Spurious Constraints Research Articles

Size-dependent electro-static analysis of smart micro-sandwich panels with functionally graded core

This paper investigates the electro-static response of smart micro-sandwich panels with functionally graded core, nano-composite facing, and piezoelectric layers. To consider the size-dependent effect, nonlocal theory is adopted to governing equations and boundary conditions. Three-dimensional approach is implemented that takes into account shear effect of thick core and drastic changes of sandwich panel and free from spurious constraints of equivalent plate theories. Closed-form solution is obtained in systematic step-by-step procedure for smart micro-panels to solve the coupled nonlocal differential equations analytically. The obtained results are compared with finite element results for the case of isotropic thick plate and excellent agreement between result is revealed. A detailed parametric study is conducted to bring out the effect of size-dependent parameter, functionally graded material, length-to-thickness ratio, and aspect ratio on the bending behavior of smart micro-sandwich panels.

Detecting dark matter cores in galaxy clusters with strong lensing

We test the ability of strong lensing data to constrain the size of a central core in the dark matter haloes of galaxy clusters, using Abell 611 as a prototype. Using simulated data, we show that modelling a cluster halo with ellipticity in the gravitational potential can bias the inferred mass and concentration, which may bias the inferred central density when weak lensing or X-ray data are added. We also highlight the possibility for spurious constraints on the core size if the radial density profile is different from the assumed model. These systematics can be ameliorated if central images are present in the data. Applying our methodology to Abell 611 and imposing a reasonable prior on the stellar mass-to-light ratio restricts the core size to be less than about 4 kpc, with a minimum reduced χ2 of 0.28, and with RMS error of 0|${^{\prime\prime}_{.}}$|12 in image positions. Such small cores imply a constraint on the dark matter self-interaction cross section of the order of |$0.1\ \mathrm{cm^2\, g}^{-1}$| at relative velocities of about 1500 km s−1. In addition, our results imply a bottom-heavy (super-Salpeter) initial mass function for the central galaxy in the Abell 611.

Dynamic snap-through buckling of CNT reinforced composite sandwich spherical caps

This paper investigates the nonlinear dynamic buckling response of axisymmetric carbon nanotubes reinforced composite sandwich spherical caps subjected to suddenly applied pressure. To solve this problem, a finite element approach is adopted using an axisymmetric shear flexible shell element, free from spurious constraints causing shear and membrane locking especially for the case of thin shells. The geometric nonlinearity is accounted for in the formulation using von Karman’s strain-displacement relations. Newmark’s integration technique along with the modified Newton-Raphson iteration scheme is employed to solve the nonlinear governing equations. The critical dynamic pressure value is considered as the pressure load beyond which the maximum average displacement response shows instant growth in the time history of the shell structure. The obtained results are validated against the available analytical solutions for the case of isotropic spherical caps. A detailed parametric study is carried out to bring out the effects of shell geometry parameter, volume fraction of the CNT, core-to-face sheet thickness, temperature, boundary conditions and different types of pulse on the dynamic snap-through characteristics of spherical shells.

Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams

The performance of two curved beam finite element models based on coupled polynomial displacement fields is investigated for out-of-plane vibration of arches. These two-noded beam models employ curvilinear strain definitions and have three degrees of freedom per node namely, out-of-plane translation (v), out-of-plane bending rotation (θz) and torsion rotation (θs). The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler–Bernoulli beam elements using the force-moment equilibrium equations. Numerical performance of these elements for constrained and unconstrained arches is compared with the conventional curved beam models which are based on independent polynomial fields. The formulation is shown to be free from any spurious constraints in the limit of ‘flexureless torsion’ and ‘torsionless flexure’ and hence devoid of flexure and torsion locking. The resulting stiffness and consistent mass matrices generated from the coupled displacement models show excellent convergence of natural frequencies in locking regimes. The accuracy of the shear flexibility added to the elements is also demonstrated. The coupled polynomial models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena.

