scholarly journals On the Fredholm Property of the Trace Operators Associated with the Elastic Layer Potentials

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 134 ◽  
Author(s):  
Giulio Starita ◽  
Alfonsina Tartaglione
Keyword(s):  
Elastic Body ◽  
Elastic Layer ◽  
Fredholm Property ◽  
System Of Equations ◽  
Layer Potentials ◽  
Connected Set ◽  
Equilibrium Configurations ◽  
Linear Elastostatics ◽  
Class C

We deal with the system of equations of linear elastostatics, governing the equilibrium configurations of a linearly elastic body. We recall the basics of the theory of the elastic layer potentials and we extend the trace operators associated with the layer potentials to suitable sets of singular densities. We prove that the trace operators defined, for example, on W 1 − k − 1 / q , q ( ∂ Ω ) (with k ≥ 2 , q ∈ ( 1 , + ∞ ) and Ω an open connected set of R 3 of class C k ), satisfy the Fredholm property.

scholarly journals A Note on the Displacement Problem of Elastostatics with Singular Boundary Values

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 46 ◽  
Author(s):  
Alfonsina Tartaglione
Keyword(s):  
Elastic Body ◽  
Function Class ◽  
Singular Boundary ◽  
Regular Boundary ◽  
Boundary Values ◽  
Exterior Domains ◽  
Displacement Problem ◽  
Natural Function ◽  
Linear Elastostatics ◽  
Class C

The displacement problem of linear elastostatics in bounded and exterior domains with a non-regular boundary datum a is considered. Precisely, if the elastic body is represented by a domain of class C k ( k ≥ 2 ) of R 3 and a ∈ W 2 − k − 1 / q , q ( ∂ Ω ) , q ∈ ( 1 , + ∞ ) , then it is proved that there exists a solution which is of class C ∞ in the interior and takes the boundary value in a well-defined sense. Moreover, it is unique in a natural function class.

Mechanics of a thin anisotropic elastic layer and a layer that is bonded to an anisotropic elastic body or bodies

2007 ◽  
Vol 463 (2085) ◽  
pp. 2223-2239 ◽  
Author(s):  
T.C.T Ting
Keyword(s):  
Boundary Conditions ◽  
Thin Layer ◽  
Elastic Body ◽  
Elastic Layer ◽  
Elastic Half Space ◽  
The Body ◽  
Thin Layers ◽  
Effective Boundary ◽  
Effective Boundary Conditions ◽  
Anisotropic Elastic

When a very thin elastic layer is bonded to an elastic body, it is desirable to have effective boundary conditions for the interface between the layer and the body that take into account the existence of the layer. In the literature, this has been done for special anisotropic elastic layers. We consider here the layer that is a general anisotropic elastic material. The mechanics of a thin layer is studied for elastostatics as well as steady state waves. It is shown that one-component surface waves cannot propagate in a semi-infinite thin layer. We then present Love waves in an anisotropic elastic half-space bonded to a thin anisotropic elastic layer. The dispersion equation so obtained is valid for long wavelength. Finally, effective boundary conditions are presented for two thin layers bonded to two surfaces of a plate and a thin layer bonded between two anisotropic elastic half-spaces.

scholarly journals Structural stability in porous elasticity

2006 ◽  
Vol 462 (2073) ◽  
pp. 2593-2605 ◽  
Author(s):  
S Chiriţă ◽  
M Ciarletta ◽  
B Straughan
Keyword(s):  
Elastic Body ◽  
Structural Stability ◽  
Elastic Deformation ◽  
Coupled System ◽  
System Of Equations ◽  
Coupling Coefficients ◽  
Linearized System

We consider the linearized system of equations for an elastic body with voids as derived by Cowin & Nunziato. We demonstrate that the solution depends continuously on changes in the coefficients, which couple the equations of elastic deformation and of voids. It is also shown that the solution to the coupled system converges, in an appropriate measure, to the solutions of the uncoupled systems as the coupling coefficients tend to zero.

