Microscopic study of higher-order deformation effects on the ground states of superheavy nuclei around Hs-270

We study the effects of higher-order deformations βλ (λ = 4,6,8, and 10) on the ground state properties of superheavy nuclei (SHN) near the deformed doubly magic nucleus 270Hs by using the multidimensionally-constrained (MDC) relativistic mean-field (RMF) model with five effective interactions PC-PK1, PK1, NL3∗, DD-ME2, and PKDD. The doubly magic properties of 270Hs are featured by the large energy gaps at N = 162 and Z = 108 in the single-particle spectra. By investigating the binding energies and single-particle levels of270Hs in multidimensional deformation space, we find that the deformation β6 has the greatest impact on the binding energy among these higher-order deformations and influences the shell gaps considerably. Similar conclusions hold for other SHN near 270Hs. Our calculations demonstrate that the deformation β6 must be considered when studying SHN by using MDC-RMF.

Gradient Nonlocal Enhanced Microprestress-Solidification Theory and Its Finite Element Implementation

Time-dependent responses of cracked concrete structures are complex, due to the intertwined effects between creep, shrinkage, and cracking. There still lacks an effective numerical model to accurately predict their nonlinear long-term deflections. To this end, a computational framework is constructed, of which the aforementioned intertwined effects are properly treated. The model inherits merits of gradient-enhanced damage (GED) model and microprestress-solidification (MPS) theory. By incorporating higher order deformation gradient, the proposed GED-MPS model circumvents damage localization and mesh-sensitive problems encountered in classical continuum damage theory. Moreover, the model reflects creep and shrinkage of concrete with respect to underlying moisture transport and heat transfer. Residing on the Kelvin chain model, rate-type creep formulation works fully compatible with the gradient nonlocal damage model. 1-D illustration of the model reveals that the model could regularize mesh-sensitivity of nonlinear concrete creep affected by cracking. Furthermore, the model depicts long-term deflections and cracking evolutions of simply-supported reinforced concrete beams in an agreed manner. It is noteworthy that the gradient nonlocal enhanced microprestress-solidification theory is implemented in the general finite element software Abaqus/Standard with the implicit solver, which renders the model suitable for large-scale creep-sensitive structures.

Thermal Buckling Analysis of Composite Plates using Isogeometric Analysis based on Bezier Extraction

Data transmission back and forth between finite element analysis (FEA) and computer-aided design (CAD) is a matter of huge concern today [2] and Isogeometric analysis [1] has been successful in merging these two fields in the recent past. The presentation will address isogeometric finite element approach (IGA) in combination with the first-order deformation plate theory (FSDT) for thermal buckling analysis of laminated composite plates. The IGA utilizes non-uniform rational B-spline (NURBS) as basis functions, resulting in both exact geometric representation and high order approximations [3] [4]. It enables to achieve easily the smoothness with arbitrary continuous order. The analyses have been performed using Bezier extraction and conventional IGA. In conventional isogeometric analysis the basis functions are not confined to one single element, but span a global domain whereas the Bézier extraction operator decomposes a set of linear combinations of Bernstein polynomials. The presentation will give a theoretical overview of B-splines, as well as NURBS, and also the concept of Bézier decomposition of these spline functions. The focus will then be on how the use of Bézier extraction eased the implementation into an already existing finite element code. This theoretical background will then be used to explain an isogeometric finite element analysis program. With the advent of More Electric Aircrafts [5], solving thermal structural problems [6] are of utmost importance in the aerospace industry. A static thermal structural validation problem will be presented for both constant and linear thermal temperature variation along the thickness. The presentation will then explain the procedures implemented for stress recovery and computing the geometric stiffness matrix. Numerical results of circular and elliptical plates will be provided to validate the effectiveness of the proposed method as compared to traditional FEA. The final section of the presentation proposes to detail the influences of length to thickness ratio, aspect ratio, boundary conditions, stacking sequence and material property on the critical buckling temperature. A special section would cover the idea of third order deformation theory for thicker plates and the effect of degree of NURBS basis on the results.

