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In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the consistent mass matrix that follows from the integral of the traction jump across element boundaries. The added term is weighted by a small factor, for which we derive a suitable, and simple, element-local parameter choice. We perform numerical experiments for the linear wave equation in one and two dimensions, for quadrilateral elements and triangular elements, and for up to fourth order polynomial basis functions. Despite the increase in critical time-step size, we do not observe adverse effects in terms of spatial accuracy and orders of convergence. To extend the method to non-linear problems, we introduce a linear approximation. Our three-dimensional experiments with tetrahedral and hexahedral elements show that a sizeable increase in critical time-step size can be achieved while only causing minor (even beneficial) influences on the dynamic response.

Predictive simulations are useful in biomechanics to determine the optimal trajectories between two mechanical states and their forces in an in-silico approach. To perform these predictions, optimal control problems are increasingly in use. However, the efficiency of their formulation is crucial: in order to converge to the same optimal solution, some formulations could take a higher number of iterations than others. The paper presents an analysis of how certain key factors affect the convergence of these simulations. We compare the convergence of several optimal control problems solved using a direct collocation method. Eight planar torque-driven models of a human skeleton are used with four different types of coordinates and two dynamic formulations. The results show that both the mass matrix of the multibody system and the Hessian matrix of the non-linear problem affect the convergence of the solution: there is a statistical significant relationship among the number of iterations and the conditioning of these two matrices. Moreover, the study shows that the optimal control problems formulated with absolute coordinates are the ones requiring the lowest number of iterations overall. These findings suggest that formulations leading to poor conditioning of mass and Hessian matrices should be avoided., Peer Reviewed, Postprint (author's final draft)

In this paper, we propose a fully smoothed extended finite element method (SmXFEM) for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrixes can be computed by smoothing technique. This is accomplished by combining the Green’s divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub-triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion.

In this paper, we propose a fully smoothed extended finite element method (SmXFEM) for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrixes can be computed by smoothing technique. This is accomplished by combining the Green’s divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub-triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion.

The presence of a zero texture in the neutrino mass matrix can indicate the presence of an underlying symmetry which can generate neutrino mass and mixing. In this paper, for the first time, we study the four-zero textures of the low energy neutrino mass matrix in the presence of an extra light-sterile neutrino, i.e., the 3 + 1 neutrino scheme. In our analysis, we find that out of the 210 possible four-zero textures only 15 textures are allowed. We divide the allowed four-zero textures into two classes-A in which the value of mass matrix element M-ee is zero and class B in which M-ee is nonzero. In this way, we obtain ten possible four-zero textures in class A and five possible four-zero textures in class B. In our analysis, we find that for normal hierarchy the allowed number of textures in class A (B) is nine (three). For the case of inverted hierarchy, we find that two textures in class A are disallowed, and these textures are different from the disallowed textures for normal hierarchy in class A. However, we find that all the five textures in class B are allowed for the inverted hierarchy. Based on analytic expressions for the elements M-alpha beta, we discuss the reasons for certain textures being disallowed. We also discuss the correlations between the different parameters of the allowed textures. Finally, we present the implications of our study on experimental searches for neutrinoless double beta decay., QC 20170102

The method of building the computational model of attachment interconnects relationships which uses beam type finite element, superelements, absolutely rigid and kinematic constraints for the dynamic packet-rod model of a carrier rocket is presented. Using the results of computer tests the stiffness and inertial mass characteristics of two-node superelements approximating the attachment points of the main unit and suspension modules of a "Cyclone-4" rocket is determined. Using the data of finite element modeling of the three-dimensional elastic stress-strain state of the twenty-four calculating schemes, the stiffness matrix of two-node superelements approximating the attachment points of the main (central) and auxiliary (suspended) blocks of the rocket is defined. To assess the influence of inertial-mass characteristics of the power frames at the corresponding nodes of the discrete model of central unit and suspension modules, the corresponding equivalent masses with respective inertia moments are included, Представлена методика построения расчетной модели узлов крепления межблочных связей с применением конечных элементов балочного типа, суперэлементов, абсолютно жестких и кинематических связей для динамической пакетно-стержневой модели ракетоносителя Используя результаты компьютерных тестов определены жесткостные и инерционно-массовые характеристики двухузловых суперэлементов, аппроксимирующих узлы крепления основного блока и подвесных модулей ракетоносителя «Циклон-4», Представлена методика побудови розрахункової моделі вузлів кріплення міжблочних зв'язків із застосуванням скінченних елементів балкового типу, суперелементів, абсолютно жорстких і кінематичних зв'язків для динамічної пакетно-стрижневий моделі ракетоносія. Використовуючи результати комп'ютерних тестів визначені жорсткістні та інерційно-масові характеристики двовузлового суперелементу, що застосовується для аппроксимації вузлів кріплення основного блоку і підвісних модулів ракетоносія «Циклон-4»

We suggest a minimal extension of the simplest A(4) flavor model that can induce a nonzero theta(13) value, as required by recent neutrino oscillation data from reactors and accelerators. The predicted correlation between the atmospheric mixing angle theta(23) and the magnitude of theta(13) leads to an allowed region substantially smaller than indicated by neutrino-oscillation global fits. Moreover, the scheme correlates CP violation in neutrino oscillations with the octant of the atmospheric mixing parameter theta(23) in such a way that, for example, maximal mixing necessarily violates CP. We briefly comment on other phenomenological features of the model.