Simply and doubly periodic arrangements of the equi-stress holes in a perforated elastic plane: The single-layer potential approach

2017 ◽  
Vol 23 (5) ◽  
pp. 805-819 ◽  
Author(s):  
Shmuel Vigdergauz
Keyword(s):  
Periodic Structures ◽  
Rotational Symmetry ◽  
Infinite Plate ◽  
Single Layer ◽  
Mapping Technique ◽  
Elastic Plane ◽  
Layer Potentials ◽  
Layer Potential ◽  
Linear Elastostatics ◽  
Wide Range

The layer potentials of two-dimensional linear elastostatics are applied as a novel building block for the semi-analytical design of non-standard arrangements of the equi-stress holes in an infinite plate under a given bulk-type loading. Thematically, this paper begins where our previous work left off with the main attention being focused on periodic structures of low rotational symmetry which are hard to tackle by the more customary conformal mapping technique. The analytical derivations are backed up by numerical simulations, in which a genetic algorithm is utilized to identify the optimal interface shapes for different geometries and a wide range of the governing parameters.

Unification in Varieties of Groups: Nilpotent Varieties

1994 ◽  
Vol 46 (06) ◽  
pp. 1135-1149 ◽  
Author(s):  
Michael H. Albert ◽  
John Lawrence
Keyword(s):  
General Solution ◽  
Nilpotent Group ◽  
System Of Equations ◽  
Free Nilpotent Group ◽  
Class C ◽  
Proper Generalization

Abstract In this paper we show that any system of equations over a free nilpotent group of class c is either unitary or miliary. In fact, such a system either has a most general solution (akin to the most general solution of a system of linear dipohantine equations), or every solution has a proper generalization. In principle we provide an algorithm for determining whether or not a most general solution exists, and exhibiting it if it does.

Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions

1983 ◽  
Vol 94 (2) ◽  
pp. 315-339 ◽  
Author(s):  
J. M. Ball ◽  
D. G. Schaeffer
Keyword(s):  
Elastic Body ◽  
Deformation Gradient ◽  
The Body ◽  
Reference Configuration ◽  
Equilibrium Solutions ◽  
Dead Load ◽  
Homogeneous Equilibrium ◽  
Equilibrium Configurations ◽  
The Stability ◽  
Static Criterion

In this paper we consider the equilibrium configurations of a homogeneous, incompressible, isotropic elastic body subjected to a uniform dead load surface traction of magnitude T whose direction is normal to the surface of the body in the reference configuration, and to no other forces. We concentrate on homogeneous equilibrium solutions, that is those for which the deformation gradient F is constant, and we study their bifurcations and stability (with respect to an appropriate static criterion) as T varies. Since it turns out that the equations for homogeneous equilibrium solutions, and the stability properties that we consider of these solutions, are independent of the shape of the body in the reference configuration, we can suppose if desired that this shape is a cube. (See Fig. 1.1.)

Surgical Management of Class C and D Glomus Jugulare Tumors: Fisch Infratemporal Fossa Type A Approach

2020 ◽  
Author(s):  
Yin Xia ◽  
Yubin Xue ◽  
Ting Ye ◽  
Xiaopeng Qu ◽  
Xukun Yan ◽  
...  
Keyword(s):  
Surgical Management ◽  
Infratemporal Fossa ◽  
Type A ◽  
Glomus Jugulare ◽  
Class C

Canonical Submersion and Lie Homomorphisms Normal Subgroup

2020 ◽  
Vol 23 (1) ◽  
pp. 97-101
Author(s):  
Mikhail Petrichenko ◽  
Dmitry W. Serow
Keyword(s):  
Normal Subgroup ◽  
Canonical System ◽  
System Of Equations ◽  
Core Group ◽  
The Core ◽  
Switch Group

