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This work suggests to optimize the geometry of a quadrupole magnet by means of a genetic algorithm adapted to solve multi-objective optimization problems. To that end, a non-domination sorting genetic algorithm known as NSGA-III is used. The optimization objectives are chosen such that a high magnetic field quality in the aperture of the magnet is guaranteed, while simultaneously the magnet design remains cost-efficient. The field quality is computed using a magnetostatic finite element model of the quadrupole, the results of which are post-processed and integrated into the optimization algorithm. An extensive analysis of the optimization results is performed, including Pareto front movements and identification of best designs. [ABSTRACT FROM AUTHOR]

As there are different computational methods for simulating problems in generalized mechanics, we present simple applications and their closed‐form solutions for verifying a numerical implementation. For such a benchmark, we utilize these analytical solutions and examine three‐dimensional numerical simulations by the finite element method (FEM) using IsoGeometric Analysis (IGA) with the aid of open source codes, called tIGAr, developed within the FEniCS platform. A study for the so‐called wedge forces and double tractions help to comprehend their roles in the displacement solution as well as examine the significance by comparing to the closed form solutions for given boundary conditions. It is found that numerical results are in a good agreement with the analytical solutions if wedge forces and double tractions are considered. It is also presented how the wedge forces become necessary in order to maintain equilibrium in strain gradient materials. [ABSTRACT FROM AUTHOR]

Based on the progress and advances of additive manufacturing technologies, design and production of complex structures became cheaper and therefore rather possible in the recent past. A promising example of such complex structure is a socalled pantographic structure, which can be described as a metamaterial consisting of repeated substructure. In this substructure, two planes, which consist of two arrays of beams being orthogonally aligned to each other, are interconnected by cylinders/pivots. Different inner geometries were taken into account and additively manufactured by means of fused deposition modeling technique using polyethylene terephthalate glycol (PETG) as filament material. To further understand the effect of different manufacturing parameters on the mechanical deformation behavior, three types of specimens have been investigated by means of displacement-controlled extension tests. Different slicing approaches were implemented to eliminate process-related problems. Small and large deformations are investigated separately. Furthermore, 2D digital image correlation was used to calculate strains on the outer surface of the metamaterial. Two finiteelement simulations based on linear elastic isotropic model and linear elastic transverse isotropic model have been carried out for small deformations. Standardized extension tests have been performed on 3D-printed PETG according to ISO 527-2. Results obtained from finite-element method have been validated by experimental results of small deformations. These results are in good agreement with linear elastic transverse isotropic model (up to about εxx = 1:2% of axial elongation), though the response of large deformations indicates a nonlinear inelastic material behavior. Nevertheless, all samples are able to withstand outer loading conditions after the first rupture, resulting in resilience against ultimate failure. [ABSTRACT FROM AUTHOR]

By using modern additive manufacturing techniques, a structure at the millimeter length scale (macroscale) can be produced showing a lattice substructure of micrometer dimensions (microscale). Such a system is called a metamaterial at the macroscale, because its mechanical characteristics deviate from the characteristics at the microscale. Consequently, a metamaterial is modeled by using additional parameters. These we intend to determine. A homogenization approach based on asymptotic analysis establishes a connection between these different characteristics at micro- and macroscales. A linear elastic first-order theory at the microscale is related to a linear elastic second-order theory at the macroscale. Small strains (and, correspondingly, small gradients) are assumed at both scales. A relation for the parameters at the macroscale is derived by using the equivalence of energy at macro- and microscales within a so-called representative volume element (RVE). The determination of the parameters becomes possible by solving a boundary value problem within the framework of the finite element method. The proposed approach guarantees that the additional parameters vanish if the material is purely homogeneous; in other words, it is fully compatible with conventional homogenization schemes based on spatial averaging techniques. Moreover, the proposed approach is reliable, because it ensures that the obtained additional parameters are insensitive to choices of the RVE consisting of a repetition of smaller RVEs depending upon the intrinsic size of the structure. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a new shield configuration for cryogenic current comparators (CCCs), namely the folded coaxial geometry. An analytical model describing its shielding performance is first developed, and then validated by means of finite element simulations. Thanks to this model, the fundamental properties of the new shield are highlighted. Additionally, this paper compares the volumetric performance of the folded coaxial shield to the one of a ring shield, the latter being installed in many CCCs for measuring particle beam currents in accelerator facilities. [ABSTRACT FROM AUTHOR]

