation techniques, development and production of high performance materials (using 3d printers for example) and as a consequence optimisation and design of materials is reality. The objective is to find optimal structures with optimal material distribution under given constraints related to posed problems and tailoring applications to their special requirements. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural design sensitivity analysis in context of non-linear buckling

Structural stability is an important issue to ensure the safety of thin walled structures. Shell structures are considered in context of linear and non-linear buckling. The design sensitivity analysis with respect to modifications in shape is motivated. Analytically derived gradient information is employed for shape optimisation purposes using solid shells. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational design sensitivity analysis of dual problems with applications to error analysis

Dual or adjoint solutions play an important role in many fields which deal with local quantities of interest. This contribution is concerned with a novel approach for the sensitivity of the dual solution itself, i.e. we investigate the change in the dual solution at a deformed configuration of the material body due to changes in the design of the body. We consider a general variational framework and present the application of the proposed approach to the prediction of changes in the quantity of interest as well as error analysis for the truncation error of classical first-order sensitivity relations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Shape sensitivity analysis in the extended finite element method

The contribution is concerned with the derivation and implementation of shape sensitivity analysis in the context of the extended finite element method (xfem). Here, the displacement approximation is enhanced in order to model strong and weak discontinuities along the interfaces and cracks. Consequently, sensitivity analysis must be accomplished for the extended formulation based on a sub-integration technique on sub-domains of the cut elements. This cumbersome and error-prone work can be circumvent using a standard treatment of sub-elements on an appropriately defined sub-mesh. These modifications guarantee exact analytical sensitivities even for distorted finite element domains. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variational sensitivity analysis and changes in the material configuration

This contribution is concerned with some aspects of variational design sensitivity analysis in the physical and material configuration. Sensitivity analysis is a branch of structural optimization, e.g. shape or topology optimization. In these disciplines we consider variations of the material configuration and we are interested in the change of the state variables and the objective functional due to these variations. In the context of structural optimization this is termed as design sensitivity analysis. The sensitivities are required in order to solve the corresponding Lagrangian equation within standard nonlinear programming algorithms. In many engineering applications, the energy functional of the problem is used as the objective functional. In this paper, we consider variations of the energy with respect to the state and the design and we investigate sensitivity relations for the physical and material problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Enhanced shot noise in tunneling through a stack of coupled quantum dots

We have investigated the noise properties of the tunneling current through vertically coupled self-assembled InAs quantum dots. We observe super-Poissonian shot noise at low temperatures. For increased temperature this effect is suppressed. The super-Poissonian noise is explained by capacitive coupling between different stacks of quantum dots.     

Salem Numbers and Growth Series of Some Hyperbolic Graphs

Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the -regular graphs associated to regular tessellations of the hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs are Salem numbers. We also prove that these denominators are essentially irreducible (they have a factor of X + 1 when m 2 mod 4; and when = 3 and m 4 mod 12, for instance, they have a factor of X ² – X + 1). We then derive some regularity properties for the coefficients f _n of the growth series: they satisfy K ⁿ – R < f _n < K ⁿ + R for some constants K, R < 0, < 1.     

Optimisation of Structures with Inelastic Deformations

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 based optimisation algorithms. Considering path-dependent materials the sensitivities of internal variables that represent the deformation history have to be additionally calculated. A numerical effective way of determining sensitivities is the variational sensitivity analysis. This approach is applied to develop a powerful and effective algorithm to compute sensitivities of the structural response with respect to their geometric design. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Design space exploration based on variational sensitivity analysis

This contribution deals with variational sensitivity analysis of a non-linear solid shell in context of shape optimisation. A technique to explore the structural design is outlined. It is based on the analytical derivation and efficient computation of the Fréchet derivatives of the state functions with respect to the full space of all possible design parameters. This overhead of sensitivity information is examined by a principal component analysis (PCA) in order to detect design changes with major and minor influence on the structural response, the objectives and constraints. This knowledge enables the engineers to understand and improve structural optimisation models and to detect possible numerical defects in the early stage. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)