Normal subgroup module f (module over the ring F = [ f ] 1; 2-diffeomorphisms) coincides with the kernel Ker Lf derivations along the field. The core consists of the trivial homomorphism (integrals of the system v = x = f (t; x )) and bundles with zero switch group Lf , obtained from the condition ᐁ( ω × f ) = 0. There is the analog of the Liouville for trivial immersion. In this case, the core group Lf derivations along the field replenished elements V ( z ), such that ᐁz = ω × f. Hence, the core group Lf updated elements helicoid (spiral) bundles, in particular, such that f = ᐁU. System as an example Crocco shown that the canonical system does not permit the trivial embedding: the canonical system of equations are the closure of the class of systems that permit a submersion.

LIQUIDUS THERMO-BAROMETER FOR THE MODELING OF MAGNETITE — MELT EQUILIBRIUM

2018 ◽  
pp. 71-80
Author(s):  
N. S. Aryaeva ◽  
E. V. Koptev-Dvornikov ◽  
D. A. Bychkov
Keyword(s):  
Experimental Data ◽  
Liquidus Temperature ◽  
Vertical Structure ◽  
Maximum Error ◽  
Silicate Melt ◽  
System Of Equations ◽  
Wide Range ◽  
Basaltic Melts ◽  
Multidimensional Statistics

A system of equations of thermobarometer for magnetite-silicate melt equilibrium was obtained by method of multidimensional statistics of 93 experimental data of a magnetite solubility in basaltic melts. Equations reproduce experimental data in a wide range of basalt compositions, temperatures and pressures with small errors. Verification of thermobarometers showed the maximum error in liquidus temperature reproducing does not exceed ±7 °C. The level of cumulative magnetite appearance in the vertical structure of Tsypringa, Kivakka, Burakovsky intrusions predicted with errors from ±10 to ±50 m.

Study on the Modes of Operation of a Multi-Machine Installations with Mechanical Reduction

2019 ◽  
pp. 12-22
Author(s):  
A. M. Oleynikov ◽  
L. N. Kanov
Keyword(s):  
Mathematical Description ◽  
Reactive Power ◽  
Maximum Efficiency ◽  
Wind Flow ◽  
System Of Equations ◽  
Mechanical Equilibrium ◽  
Synchronous Generators ◽  
Electromagnetic Excitation ◽  
Number Of Generators ◽  
Wide Range

The paper gives the description of the original wind electrical installation with mechanical reduction in which the output of vertical axis wind turbine with rather low rotation speed over multiplicator is distributed to a certain number of generators. The number of acting generators is determined by the output of actual operating wind stream at each moment. According to this constructive scheme, it is possible to provide effective and with maximum efficiency installation work in a wide range of wind speeds and under any schedule issued to the consumer of electricity. As there are no any experience in using such complexes, mathematical description of its main elements is given, namely windwheels, generators with electromagnetic excitation of magnetic electrical type, then their interaction with windwheel, and also the results of mathematical modeling of work system regimes under using the offered system of equations. The basis for the mathematical description of the main elements of the installation – synchronous generators – are the system of equations of electrical and mechanical equilibrium in relative units in rotating coordinates without considering saturation of the magnetic circuit. The equation of mechanical equilibrium systems includes torque and brake windwheel electromagnetic moments of generators with taking into account the reduction coefficients and friction. In addition, we specify the alternator rotor dynamics resulting from continuous torque of windwheel fluctuations under the influence of unsteady wind flow and wind speed serving as the original variable is modeled by a set of sinusoids. Model simplification is achieved by equivalization of similar generators and by disregarding these transitions with a small time constant. Calculation the installation with synchronous generators of two types of small and medium capacity taking into account the operational factors allowed us to demonstrate the logic of interactions in the main elements of the reported complex in the process of converting wind flow into the generated active and reactive power. We have shown the possibility of stable system work under changeable wind stream condition by regulating of the plant blade angle and with simultaneous varying of generator number of different types. All these are in great interest for project organizations and power producers.

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