Granular materials: Parameter identification and modelling of localisation problems

The prediction of landsliding requires an exact knowledge of the mechanical behaviour of granular materials. This kind of materials, e. g., sand, have a very complex deformation behaviour, which depend on the stress state and on the loading history. In this work, the deformation behaviour of the solid skeleton is characterised via homogeneous triaxial tests on dry sand specimens. Additionally, an appropriate elasto-plastic material law to describe the solid skeleton in the frame of Theory of Porous Media (TPM) is used, which is implemented in the FE tool PANDAS. Furthermore, a single-surface yield criterion with isotropic hardening, which limits the elastic domain, and a non-associated plastic flow are employed. The determination of the material parameters of the linear elasticity law as well as the single-surface yield criterion are based on test data of triaxial experiments. The material parameters are identified using a derivative-based optimisation method (donlp2), which is coupled with PANDAS. Finally, a simulation of a benchmark test is presented to show shear band localisation effects, where the material behaviour is described by a triphasic porous media model based on the TPM, where the constituents are a deformable solid skeleton and two pore fluids, water and air. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exploration of Internal Response Sensitivities of Materially Nonlinear Structures

In this paper the idea of design exploration in the context of structural design sensitivity analysis considering elastoplastic material behaviour is outlined. Sensitivity information involves the influence of history dependent material behaviour and is obtained analytically by means of a variational approach. Applying singular value decomposition (SVD) to response sensitivities provides deep insight into sensitivity information and can be used to identify design changes with major influence on structural response. With this additional information, it is possible to refine an optimisation problem and reduce its complexity. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On regularization in parameter-free shape optimization

This contribution is concerned with a parameter-free approach to computational shape optimization of mechanically-loaded structures. Thereby the term ’parameter-free’ refers to approaches in shape optimization in which the design variables are not derived from an existing CAD-parametrization of the model geometry but rather from its finite element discretization. One of the major challenges in using this type of approach is the avoidance of oscillating boundaries in the optimal design trials. This difficulty is mainly attributed to a lack of smoothness of the objective sensitivities and the relatively high number of design variables within the parameter-free regime. To compensate for these deficiencies, Azegami introduced the concept of the so-called traction method, in which the actual design update is deduced from the deformation of a fictitious continuum that is loaded in proportion to the negative shape gradient. We investigate a discrete variant of the traction method, in which the design sensitivities are computed with respect to variations of the design nodes for a given finite element mesh rather than on the abstract level by means of the speed method. Moreover, the design update process is accompanied by adaptive mesh refinement based on discrete material residual forces. Therein, we consider radaptive node relocation as well as hadaptive mesh refinement. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discrete boundary smoothing using control node parameterisation for aerodynamic shape optimisation

This paper presents an automated aerodynamic optimisation algorithm using a novel method of parameterising the search domain and geometry by employing user–defined control nodes. The displacement of the control nodes is coupled to the shape boundary movement via a ‘discrete boundary smoothing’. This is initiated by a linear deformation followed by a discrete smoothing step to act on the boundary during the mesh movement based on the change in its second derivative. Implementing the discrete boundary smoothing allows both linear and non-linear shape deformation along the same boundary dependent on the preference of the user. The domain mesh movement is coupled to the shape boundary movement via a Delaunay graph mapping. An optimisation algorithm called Modified Cuckoo Search (MCS) is used acting within the prescribed design space defined by the allowed range of control node displacement. In order to obtain the aerodynamic design fitness a finite volume compressible Navier-Stokes solver is utilized. The resulting coupled algorithm is applied to a range of case studies in two dimensional space including the optimisation of a RAE2822 aerofoil and the optimisation of an intake duct under subsonic, transonic and supersonic flow conditions. The discrete mesh–based optimisation approach outlined is shown to be effective in terms of its generalised applicability, intuitiveness and design space definition.     

A convergent adaptive finite element method for an optimal design problem

The optimal design problem for maximal torsion stiffness of an infinite bar of given geometry and unknown distribution of two materials of prescribed amounts is one model example in topology optimisation. It eventually leads to a degenerate convex minimisation problem. The numerical analysis is therefore delicate for possibly multiple primal variables u but unique derivatives σ : = DW(D u). Even fine a posteriori error estimates still suffer from the reliability-efficiency gap. However, it motivates a simple edge-based adaptive mesh-refining algorithm (AFEM) that is not a priori guaranteed to refine everywhere. Its convergence proof is therefore based on energy estimates and some refined convexity control. Numerical experiments illustrate even nearly optimal convergence rates of the proposed AFEM. Supported by the DFG Research Center MATHEON “Mathematics for key technologies” in Berlin.     

