1,332 research outputs found
Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces
We introduce a coupled finite and boundary element formulation for acoustic
scattering analysis over thin shell structures. A triangular Loop subdivision
surface discretisation is used for both geometry and analysis fields. The
Kirchhoff-Love shell equation is discretised with the finite element method and
the Helmholtz equation for the acoustic field with the boundary element method.
The use of the boundary element formulation allows the elegant handling of
infinite domains and precludes the need for volumetric meshing. In the present
work the subdivision control meshes for the shell displacements and the
acoustic pressures have the same resolution. The corresponding smooth
subdivision basis functions have the continuity property required for the
Kirchhoff-Love formulation and are highly efficient for the acoustic field
computations. We validate the proposed isogeometric formulation through a
closed-form solution of acoustic scattering over a thin shell sphere.
Furthermore, we demonstrate the ability of the proposed approach to handle
complex geometries with arbitrary topology that provides an integrated
isogeometric design and analysis workflow for coupled structural-acoustic
analysis of shells
Manifold-based isogeometric analysis basis functions with prescribed sharp features
We introduce manifold-based basis functions for isogeometric analysis of
surfaces with arbitrary smoothness, prescribed continuous creases and
boundaries. The utility of the manifold-based surface construction techniques
in isogeometric analysis was demonstrated in Majeed and Cirak (CMAME, 2017).
The respective basis functions are derived by combining differential-geometric
manifold techniques with conformal parametrisations and the partition of unity
method. The connectivity of a given unstructured quadrilateral control mesh in
is used to define a set of overlapping charts. Each vertex with
its attached elements is assigned a corresponding conformally parametrised
planar chart domain in , so that a quadrilateral element is
present on four different charts. On the collection of unconnected chart
domains, the partition of unity method is used for approximation. The
transition functions required for navigating between the chart domains are
composed out of conformal maps. The necessary smooth partition of unity, or
blending, functions for the charts are assembled from tensor-product B-spline
pieces and require in contrast to earlier constructions no normalisation.
Creases are introduced across user tagged edges of the control mesh. Planar
chart domains that include creased edges or are adjacent to the domain boundary
require special local polynomial approximants. Three different types of chart
domain geometries are necessary to consider boundaries and arbitrary number and
arrangement of creases. The new chart domain geometries are chosen so that it
becomes trivial to establish local polynomial approximants that are always
continuous across tagged edges. The derived non-rational manifold-based
basis functions are particularly well suited for isogeometric analysis of
Kirchhoff-Love thin shells with kinks
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Multiscale modelling of woven and knitted fabric membranes
Light-weight fabric membranes have gained increasing popularity over the past years due to their tailorable structural and material performances. These tailorable properties include stretch forming and deep drawing formability that exhibits excellent stretchability and drapeability properties of textiles and textile composites. Since the inception of computerised numerical control for three-dimensional textile-manufacturing machines,
technical textiles paved their way to numerous applications, certainly not limited to; aerospace, biomedical, civil engineering, defence, marine and medical industries. Digital interlooping and digital interlacing technology in additive manufacturing greatly advanced the manufacturing processes of textiles. In this work, we consider two branches of technical fabrics, namely plain-woven and weft-knitted.
Multiscale modelling is the tool of choice for homogenising periodic structures and has been used extensively to model and analyse the mechanical behaviour of woven and knitted fabrics. But there is a plethora of literature discussing the demerits of such conventional multiscale modelling. These demerits include higher computational costs,
rigid numerical models, ineffcient algorithmic computations and inability to incorporate geometric nonlinearities. We propose a data-driven nonlinear multiscale modelling technique to analyse the complex mechanical behaviour of plain-woven and weft-knitted fabrics with a neat extension to fabric material designing. We show how the integration of statistical learning techniques mitigates the weaknesses of conventional multiscale modelling. Moreover, we discuss the avenues that will open in many potential fields with regard to material modelling, structural engineering and textile industries.
In the proposed data-driven nonlinear computational homogenisation technique, we effi ciently integrate the microscale and macroscale using Gaussian Process Regression (GPR) statistical learning technique. In the microscale, representative volume elements (RVEs) are modelled using nite deformable isogeometric spatial rods and deformation is homogenised using periodic boundary conditions. This nite deformable rod is profi cient in handling large deformations, rod-to-rod contacts, arbitrary cross-section de finitions and follower loads. Respecting the principle of separation of scales, we construct response databases by applying different homogenised strain states to the RVEs and recording the respective incremental volume-averaged energy values. We use GPR
to learn a model using a 5-fold cross-validation technique by optimising the log marginal likelihood. In the macroscale, textiles are modelled as nonlinear orthotropic membranes for which the stresses and material constitutive relations are predicted by the trained GPR model. This coupling between GPR and membrane models is achieved through a
systematic and seamless nite element integration using C++ and Python environments. A neat extension to material designing is also discussed with potentials to extend the work into other related fi elds.Cambridge trust and Trinity Hall scholarshi
Point-set manifold processing for computational mechanics: thin shells, reduced order modeling, cell motility and molecular conformations
In many applications, one would like to perform calculations on smooth manifolds of dimension d embedded in a high-dimensional space of dimension D. Often, a continuous description of such manifold is not known, and instead it is sampled by a set of scattered points in high dimensions. This poses a serious challenge. In this thesis, we approximate the point-set manifold as an overlapping set of smooth parametric descriptions, whose geometric structure is revealed by statistical learning methods, and then parametrized by meshfree methods. This approach avoids any global parameterization, and hence is applicable to manifolds of any genus and complex geometry. It combines four ingredients: (1) partitioning of the point set into subregions of trivial topology, (2) the automatic detection of the local geometric structure of the manifold by nonlinear dimensionality reduction techniques, (3) the local parameterization of the manifold using smooth meshfree (here local maximum-entropy) approximants, and (4) patching together the local representations by means of a partition of unity.
