On the Indeterminancy of BIE Solutions for the Exterior Problems of Time-Harmonic Elastodynamics and Incompressible Elastostatics

1982 ◽  
pp. 282-296 ◽  
Author(s):  
S. Kobayashi ◽  
N. Nishimura
Keyword(s):  
Exterior Problems ◽  
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.

Layer Potential Techniques

2015 ◽  
Author(s):  
Habib Ammari ◽  
Elie Bretin ◽  
Josselin Garnier ◽  
Hyeonbae Kang ◽  
Hyundae Lee ◽  
...  
Keyword(s):  
Linear Elasticity ◽  
Free Field ◽  
Decomposition Theorem ◽  
Radiation Condition ◽  
Regularity Of Solutions ◽  
Layer Potentials ◽  
Displacement Fields ◽  
Exterior Problems ◽  
Elasticity Equations ◽  
Time Harmonic

This chapter considers some well-known results on the solvability and layer potentials for static and time-harmonic elasticity equations. It first reviews commonly used function spaces before introducing equations of linear elasticity and decomposing the displacement field into the sum of an irrotational (curl-free) and a solenoidal (divergence-free) field using the Helmholtz decomposition theorem. It then discusses the radiation condition for the time-harmonic elastic waves, which is used to select the physical solution to exterior problems. It also describes the layer potentials associated with the operators of static and time-harmonic elasticity, along with their mapping properties, and proves decomposition formulas for the displacement fields. Finally, it derives the Helmholtz–Kirchhoff identities, analyzes Neumann and Dirichlet functions, and states a generalization of Meyer's theorem concerning the regularity of solutions to the equations of linear elasticity.

THREE-DIMENSIONAL INFINITE ELEMENTS BASED ON A TREFFTZ FORMULATION

2001 ◽  
Vol 09 (02) ◽  
pp. 381-394 ◽  
Author(s):  
ISAAC HARARI ◽  
PARAMA BARAI ◽  
PAUL E. BARBONE ◽  
MICHAEL SLAVUTIN
Keyword(s):  
Separation Of Variables ◽  
Outer Boundary ◽  
Three Dimensional ◽  
Legendre Functions ◽  
Spherical Coordinates ◽  
Singular Behavior ◽  
Associated Legendre Functions ◽  
Exterior Problems ◽  
Infinite Elements ◽  
Time Harmonic

Three-dimensional infinite elements for exterior problems of time-harmonic acoustics are developed. The infinite elements mesh only the outer boundary of the finite element domain and need not match the finite elements on the interface. A four-noded infinite element, based on separation of variables in spherical coordinates, is presented. Singular behavior of associated Legendre functions at the poles is circumvented. Numerical results validate the good performance of this approach.

Newton-Raphson Formulation and Modeling of Magnetization Property in Nonlinear Time-harmonic Eddy-current Analysis

2017 ◽  
Vol 137 (3) ◽  
pp. 238-244
Author(s):  
Yasuhito Takahashi ◽  
Takeshi Mifune ◽  
Koji Fujiwara
Keyword(s):  
Eddy Current ◽  
Current Analysis ◽  
Time Harmonic ◽  
Newton Raphson

Calculating the response of waveguides to base excitation using the wave and finite element method

2021 ◽  
pp. 107754632098131
Author(s):  
Jamil Renno ◽  
Sadok Sassi ◽  
Wael I Alnahhal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Functions ◽  
Travelling Waves ◽  
Model Free ◽  
Time Harmonic ◽  
Element Approach ◽  
Response Transfer ◽  
Free Wave Propagation ◽  
Element Method

The prediction of the response of waveguides to time-harmonic base excitations has many applications in mechanical, aerospace and civil engineering. The response to base excitations can be obtained analytically for simple waveguides only. For general waveguides, the response to time-harmonic base excitations can be obtained using the finite element method. In this study, we present a wave and finite element approach to calculate the response of waveguides to time-harmonic base excitations. The wave and finite element method is used to model free wave propagation in the waveguide, and these characteristics are then used to find the amplitude of excited waves in the waveguide. Reflection matrices at the boundaries of the waveguide are then used to find the amplitude of the travelling waves in the waveguide and subsequently the response of the waveguide. This includes the displacement and stress frequency response transfer functions. Numerical examples are presented to demonstrate the approach and to discuss the numerical efficiency of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document