Shell Finite Cell Method: A high order fictitious domain approach for thin-walled structures

This article presents a generalization of the recently proposed Finite Cell Method to thin-walled structures. This approach uses a combination of well known Fictitious Domain Methods with high order hierarchical Ansatz spaces known from the p-version of the Finite Element Method. Whereas the original concept embeds a three-dimensional structure in a simple domain being meshed into a grid of cube shaped cells, the extension presented in this paper applies the fictitious domain approach to a two-dimensional master domain defined in the parameter plane of the geometric model. Implementation details are discussed and numerical benchmark problems show the high accuracy and computational efficiency of the new approach. It is also remarked, that the present approach can easily be carried over to isogeometric analysis, opening an attractive possibility to simulate trimmed NURBS-surfaces.     

Turbulent premixed flame model based on a recent dispersion model

A model of turbulent premixed combustion is formulated based on a recent dispersion model and on earlier flame models. The dispersion model accounts for the effect of velocity correlation on turbulent dispersion without using parameters that are explicitly dependent on time or space. The earlier flame models are used as a basis for formulating an appropriate chemical source term. The resulting model is more general than the earlier models.The proposed model and one of the earlier models are validated against various experimental flames. It is shown that the proposed model is more accurate and requires less calibration. Furthermore, the proposed model is tested successfully against general criteria for premixed combustion modeling formulated in earlier works. It is therefore concluded that the dispersion model is a useful tool for premixed combustion modeling.     

Iso-Kinematic Maps from statistical analysis of PS-InSAR data of Piemonte, NW Italy: Comparison with geological kinematic trends

SAR interferometry based on Permanent Scatterers (PS-InSAR™) is used here to study the present crustal mobility of a large area of NW Italy, in the Piemonte region.Thirty-eight satellite scenes (ERS SAR), taken from May 1992 to January 2001, were analysed for detecting more than 2 million PS on the study area. Continuous velocity surface maps (Iso-Kinematic Maps: IKM) were obtained from geo-statistical and spatial cluster techniques (Hot Spot analysis) of PS “short-period” data, to identify relative ground motions and to compare them with “long-period” tectonic mobility trends, i.e. those inferred at regional scale over geological times (some million years).The comparison was made by individuation of homogeneous kinematic areas, represented in the IKM, and characterization of the boundaries between them (Iso-Kinematic Boundaries: IKB). The IKB were used as tools to asses if the PS-InSAR data on present-day crustal mobility could fit with the distribution of real tectonic structures or field geological elements.IKM were drawn for uplifting geological sectors of Piemonte (Maritime Alps, Gran Paradiso, Langhe) where moderate to very low seismicity is recorded, and gravitational instabilities of rock mass on mountain slopes are widespread. The land sectors have been chosen in order to test the suitability of IKM in very different geo-morphological conditions.Different types of correspondence between the IKM and the geological kinematic trend were found:

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a first type in which the kinematic trend of short-period (a decade of years, i.e. the PS-InSAR detection time span) is in agreement with a long-period tectonic trend (some million years) and seem to be driven by well known faults subparallel to the IKB. These kinematic trends can be hidden by the slope movement due to gravitational instabilities;

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a second type in which the kinematic trend of short-period does not strictly correspond to the long-period trend, but can be considered as minor-order, uplifting-subsidence cycles, even if in contrast with the long-period kinematic trend. Alternatively, the short-period kinematic trends could reflect the action of deep-seated geological forces or structures, not yet known or inferable (at least with the recorded PS-InSAR velocities) on the basis of the available geological data and models.

     

A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner–Mindlin plates

This paper proposes a quadrilateral finite element method of the lowest order for Reissner–Mindlin (R–M) plates on the basis of Hellinger–Reissner variational principle, which includes variables of displacements, shear stresses and bending moments. This method uses continuous piecewise isoparametric bilinear interpolation for the approximation of transverse displacement and rotation. The piecewise-independent shear stress/bending moment approximation is constructed by following a self-equilibrium criterion and a shear-stress-enhanced condition. A priori and reliable a posteriori error estimates are derived and shown to be uniform with respect to the plate thickness t. Numerical experiments confirm the theoretical results.     