A linear finite element with constant cross section can take any orientation in the plane and its ends or nodes bind it to the rest of the elements. The kinetic (T) and potential (V) energy of a dynamic elastic element are the basis for the implementation of the Hamilton principle for the definition of a finite element. The definition of kinetic and potential energy is the first step for the preliminary variational formulation to the finite element enunciation that is used to solve, say, the problems of mechanisms that move in the plane using the Hamilton Equation. The general objective was to define the equation of motion of a dynamic elastic flat linear finite element using the Hamilton equation, from the Lagrangian (T –V) obtained with the use of a fifth and first degree polynomial, with eight degrees of freedom, four in each node, which represented the deformations: axial (u (x)), transverse (w (x)), slope ((dw (x) / dx)) and curvature ((d ^ 2w ( x) / dx ^ 2)). The deformation due to the transverse, insignificant shear compared to the flexional and axial deformation, the rotational inertia and the frictional forces in the joints, were rejected in order to produce a friendly element. The specific objectives were to produce: (a) the translation mass matrix [MD], (b) the gyroscopic translation matrix [AD], (c) the total translation rigidity matrix [KD], and (d) the deformation vector (S). As a result, the equation of motion of a dynamic elastic flat linear finite element was forged, Un elemento finito lineal con sección transversal constante puede adoptar cualquier orientación en el plano y sus extremos o nodos lo ligan al resto de los elementos. La energía cinética (T ) y potencial (V ) de un elemento elástico dinámico son el basamento en la implementación del principio de Hamilton para la definición de un elemento finito. La definición de la energía cinética y potencial es el primer paso para la formulación variacional preliminar a la enunciación por elementos finitos que se utiliza para resolver, dígase, los problemas de mecanismos que se mueven en el plano utilizando la Ecuación de Hamilton. El objetivo general consistió en definir la Ecuación del movimiento de un elemento finito lineal plano elástico dinámico utilizando la Ecuación de Hamilton, a partir de la lagrangiana (T –V ) obtenida con el uso de un polinomio de quinto y uno de primer grados, con ocho grados de libertad, cuatro en cada nodo, que representaron las deformaciones: axial (u(x)), transversal (w(x)), pendiente ((dw(x)/dx)) y curvatura ((d^2w(x)/dx^2)). La deformación debido al cizalleo transversal, insignificante comparado con la deformación flexional y la axial, la inercia rotatoria y las fuerzas friccionales en las uniones, fueron desestimadas con el fin de producir un elemento amigo. Los objetivos específicos fueron producir: (a) la matriz de masa de traslación [MD], (b) la matriz giroscópica de traslación [AD], (c) la matriz de rigidez total de traslación [KD], y (d) el vector de deformación (S). Como resultado se forjó la Ecuación del movimiento de un elemento finito lineal plano elástico dinámico

We perform a reconstruction of the mass matrix of heavy right-handed Majorana neutrinos in the framework of the left - right symmetric type I + II seesaw mechanism. An intriguing pairwise duality relation between different solutions is shown to exist., QC 20110927. Conference: 2nd Scandinavian NeutrinO Workshop. Stockholm, SWEDEN. MAY 02-06, 2006

We establish the existence of one-loop finite relations between the Cabibbo angle and the quark mass ratios, in a Standard Model with one Higgs doublet and two quark generations. The argument is based on the calculation of the divergent one-loop radiative corrections to the quark mass matrices.

Mass matrix lumping by quadrature is considered. Accuracy requirements seem to dictate the use of zero negative masses for multi-dimensional higher-order elements. It is shown that the zero and/or negative masses do not destroy the essential algebraic properties of the discrete eigen problems, in spite of the negative or infinite eigenvalues which may result. Explicit transient methods require positive definite lumping which, for some elements, may only be achieved by sacrificing accuracy to avoid the negative or zero masses that would render the lumping indefinite. An implicit-explicit time integration method based on quadratic triangles with optimal lumping is devised, analysed, and tested. It treats the nodes with nonzero masses explicitly and the nodes with zero masses implicitly. Analysis and numerical tests show that this formulation is optimally accurate and less costly than a similar method with nonzero masses, based on optimally lumped biquadratic rectangles. The method is also found to be substantially more accurate than the fully explicit method based on lumping the triangular elements in an ad-hoc fashion to retain non-zero masses. Keywords: Mass matrix; Numerical quadrature; Stability; Vibration modes. (Author), Includes errata dated 30 Apr 86.

A method is outlined for treating fluid-solid interaction vibration problems as a solid continuum by the finite element procedure. The current approach to problems of this kind is reviewed, together with the equations governing the current approach to the vibration problem of a solid structure alone. The type of finite element necessary to treat the fluid-solid problem as a solid continuum is then described and results and comparisons with previous work are presented. (Author)