P1-Nonconforming shell element and its application to topology optimization

The P1-nonconforming quadrilateral element developed by Park and Sheen [19] is employed for the formulation of a four-node degenerated shell element. The numerical stability of the P1-nonconforming quadrilateral element verified in plane elasticity problems and Stokes flow problems is investigated for the application of mitigating locking phenomena in shell problems. To facilitate the stiffness matrix computation for a non-flat general quadrilateral shell element, a nonparametric reference scheme using both affine transformation and bilinear transformation is adopted. Based on a field-consistency concept, the spurious constraints that cause locking are analyzed and an effective reduced integration scheme is found. The proposed shell element is applied to multi-physics topology optimization problems involving fluid analysis and shell analysis. For fluid analysis, the P1-nonconforming quadrilateral element is also adopted to utilize its volumetric locking-free property for incompressible materials. Vein layouts of leaves are designed by topology optimization and compared with natural vein layouts to verify the effectiveness of the proposed element.

Free vibration analysis for shells of revolution based on p-version mixed finite element formulation

In this study, an effective p-version two-node mixed finite element is newly presented for predicting the free vibration frequencies and mode shapes of isotropic shells of revolution. The present element considering shear strains is based on Reissner–Mindlin shear deformation shell theory and Hellinger–Reissner variational principle. To improve the accuracy and resolve the numerical difficulties due to the spurious constraints, field-consistent stress parameters are employed corresponding to displacement shape functions with high-order hierarchical shape functions. The elimination of stress parameters and the reduction of the nodeless degrees by the Guyan reduction yield the standard stiffness and mass matrix. Results of the proposed element are compared with analytical, experimental and numerical solutions found in the literature. We can confirm a very satisfactory numerical behavior of the present p-version mixed element.

Constructive Representation of Trust: Single Rule Paradigm

A constructive computational framework for trust and reputation assessments is presented. It is proven free from any inconsistent or contradictory assessments under any scenarios of its application. A prototype implementation has been developed. The framework focuses on a single information-theoretical rule as inference mechanism, thus avoiding any biases or spurious constraints in the solutions. The users of our model will find its results intuitively plausible, free from clustering or drift to the extrema. The entire framework is suited for a direct use in economic, financial and intelligence analyses.

Reply to Mouesca et al.: Electronic structure of the proximal [4Fe-3S] cluster of O 2 -tolerant [NiFe] hydrogenases

Mouesca et al. (1) criticize our analysis (2) of the superoxidized proximal [4Fe-3S]5+ cluster in O2-tolerant hydrogenases ( A ) that was also studied in Volbeda et al. (3), albeit from a different organism. Both analyses were based on broken-symmetry (BS) density functional theory (DFT) calculations (2, 3), which presently is the only feasible alternative for the treatment of complex systems like A . However, BS-DFT is a crude approach and we regard the differences in refs. 2 and 3 as subtle rather than major. The critique raised in Mouesca et al. (1) that our cluster model was too small and incorporated spurious constraints is unfounded. In Volbeda et al. (3), only three additional amino acid … [↵][1]2To whom correspondence may be addressed. E-mail: frank.neese{at}cec.mpg.de or wolfgang.lubitz{at}cec.mpg.de. [1]: #xref-corresp-1-1

Coupled polynomial field approach for elimination of flexure and torsion locking phenomena in the Timoshenko and Euler–Bernoulli curved beam elements

The curvature related locking phenomena in the out-of-plane deformation of Timoshenko and Euler–Bernoulli curved beam elements are demonstrated and a novel approach is proposed to circumvent them. Both flexure and Torsion locking phenomena are noticed in Timoshenko beam and torsion locking phenomenon alone in Euler–Bernoulli beam. Two locking-free curved beam finite element models are developed using coupled polynomial displacement field interpolations to eliminate these locking effects. The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler–Bernoulli beam elements using the governing equations. The presence of penalty terms in the coupled displacement fields incorporates the flexure–torsion coupling and flexure–shear coupling effects in an approximate manner and produce no spurious constraints in the extreme geometric limits of flexure, torsion and shear stiffnesses. The proposed coupled polynomial finite element models, as special cases, reduce to the conventional Timoshenko beam element and Euler–Bernoulli beam element, respectively. These models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena. The efficacy, accuracy and reliability of the proposed models to straight and curved beam applications are demonstrated through numerical examples.