About the Microstructural Effects of Polycrystalline Materials and their Macroscopic Representation at Finite Deformation

In the sheet bulk metal forming field, the strict geometrical requirements of the workpieces result in a need of a precise prediction of the material behaviour. The simulation of such forming processes requires a valid material model, performing well for a huge variety of different geometrical characteristics and finite deformation. Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level. A finite crystal plasticity model is used to model polycrystalline materials in representative volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. The validation on the macroscopic scale is performed through the reproduction of the experimentally calculated initial yield surface. Additionally, homogenised stress-strain curves from the microstructure build the outcome for a suitable effective material model. Through optimisation techniques, effective material parameters can be determined and compared to results from real forming processes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model reduction in topology optimisation analysing the inner structure of sensitivity matrices

Topology optimisation models usually contain a great number of design variables and correspondingly lead to large matrices (pseudo load matrix and sensitivity matrix) which appear in sensitivity analysis. We apply singular value decomposition (SVD) to these matrices to analyse their inner structure. Based on the obtained information, we perform model reduction by transformation of the design variables into a lower-dimensional space. Numerical examples illustrate the advocated theoretical concept. Reasonable results are obtained, based on only a fraction of all design variables. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal design of a hoist structure frame

In an attempt to find the most cost effective design of a multipurpose hoisting device that can be easily mounted on and removed from a regular farm vehicle, cost optimisation including both material and manufacturing expenditure, is performed on the main frame supporting the device. The optimisation is constrained by local and global buckling and fatigue conditions. Implementation of Snyman’s gradient-based LFOPC optimisation algorithm to the continuous optimisation problem, results in the economic determination of an unambiguous continuous solution, which is then utilised as the starting point for a neighbourhood search within the discrete set of profiles available, to attain the discrete optimum.

This optimum is further investigated for a different steel grade and for the manufacturing and material cost pertaining to different countries. The effect of variations in the formulation of the objective function for optimisation is also investigated. The results indicate that considerable cost benefits can be obtained by optimisation, that costing in different countries do not necessarily result in the same most cost effective design, and that accurate formulation of the objective function, i.e. realistic mathematical modelling, is of utmost importance in obtaining the intended design optimum.     

Computational Homogenisation of Polycrystalline Elastoplastic Microstructures at Finite Deformation

During sheet bulk metal forming processes both, flat geometries and three-dimensional structures change their shape significantly while undergoing large plastic deformations. As for forming processes, FE-simulations are often done before in situ experiments, a very accurate material model is required, performing well for a huge variety of different geometrical characteristics. Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level. A finite crystal plasticity model is used to model the behaviour of polycrystalline materials in representative volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. Through homogenisation and optimisation techniques, effective stress-strain curves are determined and can be compared to results from real forming processes leading to a suitable effective material model. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Knowledge Extraction from Aerodynamic Design Data and its Application to 3D Turbine Blade Geometries

Applying numerical optimisation methods in the field of aerodynamic design optimisation normally leads to a huge amount of heterogeneous design data. While most often only the most promising results are investigated and used to drive further optimisations, general methods for investigating the entire design dataset are rare. We propose methods that allow the extraction of comprehensible knowledge from aerodynamic design data represented by discrete unstructured surface meshes. The knowledge is prepared in a way that is usable for guiding further computational as well as manual design and optimisation processes. A displacement measure is suggested in order to investigate local differences between designs. This measure provides information on the amount and direction of surface modifications. Using the displacement data in conjunction with statistical methods or data mining techniques provides meaningful knowledge from the dataset at hand. The theoretical concepts have been applied to a data set of 3D turbine stator blade geometries. The results have been verified by means of modifying the turbine blade geometry using direct manipulation of free form deformation (DMFFD) techniques. The performance of the deformed blade design has been calculated by running computational fluid dynamic (CFD) simulations. It is shown that the suggested framework provides reasonable results which can directly be transformed into design modifications in order to guide the design process.     

