Diffraction of optical beams by a half-plane

Rigorous solution of the optical beam diffraction problem on half plane is represented. Solution is described to representation of edge dislocation wave (EDW) that was introduced for describing the diffraction plane wave on half plane. It is shown that in problem of diffraction EDW plays the role of eigenmode as plane wave in free space. Due to this the solving of mentioned problem reduces to calculation of convolution of angle spectrum of source beam and EDW

New method of apertured electromagnetic field modeling

Using a new wave treatment of rigorous Sommerfield’s solution for a problem of plane wave diffraction on a perfectly conductive half-plane, it was obtained the solution for a problem of plane wave diffraction on a slit and rectangular aperture. The result of aperture diffraction was represented as a sum of elementary rectangular unit cell waves. New integral approach to modeling of plane wave diffraction on an arbitrary two-dimensional aperture is discussed. Proposed method is very useful for providing numerical modeling of diffraction phenomena

Singular peculiarities of a plane wave diffracted on half-plane

We analyzed singular properties of edge dislocation waves («EDW») - the main information component of the field formed at plane wave diffraction on half-plane. It is shown that analytical structure of this wave is completely identical to Cornu’s spiral, while physical simulation thereof requires joining the plane wave with an edge dislocation. Dislocations of this type are rather sensitive to action of any amplitude phase distortion on them that considering the impact of actual noise essentially hampers their experimental isolation in the pure form. At the same time spatial position of such dislocation may be effectively controlled by changing the amplitude and phase of one of the wave components. We considered peculiarities of structural evolution of the field at more complicated form of diffraction aperture

Investigation of Force Factors and Stresses at Singular Points of Plate Elements in Special Cranes

The work addresses studying the possibilities of a numerical-analytical variant of the boundary elements method (BEM) in determining the internal force factors and stresses at singular points when bending thin isotropic plates. The simplest type of singularity has been investigated, a point of application of external concentrated forces and moments. The importance of a given problem is due to the fact that at these points the internal force factors tend towards infinity and it is not possible to determine the size using elementary methods. At the same time, these singular points are the significant stress concentrators (both tangential and normal), which is why calculating the limits to which the internal forces and moments tend is essential to analyze the strength of plate structures. In order to describe an external load, it is proposed to apply the Dirac delta function of two variables. The models of external loads are presented. A given proposal makes it possible to accurately calculate the limits to which the transverse forces, as well as bending and torsional moments, tend at singular points of thin plates. We simulated plate bending using the variational Kantorovich-Vlasov method, which is fully compatible with the models of external load. The internal force factors at the singular points of plates were determined while solving the boundary value problems, formed based on the algorithm of BEM. The MATLAB environment was used for programming and computation. Results of the calculations are characterized by high accuracy and reliability, in particular the errors in determining the deflections of plates at singular points do not exceed 2.0 % and the errors for bending moments are not above 3.0 %. Recommendations have been given to solving different types of boundary problems on bending the plates with singular points based on the proposed approach. It has been established that an accurate model of the external load in the form of concentrated forces and moments fundamentally enables determining the internal forces and moments at the singular points of thin plates applying an algorithm of the variational Kantorovich-Vlasov method. Up to now, there are no data on the importance of internal forces and moments at the singular points of plates. It is also shown that when calculating the internal forces and moments of plates, it is inappropriate to apply a single term from a series of the Kantorovich-Vlasov method; the errors amount to significant magnitudes of the order of 43‒44