On Shear Locking in MLPG Solid-Shell Approach

A solid-shell MLPG approach for the numerical analysis of plates and shells is presented. A special attention is devoted to the transversal shear locking effect that appears in the structure thin limit. The theoretical origins of shear locking in the purely displacement-based approach are analyzed by means of the consistency paradigm. It is shown that the spurious constraints appear in the constrained strain field, which lead to the appearance of shear locking and sub-optimal convergence rates. The behaviour of the mixed MLPG approach in the thin limit is also considered. It is determined that the mixed paradigm does not lock because the Kirchoff-Love conditions have to be satisfied only at the nodes. The validity of the theoretical predictions is supported by the presented numerical examples, where good convergence and accuracy is obtained even if the low-order meshless approximations are used.

고차 혼합 곡선보 요소에 의한 아치의 자유진동해석

The purpose of this research work is to demonstrate a successful application of hybrid-mixed formulation and nodeless degrees of freedom in developing a very accurate in-plane curved beam element for free vibration analysis. To resolve the numerical difficulties due to the spurious constraints, the present element, based on the Hellinger-Reissner variational principle and considering the effect of shear deformation, employed consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees. The stress parameters were eliminated by the stationary condition, and the nodeless degrees were condensed by Guyan Reduction. Several numerical examples indicated that the property of the mass matrix as well as that of the stiffness matrix have a great effect on the numerical performance. The element with consistent mass matrix produced best results on convergence and accuracy in the numerical analysis of Eigenvalue problems. Also, the higher-order mixed curved beam element showed a superior numerical behavior for the free vibration analyses.

An effective composite laminated curved beam element

AbstractIn this study, we present a new highly accurate composite laminated hybrid‐mixed curved beam element. The present element, which is based on the Hellinger–Reissner variational principle and the first‐order shear deformation lamination theory, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees of freedom in order to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the (6 × 6) element stiffness matrix. Several numerical examples confirm the superior behaviour of the present hybrid‐mixed laminated curved beam element. Copyright © 2005 John Wiley & Sons, Ltd.

Constraining dark energy with X-ray galaxy clusters, supernovae and the cosmic microwave background

We present new constraints on the evolution of dark energy from an analysis of Cosmic Microwave Background, supernova and X-ray galaxy cluster data. Our analysis employs a minimum of priors and exploits the complementary nature of these data sets. We examine a series of dark energy models with up to three free parameters: the current dark energy equation of state w{sub 0}, the early time equation of state w{sub et} and the scale factor at transition, a{sub t}. From a combined analysis of all three data sets, assuming a constant equation of state and that the Universe is flat, we measure w{sub 0} = 1.05{sub -0.12}{sup +0.10}. Including w{sub et} as a free parameter and allowing the transition scale factor to vary over the range 0.5 < a{sub t} < 0.95 where the data sets have discriminating power, we measure w{sub 0} = -1.27{sub -0.39}{sup +0.33} and w{sub et} = -0.66{sub -0.62}{sup +0.44}. We find no significant evidence for evolution in the dark energy equation of state parameter with redshift. Marginal hints of evolution in the supernovae data become less significant when the cluster constraints are also included in the analysis. The complementary nature of the data sets leads tomore » a tight constraint on the mean matter density, {Omega}{sub m} and alleviates a number of other parameter degeneracies, including that between the scalar spectral index n{sub s}, the physical baryon density {Omega}{sub b}h{sup 2} and the optical depth {tau}. This complementary nature also allows us to examine models in which we drop the prior on the curvature. For non-flat models with a constant equation of state, we measure w{sub 0} = -1.09{sub -0.15}{sup +0.12} and obtain a tight constraint on the current dark energy density, {Omega}{sub de} = 0.70 {+-} 0.03. For dark energy models other than a cosmological constant, energy-momentum conservation requires the inclusion of spatial perturbations in the dark energy component. Our analysis includes such perturbations, assuming a sound speed c{sub s}{sup 2} = 1 in the dark energy fluid as expected for Quintessence scenarios. For our most general dark energy model, not including such perturbations would lead to spurious constraints on w{sub et} which would be tighter than those mentioned above by approximately a factor two with the current data.« less

A new hybrid-mixed composite laminated curved beam element

In this study, we piesent a new efficient hybrid-mixed composite laminated curved beam element The present element, which is based on the Helhnger-Reissnet vatiational principle and the first-order shear deformation lamination theory, employs consistent stress parameters coriespondmg to cubic displacement polynomials with additional nodeless degrees in order to lesolve the numerical difficulties due to the spurious constraints The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the (6X6) element stiffness matrix The present study also incorporates the straightforwaid prediction of interlaminar stresses from equilibrium equations Seveial numencal examples confirm the superioi behavior of the present composite laminated curved beam element