Dynamic Behavior of Externally Prestressed Continuous Beam considering Second-Order Effect

Considering precisely the second-order deformation of external tendon, the analytical solution of natural frequencies of 2-span externally prestressed continuous beam was obtained by the energy method. The effect of external prestress compression softening is between the zero effect of unbonded prestress compression and the effect of axial outside compression and is determined by the influence coefficient ranging within 0∼1. The influence coefficient is mainly related to the number of deviators and slightly related to tendon layout. Without deviator, the influence coefficient is 1, and the effect of external prestress compression softening is the same as the effect of axial outside compression. As the number of deviators increases, the influence coefficient gradually decreases from 1 to near 0, and the effect of external prestress compression softening is close to zero effect of unbonded prestress compression. With one or more deviators, the effect of external prestress compression softening is negligible. As the eccentricity and area of tendon increase, only the first symmetric frequency increases obviously, and other frequencies almost remain unchanged. The influence of tendon layout linear transformation on the frequency is negligible.

On Interacting Higher Spin Bosonic Gauge Fields in BRST-antifield Formalism

We examine interacting bosonic higher spin gauge fields in the BRST-antifield formalism. Assuming that an interacting action S is a deformation of the free action with a deformation parameter g, we solve the master equation (S, S) = 0 from the lower orders in g. It is shown that choosing a certain cubic interaction as the first order deformation, we can solve the master equation and obtain an action containing all orders in g. The antighost number of the obtained action is less than or equal to two. Furthermore we show that the obtained action is lifted to that of interacting bosonic higher spin gauge fields on anti-de Sitter spaces.

Small Gauge Transformations and Universal Geometry in Heterotic Theories

The first part of this paper describes in detail the action of small gauge transformations in heterotic supergravity. We show a convenient gauge fixing is 'holomorphic gauge' together with a condition on the holomorphic top form. This gauge fixing, combined with supersymmetry and the Bianchi identity, allows us to determine a set of non-linear PDEs for the terms in the Hodge decomposition. Although solving these in general is highly non-trivial, we give a prescription for their solution perturbatively in α and apply this to the moduli space metric. The second part of this paper relates small gauge transformations to a choice of connection on the moduli space. We show holomorphic gauge is related to a choice of holomorphic structure and Lee form on a 'universal bundle'. Connections on the moduli space have field strengths that appear in the second order deformation theory and we point out it is generically the case that higher order deformations do not commute.

DEFORMATIONS OF SURFACES FROM STATIONARY RICCI TENSOR

In this paper, we consider infinitesimal (n. m.) first-order deformations of single-connected regular surfaces in three-dimensional Euclidean space. The search for the vector field of this deformation is generally reduced to the study and solution of a system of four equations (among them there are differential equations) with respect to seven unknown functions. To avoid uncertainty, the following restriction is imposed on a given surface: the Ricci tensor is stored (mainly) on the surface. A mathematical model of the problem is created: a system of seven equations with respect to seven unknown functions. Its mechanical content is established. It is shown that each solution of the obtained system of equations will determine the field of displacement n. m. deformation of the first order of the surface of nonzero Gaussian curvature, which will be an unambiguous function (up to a constant vector). It is proved that each regular surface of nonzero Gaussian and mean curvatures allows first-order n. m. deformation with a stationary Ricci tensor. The tensor fields are found explicitly and depend on two functions, which are the solution of a linear inhomogeneous second-order differential equation with partial derivatives. The class of rigid surfaces in relation to the specified n. m. deformations. Assuming that one of the functions is predetermined, the obtained differential equation in the General case will be a inhomogeneous differential Weingarten equation, and an equation of elliptical type. The geometric and mechanical meaning of the function that is the solution of this equation is found. The following result was obtained: any surface of positive Gaussian and nonzero mean curvatures admits n. m of first-order deformation with a stationary Ricci tensor in the region of a rather small degree. Tensor fields will be represented by a predefined function and some arbitrary regular functions. Considering the Dirichlet problem, it is proved that the simply connected regular surface of a positive Gaussian and nonzero mean curvatures under a certain boundary condition admits a single first-order deformation with a stationary Ricci tensor. The strain tensors are uniquely defined.

Irregularity of Post Mining Deformations as Indicator Revealing Effects of Processes of Unknown Origin in Area of Bochnia

The presented work deals with the problem of terrain surface and rock mass deformation in the area of the Bochnia Salt Mine. The deformations are related to natural causes (mainly the tectonic stress of the Carpathian orogen) as well as anthropogenic ones related to the past mining activity conducted directly under the buildings of the town of Bochnia. The discussed characteristics of land surface deformation are important from the point of view of threats to surface features and contribute to spatial development. Particularly anomalous zones of observed subsidence basins are examined as places of second order deformation effects. The author presents a method of determinations of these anomalous areas and he discusses their origins.