A General Meta-Heuristic Based Solver for Combinatorial Optimisation Problems

In recent years, there have been many studies in which tailored heuristics and meta-heuristics have been applied to specific optimisation problems. These codes can be extremely efficient, but may also lack generality. In contrast, this research focuses on building a general-purpose combinatorial optimisation problem solver using a variety of meta-heuristic algorithms including Simulated Annealing and Tabu Search. The system is novel because it uses a modelling environment in which the solution is stored in dense dynamic list structures, unlike a more conventional sparse vector notation. Because of this, it incorporates a number of neighbourhood search operators that are normally only found in tailored codes and it performs well on a range of problems. The general nature of the system allows a model developer to rapidly prototype different problems. The new solver is applied across a range of traditional combinatorial optimisation problems. The results indicate that the system achieves good performance in terms of solution quality and runtime.     

Beamforming and Interference Cancellation for Capacity Gain in Mobile Networks

The growth of wireless communication continues. There is a demand for more user capacity from new subscribers and new services such as wireless internet. In order to meet these expectations new and improved technology must be developed. A way to increase the capacity of an existing mobile radio network is to exploit the spatial domain in an efficient way. An antenna array adds spatial domain selectivity in order to improve the Carrier-to-Interference ratio (C/I) as well as Signal-to-Noise Ratio (SNR). An adaptive antenna array can further improve the Carrier-to-Interference ratio (C/I) by suppressing interfering signals and steer a beam towards the user. The suggested scheme is a combination of a beamformer and an interference canceller.The proposed structure is a circular array consisting of K omni-directional elements and combines fixed beamforming with interference cancelling. The fixed beamformers use a weight matrix to form multiple beams. The interference cancelling stage suppresses undesired signals, leaking into the desired beam.The desired signal is filtered out by the fixed beamforming structure. Due to the side-lobes, interfering signals will also be present in this beam. Two alternative strategies were chosen to cancel these interferers; use the other beamformer outputs as inputs to an adaptive interference canceller; or regenerate the outputs from the other beamformer outputs and generate clean signals which are used as inputs to adaptive interference cancellers.Resulting beamformer patterns as well as interference cancellation simulation results are presented. Two different methods have been used to design the beamformer weights, Least Square (LS) and minimax optimisation. In the minimax optimisation a semi-infinite linear programming approach was used. Although the optimisation plays an essential role in the performance of the beamformer, this paper is focused on the application rather then the optimisation methods.     

Counting and enumeration complexity with application to multicriteria scheduling

In this paper we tackle an important point of combinatorial optimisation: that of complexity theory when dealing with the counting or enumeration of optimal solutions. Complexity theory has been initially designed for decision problems and evolved over the years, for instance, to tackle particular features in optimisation problems. It has also evolved, more or less recently, towards the complexity of counting and enumeration problems and several complexity classes, which we review in this paper, have emerged in the literature. This kind of problems makes sense, notably, in the case of multicriteria optimisation where the aim is often to enumerate the set of the so-called Pareto optima. In the second part of this paper we review the complexity of multicriteria scheduling problems in the light of the previous complexity results. This paper appeared in 4OR 3(1), 1–21, 2005.     

Remarks on different strategies for sensitivity analysis of multiscale problems in structural optimisation

The adjustment of properties of materials to special requirements plays a more and more important role in engineering applications. Thus, the question about design and optimisation of materials arises. In this contribution some basic and necessary aspects for the treatment of structural optimisation problems in terms of multiscale modelling are given. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the computation of a versal family of matrices

The aim of this article is to present algorithms for the computation of versal deformations of matrices. A deformation of a matrixA ₀ is a holomorphic matrix-valued function whose value at a pointt ₀C ^p is the matrixA ₀. We want to study the properties of these matrices in a neighbourhood oft ₀. One could, for each valuet in this neighbourhood, compute the Jordan form as well as the change of basis matrix; but, generally, the results will not be analytic. So, we want to construct a deformation of the matrixA ₀ into which any deformation can be transformed by an invertible deformation of the matrixId. After having introduced the notion of versal deformation, we shall provide computer algebra algorithms to computer these normal forms. In the last section, we shall show that a one-parameter deformation can be transformed into a simpler form than the general versal deformation.     

