Математическая модель распространения лазерного излучения в морской воде

Based on the well-known models of optical properties of a seawater layer in the spectral range of 530–550 nm, a mathematical model of the propagation of laser radiation is proposed. The mathematical model is obtained by solving radiative transfer equation for a narrow beam using a few-parameter approximation of the scattering indicatrix of the seawater layer. The model makes it possible to determine the spatial distribution of irradiance at a given distance from the laser radiation source by the known Secchi disk depth. The results of numerical experiments for water areas with known optical properties are given.

Analytical Approximation of Crack-Tip Stress Field: Study on Efficient Determination of Coefficients of Higher Order Terms of Williams Power Expansion

The paper presents a study on accuracy of the multi-parameter approximation of the stress field in a cracked body using Williams power series calibrated according to results of FEM computation. Main attention is paid to a detailed analysis of suitable selection of FE nodes, whose results serve as inputs to the over-deterministic method (ODM) employed for determination of the coefficients of terms of the Williams expansion describing the crack-tip field. Two different ways of FE nodal selection are compared – nodes selected from the crack tip vicinity versus nodes selected from a specific part of the test specimen body in a specific way. Comparison is made with the usage of the authors’ own developed procedures enabling both the determination of the coefficients of the analytical approximation of stress field based on the FE results and the backward reconstruction of the field from those determined terms’ coefficients/functions. The wedge-splitting test (WST) specimen with a crack is taken as example for the study.