Acoustic Forward Model for Guided Wave Propagation and Scattering in a Pipe Bend

The sections of pipe bends are hot spots for wall thinning due to accelerated corrosion by fluid flow. Conventionally, the thickness of a bend wall is evaluated by local point-by-point ultrasonic measurement, which is slow and costly. Guided wave tomography is an attractive method that enables the monitoring of a whole bend area by processing the waves excited and received by transducer arrays. The main challenge associated with the tomography of the bend is the development of an appropriate forward model, which should simply and efficiently handle the wave propagation in a complex bend model. In this study, we developed a two-dimensional (2D) acoustic forward model to replace the complex three-dimensional (3D) bend domain with a rectangular domain that is made artificially anisotropic by using Thomsen parameters. Thomsen parameters allow the consideration of the directional dependence of the velocity of the wave in the model. Good agreement was found between predictions and experiments performed on a 220 mm diameter (d) pipe with 1.5d bend radius, including the wave-field focusing effect and the steering effect of scattered wave-fields from defects.

On One Initial Boundary Value Problem for the Burgers Equation in a Rectangular Domain

We consider some initial boundary value problems for the Burgers equation in a rectangular domain, which in a sense can be taken as a model one. The fact is that such a problem often arises when studying the Burgers equation in domains with moving boundaries. Using the methods of functional analysis, priori estimates, and Faedo-Galerkin in Sobolev spaces and in a rectangular domain, we show the correctness of the initial boundary value problem for the Burgers equation with nonlinear boundary conditions of the Neumann type.

Approximation, characterization, and continuity of multivariate monotonic regression functions

We deal with monotonic regression of multivariate functions [Formula: see text] on a compact rectangular domain [Formula: see text] in [Formula: see text], where monotonicity is understood in a generalized sense: as isotonicity in some coordinate directions and antitonicity in some other coordinate directions. As usual, the monotonic regression of a given function [Formula: see text] is the monotonic function [Formula: see text] that has the smallest (weighted) mean-squared distance from [Formula: see text]. We establish a simple general approach to compute monotonic regression functions: namely, we show that the monotonic regression [Formula: see text] of a given function [Formula: see text] can be approximated arbitrarily well — with simple bounds on the approximation error in both the [Formula: see text]-norm and the [Formula: see text]-norm — by the monotonic regression [Formula: see text] of grid-constant functions [Formula: see text]. monotonic regression algorithms. We also establish the continuity of the monotonic regression [Formula: see text] of a continuous function [Formula: see text] along with an explicit averaging formula for [Formula: see text]. And finally, we deal with generalized monotonic regression where the mean-squared distance from standard monotonic regression is replaced by more complex distance measures which arise, for instance, in maximum smoothed likelihood estimation. We will see that the solution of such generalized monotonic regression problems is simply given by the standard monotonic regression [Formula: see text].

Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct

This article is concerned with the global exact controllability for ideal incompressible magnetohydrodynamics in a rectangular domain where the controls are situated in both vertical walls. First, global exact controllability via boundary controls is established for a related Elsässer type system by applying the return method, introduced in [Coron J.M., Math. Control Signals Systems, 5(3) (1992) 295--312]. Similar results are then inferred for the original magnetohydrodynamics system with the help of a special pressure-like corrector in the induction equation. Overall, the main difficulties stem from the nonlinear coupling between the fluid velocity and the magnetic field in combination with the aim of exactly controlling the system. In order to overcome some of the obstacles, we introduce ad-hoc constructions, such as suitable initial data extensions outside of the physical part of the domain and a certain weighted space.

Synthesis and Numerical Analysis of Compliant devices – A Topology Optimization Approach for Mechanisms and Robotic Systems

The Topology Optimization design invariably shall be used in various applications like Aerojet designs, Aircraft Engineering designs and innovative systems for improving the efficiency of structure. The paper emphasizes more on general Topology Optimization design for a rectangular domain. The domain numerically analyzed with defined geometry setting and defined boundary conditions for finding the Stress and displacement. In this Topology Optimization Design synthesis, the result is suitable volume and mass reduction in the Aerojet application parts which further can be taken for Prototype development in 3D printing and experimentally test with safety characteristics and compares Objective functions chosen for design and development. The design can be used for other various automotive and aerospace devices based on deformation level and application of external forces. The Final destination of this design and development ends with passing Fatigue Endurance test cycle test pass condition in Aerojet and automotive vehicles in static and dynamic state.

