scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

Boundary Integral Equation Methods for a Refined Model of Elastic Plates

2006 ◽  
Vol 11 (6) ◽  
pp. 642-654
Author(s):  
Radu Mitric ◽  
Christian Constanda
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Normal Strain ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Neumann Problems ◽  
Integral Equation Methods ◽  
Transverse Normal Strain ◽  
System Of Equilibrium Equations

A theory of bending of elastic plates is considered, in which the effect of transverse shear deformation and transverse normal strain are taken into account through a specific form of the displacement field. It is shown that the system of equilibrium equations is elliptic and that Betti and Somigliana formulae can be established, which permit the solution of the interior and exterior Dirichlet and Neumann problems by means of boundary integral equation methods.

Hybrid modeling of elastic‐wave propagation in two‐dimensional laterally inhomogeneous media

Geophysics ◽  
1987 ◽  
Vol 52 (6) ◽  
pp. 765-771 ◽  
Author(s):  
B. Kummer ◽  
A. Behle ◽  
F. Dorau
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Hybrid Scheme ◽  
Finite Difference Techniques

We have constructed a hybrid scheme for elastic‐wave propagation in two‐dimensional laterally inhomogeneous media. The algorithm is based on a combination of finite‐difference techniques and the boundary integral equation method. It involves a dedicated application of each of the two methods to specific domains of the model structure; finite‐difference techniques are applied to calculate a set of boundary values (wave field and stress field) in the vicinity of the heterogeneous domain. The continuation of the near‐field response is then calculated by means of the boundary integral equation method. In a numerical example, the hybrid method has been applied to calculate a plane‐wave response for an elastic lens embedded in a homogeneous environment. The example shows that the hybrid scheme enables more efficient modeling, with the same accuracy, than with pure finite‐difference calculations.

New solutions for periodic interfacial gravity waves

2021 ◽  
Vol 928 ◽  
Author(s):  
X. Guan ◽  
J.-M. Vanden-Broeck ◽  
Z. Wang
Keyword(s):  
Integral Equation ◽  
Excellent Agreement ◽  
Gravity Waves ◽  
Global Bifurcation ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Fourier Expansions ◽  
Wave Profiles

Two-dimensional periodic interfacial gravity waves travelling between two homogeneous fluids of finite depth are considered. A boundary-integral-equation method coupled with Fourier expansions of the unknown functions is used to obtain highly accurate solutions. Our numerical results show excellent agreement with those already obtained by Maklakov & Sharipov using a different scheme (J. Fluid Mech., vol. 856, 2018, pp. 673–708). We explore the global bifurcation mechanism of periodic interfacial waves and find three types of limiting wave profiles. The new families of solutions appear either as isolated branches or as secondary branches bifurcating from the primary branch of solutions.

scholarly journals Stern waves with vorticity

2002 ◽  
Vol 43 (3) ◽  
pp. 321-332 ◽  
Author(s):  
Y. Kang ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Integral Equation ◽  
Numerical Solutions ◽  
Free Surface Flow ◽  
Integral Equation Method ◽  
Surface Flow ◽  
Boundary Integral ◽  
Analytical Relation ◽  
Far Field ◽  
Two Dimensional ◽  
The Waves

AbstractSteady two-dimensional free surface flow past a semi-infinite flat plate is considered. The vorticity in the flow is assumed to be constant. For large values of the Froude number F, an analytical relation between F, the vorticity parameter ω and the steepness s of the waves in the far field is derived. In addition numerical solutions are calculated by a boundary integral equation method.

scholarly journals Research on Error Estimations of the Interpolating Boundary Element Free-Method for Two-Dimensional Potential Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Jufeng Wang ◽  
Fengxin Sun ◽  
Ying Xu
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Potential Problems ◽  
Element Free Method ◽  
Error Estimations ◽  
Element Free

The interpolating boundary element-free method (IBEFM) is a direct solution method of the meshless boundary integral equation method, which has high efficiency and accuracy. The IBEFM is developed based on the interpolating moving least-squares (IMLS) method and the boundary integral equation method. Since the shape function of the IMLS method satisfies the interpolation characteristics, the IBEFM can directly and accurately impose the essential boundary conditions, which overcomes the shortcomings of the original boundary element-free method in enforcing the essential boundary approximately. This paper will study the error estimations of the IBEFM for two-dimensional potential problems and the relationship between the errors and the influence radius and the condition number of the coefficient matrix. Two numerical examples are presented to verify the correctness of the theoretical results in this paper.

AN IMPROVED LOCAL BOUNDARY INTEGRAL EQUATION METHOD FOR TWO-DIMENSIONAL POTENTIAL PROBLEMS

2010 ◽  
Vol 02 (02) ◽  
pp. 421-436 ◽  
Author(s):  
BAODONG DAI ◽  
YUMIN CHENG
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Computational Efficiency ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Potential Problems

Combining the local boundary integral equation with the improved moving least-squares (IMLS) approximation, an improved local boundary integral equation (ILBIE) method for two-dimensional potential problems is presented in this paper. In the IMLS approximation, the weighted orthogonal functions are used as basis functions. The IMLS approximation has greater computational efficiency and precision than the existing moving least-squares (MLS) approximation and does not lead to an ill-conditioned equations system. The corresponding formulae of the ILBIE method are obtained. Comparing with the conventional local boundary integral equation (LBIE) method, the ILBIE method is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be implemented directly and easily as in the finite element method. The ILBIE method has greater computational efficiency and precision. Some numerical examples to demonstrate the efficiency of the method are presented in this paper.

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