The determination of the appropriate boundary conditions for a two-dimensional theory of elastic flat plates (and shells) consistent with the expected order of accuracy of the theory is both critical and challenging. The reciprocal theorem of elasticity will be applied in a novel way to obtain the appropriate stress boundary conditions for plate bending accurate to all order (with respect to th...

This paper presents a theory of the radar cross section (RCS) of objects in multiple scattering random media. The general formulation includes the fourthorder moments including the correlation between the forward and the backward waves. The fourth moments are reduced to the second-order moments by using the circular complex Gaussian assumption. The stochastic Green’s functions are expressed in ...

Modal signals of transverse sensing of truncated conical shells with simply supported boundary condition at both ends are investigated. The embedded piezoelectric layer on the surface of conical shell is used as sensors and output voltages of them in considered modes are calculated. The Governing sensing signal displacement equations are derived based on the Kirchhoff theory, thin-shell assumpt...

We study delamination in a sandwich panel due to transient finite plane strain elastic deformations caused by local water slamming loads and use the boundary element method to analyze motion of water and the finite element method to determine deformations of the panel. The cohesive zone model is used to study delamination initiation and propagation. The fluid is assumed to be incompressible and...

We study a nonlocal elliptic equation of $p$-Kirchhoff type involving the critical Sobolev exponent. First we give sufficient conditions for $(\text{PS})$ condition to hold. Then prove some existence and multiplicity results using tools from Morse theory, in particular, notion cohomological local splitting eigenvalues based on Fadell-Rabinowitz index.

Suitable, yet general enough, choices of functional grading along the radius and thickness axisymmetric circular plates may lead to closed-form solutions for linear elastic direct problem. The are modeled according usual Kirchhoff—Love theory, because they supposed be thin; abstract from actual values geometric material parameters, governing equations dealt with in nondimensional form. Some ins...

The comparison of subsalt images obtained by common-azimuth migration and singlearrival Kirchhoff migration demonstrates the potential of wave-equation migration when the velocity model causes complex multipathing. Subsalt reflectors are better imaged and the typical Kirchhoff artifacts caused by severe multipathing disappear. A detailed analysis of common-azimuth images indicates that the resu...

We show here that the Kirchhoff index of a network is the average of the Wiener capacities of its vertices. Moreover, we obtain a closed-form formula for the effective resistance between any pair of vertices when the considered network has some symmetries which allows us to give the corresponding formulas for the Kirchhoff index. In addition, we find the expression for the Foster’s n-th Formula.

Knot Theory is currently a very broad field. Even a long survey can only cover a narrow area. Here we concentrate on the path from Goeritz matrices to quasi-alternating links. On the way, we often stray from the main road and tell related stories, especially if they allow as to place the main topic in a historical context. For example, we mention that the Goeritz matrix was preceded by the Kirc...