In this thesis we show the generality, flexibility, and accuracy of the method in four different problems. First, we exercise it in the context of Kirchhoff-Love thin shells, (d=2, D=3). We test our methodology against classical linear and non linear benchmarks in thin-shell analysis, and highlight its ability to handle point-set surfaces of complex topology and geometry. We then tackle problems of much higher dimensionality. We perform reduced order modeling in the context of finite deformation elastodynamics, considering a nonlinear reduced configuration space, in contrast with classical linear approaches based on Principal Component Analysis (d=2, D=10000's). We further quantitatively unveil the geometric structure of the motility strategy of a family of micro-organisms called Euglenids from experimental videos (d=1, D~30000's). Finally, in the context of enhanced sampling in molecular dynamics, we automatically construct collective variables for the molecular conformational dynamics (d=1...6, D~30,1000's)
A comparison of smooth basis constructions for isogeometric analysis
In order to perform isogeometric analysis with increased smoothness on
complex domains, trimming, variational coupling or unstructured spline methods
can be used. The latter two classes of methods require a multi-patch
segmentation of the domain, and provide continuous bases along patch
interfaces. In the context of shell modeling, variational methods are widely
used, whereas the application of unstructured spline methods on shell problems
is rather scarce. In this paper, we therefore provide a qualitative and a
quantitative comparison of a selection of unstructured spline constructions, in
particular the D-Patch, Almost-, Analysis-Suitable and the
Approximate constructions. Using this comparison, we aim to provide
insight into the selection of methods for practical problems, as well as
directions for future research. In the qualitative comparison, the properties
of each method are evaluated and compared. In the quantitative comparison, a
selection of numerical examples is used to highlight different advantages and
disadvantages of each method. In the latter, comparison with weak coupling
methods such as Nitsche's method or penalty methods is made as well. In brief,
it is concluded that the Approximate and Analysis-Suitable converge
optimally in the analysis of a bi-harmonic problem, without the need of special
refinement procedures. Furthermore, these methods provide accurate stress
fields. On the other hand, the Almost- and D-Patch provide relatively easy
construction on complex geometries. The Almost- method does not have
limitations on the valence of boundary vertices, unlike the D-Patch, but is
only applicable to biquadratic local bases. Following from these conclusions,
future research directions are proposed, for example towards making the
Approximate and Analysis-Suitable applicable to more complex
geometries
Numerical Methods in Shape Spaces and Optimal Branching Patterns
The contribution of this thesis is twofold. The main part deals with numerical methods in the context of shape space analysis, where the shape space at hand is considered as a Riemannian manifold. In detail, we apply and extend the time-discrete geodesic calculus (established by Rumpf and Wirth [WBRS11, RW15]) to the space of discrete shells, i.e. triangular meshes with fixed connectivity. The essential building block is a variational time-discretization of geodesic curves, which is based on a local approximation of the squared Riemannian distance on the manifold. On physical shape spaces this approximation can be derived e.g. from a dissimilarity measure. The dissimilarity measure between two shell surfaces can naturally be defined as an elastic deformation energy capturing both membrane and bending distortions. Combined with a non-conforming discretization of a physically sound thin shell model the time-discrete geodesic calculus applied to the space of discrete shells is shown to be suitable to solve important problems in computer graphics and animation. To extend the existing calculus, we introduce a generalized spline functional based on the covariant derivative along a curve in shape space whose minimizers can be considered as Riemannian splines. We establish a corresponding time-discrete functional that fits perfectly into the framework of Rumpf and Wirth, and prove this discretization to be consistent. Several numerical simulations reveal that the optimization of the spline functional—subject to appropriate constraints—can be used to solve the multiple interpolation problem in shape space, e.g. to realize keyframe animation. Based on the spline functional, we further develop a simple regression model which generalizes linear regression to nonlinear shape spaces. Numerical examples based on real data from anatomy and botany show the capability of the model. Finally, we apply the statistical analysis of elastic shape spaces presented by Rumpf and Wirth [RW09, RW11] to the space of discrete shells. To this end, we compute a Fréchet mean within a class of shapes bearing highly nonlinear variations and perform a principal component analysis with respect to the metric induced by the Hessian of an elastic shell energy. The last part of this thesis deals with the optimization of microstructures arising e.g. at austenite-martensite interfaces in shape memory alloys. For a corresponding scalar problem, Kohn and Müller [KM92, KM94] proved existence of a minimizer and provided a lower and an upper bound for the optimal energy. To establish the upper bound, they studied a particular branching pattern generated by mixing two different martensite phases. We perform a finite element simulation based on subdivision surfaces that suggests a topologically different class of branching patterns to represent an optimal microstructure. Based on these observations we derive a novel, low dimensional family of patterns and show—numerically and analytically—that our new branching pattern results in a significantly better upper energy bound
Positive displacement compounding of a heavy duty diesel engine
A helical screw type positive displacement (PD) compressor and expander was considered as an alternative to the turbocharger and the power turbine in the Cummins advanced turbocompound engine. The Institute of Gas Technology (IGT) completed the design, layout, and performance prediction of the PD machines. The results indicate that a screw compressor-expander system is feasible up to at least 750 HP, dry operation of the rotors is feasible, cost and producibility are uncertain, and the system will yield about 4% improvement in brake specific fuel consumption (BSFC) over the advanced turbocompound engine
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