scholarly journals On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model

2019 ◽  
Vol 17 (6) ◽  
pp. 1487-1529 ◽  
Author(s):  
Laurent Bourgeois ◽  
Lucas Chesnel ◽  
Sonia Fliss
Keyword(s):  
Thin Plate ◽  
Well Posedness ◽  
Plate Model ◽  
Time Harmonic

Well Posedness

2012 ◽  
Author(s):  
G. F. Roach ◽  
I. G. Stratis ◽  
A. N. Yannacopoulos
Keyword(s):  
Variational Formulation ◽  
Eigenvalue Problems ◽  
Dimensional Space ◽  
Well Posedness ◽  
Finite Dimensional Space ◽  
Chiral Media ◽  
Exterior Problems ◽  
Finite Dimensional ◽  
Time Harmonic ◽  
Interior Domain

This chapter presents rigorous mathematical results concerning the solvability and well posedness of time-harmonic problems for complex electromagnetic media, with a special emphasis on chiral media. It also presents some results concerning eigenvalue problems in cavities filled with complex electromagnetic materials. The chapter also studies the behaviour of the interior domain problem for a chiral medium in the limit of low chirality. Next, it presents some comments related to the well posedness and solvability of exterior problems. Finally, using an appropriate finite-dimensional space and the variational formulation of the discretised version of the original boundary value problem, this chapter obtains numerical methods for the solution of the Maxwell equations for chiral media.

A Simplified Large Thin Plate Model for Modeling Fracture Behavior of a Hydrided Irradiated Zr-2.5Nb Pressure Tube Specimen With an Axial Crack

2019 ◽  
Author(s):  
Shin-Jang Sung ◽  
Jwo Pan ◽  
Cheng Liu ◽  
Douglas A. Scarth
Keyword(s):  
Thin Plate ◽  
Crack Front ◽  
Pressure Tube ◽  
Upper And Lower Bounds ◽  
Plastic Strains ◽  
Plate Model ◽  
Constraint Condition ◽  
Symmetry Constraint ◽  
Modeling Fracture ◽  
Axial Crack

Abstract The crack tip opening displacements (CTODs) and the effective plastic strains ahead of the crack front in a hydrided irradiated Zr-2.5Nb pressure tube specimen with an axial crack are investigated using two 3-D finite element models in this paper. The first model is a pressure tube with 80 split circumferential hydrides distributed through the thickness ahead of the crack front. The second model is a large thin plate with a central crack with four split circumferential hydrides under symmetry/symmetry, free/symmetry and free/free constraint conditions. The results for CTOD indicate that the CTOD of the pressure tube specimen with 80 hydrides is slightly smaller than that for the large thin plate with the free/symmetry constraint condition and larger than that for the large thin plate with the symmetry/symmetry constraint condition. The effective plastic strain of the pressure tube specimen with 80 hydrides is smaller than that for the large thin plate with the free/symmetry constraint condition and larger than that for the large thin plate with the symmetry/symmetry constraint condition at large normalized loads. The computational results show that instead of modeling a full 3-D pressure tube with a larger number of hydrides, a large thin plate model with a limited number of hydrides can be used to efficiently determine the upper and lower bounds of the CTODs and the effective plastic strains ahead of the crack front in a pressure tube specimen.

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

Interpretation of borehole VLF logs: The thin plate model

1984 ◽  
Author(s):  
Robert Bazinet ◽  
Diane Couture
Keyword(s):  
Thin Plate ◽  
Plate Model

Strength Design of Reinforced Soil in the Front of Shield Departure Shaft

2011 ◽  
Vol 261-263 ◽  
pp. 1584-1588
Author(s):  
Xian Yang ◽  
Ke Neng Zhang
Keyword(s):  
Shear Strength ◽  
Thin Plate ◽  
Maximum Stress ◽  
Reinforced Soil ◽  
Shield Tunnel ◽  
Plate Model ◽  
Elastic Structures ◽  
Strength Design

In the construction of shield tunnel, the strength of reinforced soil in the front of departure shaft concerns directly the security of construction. Based on Mechanics of Elastic Structures theory, a thin plate model about reinforced soil is introduced, the maximum stress on reinforced soil is calculated. The security of strength in reinforced area is discussed. With the derived formulas, the needed bending and shear strength of reinforced soil in the project of Beijing Metro Line No. 4 is calculated beforehand, and appropriate material and construction parameters are selected in reinforcement according to the calculate result.

scholarly journals Error estimates for the unilateral buckling load of a plate involving the membrane efforts consistency error

2008 ◽  
pp. 1003-1038
Author(s):  
Mekki Ayadi
Keyword(s):  
Finite Elements ◽  
Error Estimate ◽  
Critical Load ◽  
Error Estimates ◽  
Thin Plate ◽  
Numerical Experiments ◽  
Mesh Size ◽  
Buckling Load ◽  
Plate Model ◽  
Consistency Error

The paper deals with error estimates for the unilateral buckling critical load of a thin plate in presence of an obstacle. The error on the membrane efforts tensor is taken into account. First, using the Mindlin’s plate model together with a finite elements scheme of degree one, an error estimate, depending on the mesh size h, is established. In order to validate this theoretical error estimate, some numerical experiments are presented. Second, using the Kirchhoff-Love’s plate model, an abstract error estimate is achieved. Its drawback is that it contains a hard term to evaluate.

Sign in / Sign up

Export Citation Format

Share Document