In continuum mechanics, there exists a unique theory for elasticity, which includes the first gradient of displacement. The corresponding generalization of elasticity is referred to as strain gradient elasticity or higher gradient theories, where the second and higher gradients of displacement are involved. Unfortunately, there is a lack of consensus among scientists how to achieve the generalization. Various suggestions were made, in order to compare or even verify these, we need a generic computational tool. In this paper, we follow an unusual but quite convenient way of formulation based on action principles. First, in order to present its benefits, we start with the action principle leading to the well-known form of elasticity theory and present a variational formulation in order to obtain a weak form. Second, we generalize elasticity and point out, in which term the suggested formalism differs. By using the same approach, we obtain a weak form for strain gradient elasticity. The weak forms for elasticity and for strain gradient elasticity are solved numerically by using open-source packages-by using the finite element method in space and finite difference method in time. We present some applications from elasticity as well as strain gradient elasticity and simulate the so-called size effect. [ABSTRACT FROM AUTHOR]

We present a finite element implementation of a Cosserat elasto-plastic model and provide a rigorous numerical analysis of the introduced time-incremental algorithm. The model allows the use of standard tools from convex analysis as known from classical Prandtl–Reuss plasticity. We derive the dual stress formulation and prove that for vanishing Cosserat couple modulus μc → 0 the classical problem is approximated. Our numerical results show the robustness of the approximation. Notably, for positive couple modulus μc > 0 there is no need for a safe-load assumption. For small μc the response is numerically indistinguishable from the classical response. [ABSTRACT FROM AUTHOR]

In this research, we delve into the intricacies of viscous fluid flow with electric field coupling by employing the Finite Element Method (FEM) in tandem with the level set method. We generate a weak form for satisfying governing equations for electric field and fluid velocity while two phases are tracked by the level set function. The primary focus of this study is the complex interactions between free-falling jet and electric field, and the behavior of droplet encompassing deformation, fission, and fusion under the influence of electric field. The main contribution of this paper is given a new implement by using the P1/P1 scheme to directly solve the weak forms of coupled governing equations, which significantly improves calculation efficiency compared to the P2/P1 scheme, and we open source the code. This implement is verified by comparing with the experimental results of oil droplets deforming under an electric field. Computations are performed by FEniCS open-source packages. The phenomena documented underscore the multifaceted relationship between electrodynamic forces and fluid mechanics, accentuated distinctly under non-uniform electric field conditions. [Display omitted] • We develop an FEM with the P1/P1 scheme for Conservative Level Set (CLS) method to achieve interface tracking. • Variational formulation is presented for solving electric field and fluid velocity, while the level set function tracks the two phases. • The numerical implementation is validated against experimental results of oil droplets deforming under electric field. • This paper explores the intricate dynamics of a free-falling jet in an electric field, examining how droplets undergo deformation, fission, and fusion. [ABSTRACT FROM AUTHOR]

In medicine a fundamental understanding for blood flow in human arteries is significantly important. In socalled hemodynamics engineers all over the world simulate blood flows in healthy and diseased vessels. Scientific findings in this area help to improve cardiovascular assisting devices and to plan surgical operations. The difficulty with such simulations is the interaction of the blood flow with the elastic vessel wall, which deforms due to changing flow conditions. We will present a two-dimensional model for blood flowing through an arterial vessel and investigate the balance of mass and the balance of linear momentum. We will adjust these balance equations appropriately and define time dependent boundary conditions. The necessary partial differential equations for the fluid-structure interaction will be solved by using the finite element method in FEniCS [1]. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determined with the demonstrated computational approach. Examples for epoxy carbon fiber composite, metal matrix composite, and aluminum foam illustrate the effectiveness and versatility of the proposed method. The influences of volume fraction of matrix, the stack of RVEs, and the varying unit cell lengths on the identified parameters are investigated. The homogenization computational tool is applicable to a wide class materials and makes use of open-source codes in FEniCS. We make all of the codes publicly available in order to encourage a transparent scientific exchange. [Display omitted] • We exploit asymptotic homogenization for determining all the parameters in the strain gradient theory. • An FEM based computational approach determines all parameters in rank four, five, and six tensors in generalized elasticity. • The proposed homogenization method identifies the effective parameters of composite materials with periodic microstructures. • Verification of the identified parameters is conducted in the case of a 3-D beam bending problem by using open-source packages in FEniCS. • We make all of the codes publicly available in order to encourage a transparent scientific exchange. [ABSTRACT FROM AUTHOR]

In an analysis presented in 1909, Poynting (page 546 of [1] ) had shown that for finite elastic deformations, the lines of greatest extension and contraction are inclined to the diagonals of the rhombus into which a square is sheared. The implication of this finding was that when slender structures are twisted, they undergo elongation as experimentally verified by Poynting's measurements with wires [1] . While many theoretical analyses have shown the possibility of Poynting and reverse (inverse) Poynting effect [2–7] , measurements of such effects are rather sparse [8–11] . We present here measurements of a highly nonlinear Poynting effect, including its reversal from positive to negative (elongation to compression) direction during torsion. Such atypical behavior is exhibited by a rather exceptional material system that has a pantographic internal structure. For this material system, the classical Cauchy-type continuum model fails and a 2nd gradient continuum model is necessary to describe many of its deformation behaviors. [ABSTRACT FROM AUTHOR]