Deformation Driven Homogenization of Fracturing Solids

The paper discusses numerical formulations of the homogenization for solids with discrete crack development. We focus on multi–phase microstructures of heterogeneous materials, where fracture occurs in the form of debonding mechanisms as well as matrix cracking. The definition of overall properties critically depends on the developing discontinuities. To this end, we extend continuous formulations [1] to microstructures with discontinuities [2]. The basic underlying structure is a canonical variational formulation in the fully nonlinear range based on incremental energy minimization. We develop algorithms for numerical homogenization of fracturing solids in a deformation–driven context with non–trivial formulations of boundary conditions for (i) linear deformation and (ii) uniform tractions. The overall response of composite materials with fracturing microstructures are investigated. As a key result, we show the significance of the proposed non–trivial formulation of a traction–type boundary condition in the deformation–driven context. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effective conductivity of an infinitely interchangeable mixture

We are concerned with the estimation of the effective electrical conductivity of random heterogenous materials. The purpose of this paper is to discuss a property of “statistical symmetry” verified by the symmetric cell materials of Miller. This property will be referred to as infinite interchangeability. The usual way to approach cell materials is through n-point correlation functions. The property of infinite interchangebility permits us to approach cell materials from a completely different point of view. Our main result is a simple algorithm, based on this symmetry property, for computing any coefficient of the perturbation expansion in terms of information from the dilute limit. Specifically, knowledge of the coefficients of the expansion in powers of the volume fraction up to order r allows for computation of the perturbation expansion coefficients up to order (2r + 1). This result, which was previously known for r = 2 in the isotropic case and for r = 1 in the anisotropic case, can also be obtained from the standard correlation function approach, as pointed out by Milton.     

On the representation formula for well‐ordered elastic composites: a convergence of measure approach

The aim of this paper is to derive an integral representation formula for the effective elasticity tensor for a two‐component well‐ordered composite of elastic materials without using a third reference medium and without assuming the completeness of the eigenspace of the operator ? defined in (2.16) in (J. Mech. Phys. Solids 1984; 32 (1):41–62). As shown in (J. Mech. Phys. Solids 1984; 32 (1):41–62) and (Math. Meth. Appl. Sci. 2006; 29 (6):655–664), this integral representation formula implies a relation which links the effective elastic moduli to the N‐point correlation functions of the microstructure. Such relation not only facilitates a powerful scheme for systematic incorporation of microstructural information into bounds on the effective elastic moduli but also provides a theoretical foundation for de‐homogenization. The analysis presented in this paper can be generalized to an n‐component composite of elastic materials. The relations developed here can be applied to the de‐homogenization for a special class of linear viscoelastic composites. The results will be presented in another paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Some effective heuristics for no-wait flowshops with setup times to minimize total completion time

In this work, we consider a complex flowshop scheduling problem in which both no-wait and separate setup times are considered. The optimisation criterion is the minimisation of the total completion time. We propose an effective dominance rule for the four machine case that can also be used for m machines. Five simple and fast heuristics are proposed along with two easy to code stochastic local search methods, one of them being based on Iterated Local Search (ILS). An extensive computational evaluation is carried out with two sets of 5,400 instances. All seven methods are compared to two recent algorithms. The results, confirmed by thorough statistical analyses, show that the proposed methods are more effective and efficient when compared to the best existing algorithms in the literature for the considered problem.     

A finite element formulation based on the theory of a Cosserat point

The theory of Cosserat points is the basis of a 3D finite element formulation allowing for large deformations in structural mechanics, that recently was presented by [1]. First attempts have revealed, that this formulation is free of showing undesired locking or hourglassing-phenomena. It additionally shows excellent behaviour for any type of incompressible material, for large deformations and sensitive structures such as plates or shells. Within the theory of Cosserat points, the position vectors X and x , are described through director vectors D _i and d _i by use of trilinear shape functions Nⁱ for an 8-node brick element. The special choice of shape functions Nⁱ allows for director vectors with which the deformation can be split into a homogeneous and an inhomogeneous part. This split enables the use of stiffnesses that correspond to different deformation modes. Analytical solutions to the inhomogeneous deformation modes are incorporated in the formulation and avoid the undesired phenomena. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)