ОСНОВНЫЕ УРАВНЕНИЯ, ГРАНИЧНЫЕ УСЛОВИЯ И ВАРИАЦИОННЫЙ ПРИНЦИП ПЛОСКОЙ ЗАДАЧИ ГРАДИЕНТНОЙ ТЕОРИИ УПРУГОСТИ ДЛЯ ПРЯМОУГОЛЬНОЙ ОБЛАСТИ / BASIC EQUATIONS, BOUNDARY CONDITIONS AND VARIATION PRINCIPLES OF THE PLANE PROBLEM IN THE GRADIENT THEORY OF ELASTICITY FOR A RECTANGULAR DOMAIN

В работе приведены основные уравнения плоской задачи градиентной теории упругости для прямоугольной области и устанавливается принцип возможных перемещений с соответствующем вариационном уравнением. Из вариационного уравнения теории упругости и для прямоугольной области все граничные условия. / The paper demonstrates the basic equations of the plane problem in the frames of the theory of gradient elasticity and establishes the principle of virtual work along with its variation equations. The basic balance equations of the plane problem of the theory of gradient elasticity and the boundary conditions for the rectangular plane are derived.

Problem with data on the characteristics for a loaded system of hyperbolic equations

We consider a problem with data on the characteristics for a loaded system of hyperbolic equations of the second order on a rectangular domain. The questions of the existence and uniqueness of the classical solution of the considered problem, as well as the continuity dependence of the solution on the initial data, are investigated. We propose a new approach to solving the problem with data on the characteristics for the loaded system of hyperbolic equations second order based on the introduction new functions. By introducing new unknown functions the problem is reduced to an equivalent family of Cauchy problems for a loaded system of differential with a parameters and integral relations. An algorithm for finding an approximate solution to the equivalent problem is proposed and its convergence is proved. Conditions for the unique solvability of the problem with data on the characteristics for the loaded system of hyperbolic equations of the second order are established in the terms of coefficient's system.

Conformal Topology Optimization of Heat Conduction Problems on Manifolds Using an Extended Level Set Method (X-LSM)

In this paper, the authors propose a new dimension reduction method for level-set-based topology optimization of conforming thermal structures on free-form surfaces. Both the Hamilton-Jacobi equation and the Laplace equation, which are the two governing PDEs for boundary evolution and thermal conduction, are transformed from the 3D manifold to the 2D rectangular domain using conformal parameterization. The new method can significantly simplify the computation of topology optimization on a manifold without loss of accuracy. This is achieved due to the fact that the covariant derivatives on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar with the conformal mapping. The original governing equations defined on the 3D manifold can now be properly modified and solved on a 2D domain. The objective function, constraint, and velocity field are also equivalently computed with the FEA on the 2D parameter domain with the properly modified form. In this sense, we are solving a 3D topology optimization problem equivalently on the 2D parameter domain. This reduction in dimension can greatly reduce the computing cost and complexity of the algorithm. The proposed concept is proved through two examples of heat conduction on manifolds.

A modified Fourier series-based solution with improved rate of convergence for two-dimensional rectangular isotropic linear elastic solids

This paper presents a new displacement solution based on a Modified Fourier Series (MFS) for isotropic linear elastic solids under plane strain or plane stress states subject to continuous displacement and traction boundary conditions in a two-dimensional rectangular domain. In contrast with existing approaches that are restricted to Fourier series with a rate of convergence of second order O(m-2), the MFS allows increasing the rate of convergence of the solution. The governing Partial Differential Equations (PDEs) are satisfied exactly by two displacement solutions while the boundary conditions are approximated after solving a finite system of algebraic equations. Numerical results for a solution with an MFS with rate of convergence O(m-3) are compared with results from existing numerical and analytical methods, showing the enhanced behavior of the present solution.