A2-NODE BEAM ELEMENT BASED ON COUPLED DISPLACEMENT FIELD FOR BUCKLING ANALYSIS OF CURVED COMPOSITE BEAMS

The present paper aims to explore an alternatice interpolation strategy for the assumed displacement fields in the finite element buckling analysis of straigth and curved composite beams. The elemental static equilibrium equations are employed to derive the alternate interpolation polynomials for the displacement fields. These polynomials are coupled by means of coefficients involving the generalized co-ordinates and geometrical and material properties of the element. The proposed interpolation scheme lead to an element, which is free from spurious constraints in the Euler's limit of slender beam behaviour, that is in-extensible bending, and hence exhibits no locking. The 2-node beam element having six engineering degrees of freedom per node is developed using this coupled displacement field. The accuracy and convergence characteristics of the element are shown to be independent of material lay-up and slenderness ratio. To establish the consistent performance of the element, several test problems over a wide range of slenderness ratio with straigth-to-deep arch configurations of isotropic/composite materials are considered.

Frequency assignment with complex co-site constraints

The adaption of meta-heuristic algorithms such as tabu search and simulated annealing to large frequency assignment problems with complex co-site constraints is described. The constraints considered include frequency separation constraints, intermodulation product constraints and spurious emission and response constraints. Requests for frequencies can also be prioritised. The importance of fast evaluation of the quality of the current assignment by updating techniques is stressed. Additionally, a useful lower bound for assessing the quality of assignments is described.

Higher‐order hybrid‐mixed axisymmetric thick shell element for vibration analysis

AbstractIn this study, we present free vibration analysis of shells of revolution using the hybrid‐mixed finite element. The present hybrid‐mixed element, which is based on the modified Hellinger–Reissner variational principle, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out by the Guyan reduction. Several numerical examples show that the present element with cubic displacement interpolation functions and consistent quadratic stress functions is highly accurate for the free vibration analysis of shells of revolution, especially for higher vibration modes. Copyright © 2001 John Wiley &amp; Sons, Ltd.

Qualitative system identification with the use of on-line genetic algorithms

The major problem in building qualitative models via on-line qualitative system identification is how to filter the spurious constraints that are generated from the qualitative reasoning technique. This paper proposes a solution to this problem by an integration of genetic algorithms (GA) and qualitative reasoning. The paper will demonstrate the use of qualitative reasoning to partition the input quantity space into different subsystems, and implementation of GAs to filter and optimize the predicted constraints. The proposed method is verified by simulated examples that suggest the algorithm converges to the optimal point with high speed.

Free vibration of arches using a curved beam element based on a coupled polynomial displacement field

The performance of a curved beam finite element with coupled polynomial distributions for normal displacement ( w) and tangential displacement ( u) is investigated for in-plane flexural vibration of arches. A quartic polynomial distribution for u is derived from an assumed cubic polynomial field for w using force–moment equilibrium equations. The coupling of these displacement fields makes it possible to express the strain field in terms of only six generalized degrees of freedom leading to a simple two-node element with three degrees of freedom per node. Numerical performance of the element is compared with that of the other curved beam elements based on independently assumed field polynomials. The formulation is shown to be free from any spurious constraints in the limit of inextensional flexural vibration modes and hence does not exhibit membrane locking. The resulting well-conditioned stiffness matrix with consistent mass matrix shows excellent convergence of natural frequencies even for very thin deep arches and higher vibrational modes. The accuracy of the element for extensional flexural motion is also demonstrated.

New anisoparametric 3-node elements for out-of-plane deformable curved beam

Based on numerical reduced minimization theory, new anisoparametric 3-node elements for out-of-plane curved beam are developed. The elements are designed to be free from spurious constraints. In this paper, the effect of the Jacobian upon numerical solution is analyzed and predicted through reduced minimization analysis of anisoparametric 3-node elements with different Jacobian assumption. The prediction is verified by numerical tests for circular and spiral out-of-plane deformable curved beam models. This paper proposes two kinds of 3-node elements with 7-DOF; one element employs 2-point integration for all strains, and the other element uses 3-point integration with a constant Jacobian within element for calculation of shear strain.