Finite element analysis with uncertain probabilities

This paper presents a general method for the finite element analysis of linear mechanical systems by taking into account probability density functions whose parameters are affected by fuzziness. Within this framework, the standard perturbation-based stochastic finite element method is relaxed in order to incorporate uncertain probabilities in static, dynamic and modal analyses. General formulae are provided for assessing the (fuzzy) structural reliability and several typologies of optimization problems (reliability-based design, robust design, robust/reliability-based design) are formalized. In doing this the credibility theory is extensively used to extract qualified crisp data from the available set of fuzzy results, so that standard optimizers can be adopted to solve the most important design problems. It is shown that the proposed methodology is a general and versatile tool for finite element analyses because it is able to consider, both, probabilistic and non-probabilistic sources of uncertainties, such as randomness, vagueness, ambiguity and imprecision.     

An hp finite element adaptive scheme to solve the Laplace model for fluid–solid vibrations

In this paper we introduce an hp finite element method to solve a two-dimensional fluid–structure spectral problem. This problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid. We prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues. We define an a posteriori error estimator of the residual type which can be computed locally from the approximate eigenpair. We show its reliability and efficiency by proving that the estimator is equivalent to the energy norm of the error up to higher order terms, the equivalence constant of the efficiency estimate being suboptimal in that it depends on the polynomial degree. We present an hp adaptive algorithm and several numerical tests which show the performance of the scheme, including some numerical evidence of exponential convergence.     

An interface finite element for the simulation of localized membrane-bending deformation in shells

The folding of thin shells around localized lines occurs in several situations of engineering interest, such as in buckling induced deformation, as the consequence of crash, in industrial processes like metal forming, in the deployment of folded membranes, in packaging related processes. In this paper an interface element, allowing for displacement and rotation discontinuities, to be placed between two adjacent 4-node Mindlin–Reissner shell finite elements, is developed for a computationally effective simulation of this type of localized deformation. The large displacement and rotation kinematics of the interface element is discussed, arriving at a rigid-rotation free element tangent stiffness matrix. An adaptive dynamic relaxation scheme is proposed for the evolutionary analysis of the quasi-static structural response. To test the element formulation, a simple coupled membrane-bending elastoplastic behavior is assumed. The element is used for the simulation of few examples taken from the literature, where the structural response is characterized by the formation of plastic hinges, exhibiting good accuracy and computational effectiveness.     

IsoGeometric analysis using T-splines on two-patch geometries

We develop optimal approximation estimates for T-splines in the case of geometries obtained by gluing two standard tensor product patches. We derive results both for the T-spline space in the parametric domain and the mapped T-NURBS in the physical one. A set of numerical tests in complete accordance with the theoretical developments is also presented.     

A singular ES-FEM for plastic fracture mechanics

The stress and strain fields around the crack tip for power hardening material, which are singular as r approaches zero, are crucial to fracture and fatigue of structures. To simulate effectively the strain and stress around the crack tip, we develop a seven-node singular element which has a displacement field containing the HRR term and the second order term. The novel singular element is formulated based on the edge-based smoothed finite element method (ES-FEM). With one layer of these singular elements around the crack tip, the ES-FEM works very well for simulating plasticity around the crack tip based on the small strain formulation. Two examples are presented with detailed comparison with other methods. It is found that the results of the presented singular ES-FEM are closer to reference solution, which demonstrates the applicability and the effectiveness of our method for the plastic field around the crack tip.     

Metric concepts and implications in describing compositional changes for world river's water chemistry

The paper is designed to give the reader an outline that is useful for understanding the importance of distance, as a metric concept, and its implications when compositional (geochemical) data are managed from a statistical point of view in a given sample space. Application examples are shown by considering the construction of confidence regions and mixing models. The analyzed data are related to the chemistry of the most important rivers of the world as referring to the GEMS/WATER Global Register of River Inputs when each sample (river) is represented as a composition. A compositional vector of d parts, x=[x₁,x₂,…,x_d], is defined as a vector in which the only relevant information is contained in the ratios between its components. All the components of the vector are assumed positive and are called parts (variables), while the whole compositional vector, with the sum of the parts equal to a constant, represents the composition. In this case data are not represented by variables free to vary from −∞ to +∞ within a Euclidean space but occupy a restricted part of it called the simplex. The d-part simplex, S^d, is a subset of a d-dimensional real space. In this context the metric of the R space, with the definition of basic algebraic operations and of inner product, norm and distance, thus giving an Euclidean vector space structure, cannot be applied since the scale is relative and not absolute.