A meshfree method with dynamic node reconfiguration for analysis of thermo-elastic problems with moving concentrated heat sources

In this work, a novel approach for efficient analysis of transient thermo-elastic problems including a moving point heat source is presented. This approach is based on a meshfree method with dynamic reconfiguration of the nodal points. In order to accurately capture the large temperature gradients at the location of the concentrated heat source, a fine configuration of nodal points at this location is selected. In contrast, a coarser nodal arrangement is used in other parts of the problem domain. During the problem analysis, the fine nodal arrangement moves with the point heat source. Consequently, the meshfree methods are ideally suited to this approach. In the present work, the meshfree radial point interpolation method (RPIM) is adopted for the numerical analyses. Since the density of the nodal points varies in different parts of the domain, the background decomposition method (BDM) is used for efficient computation of the domain integrals. In the BDM, the density of the integration points conform to that of the nodal points and thus the computational effort is minimized. Some numerical examples are provided to assess the accuracy and usefulness of the proposed approach in computation of the temperature, displacement, and stress fields.     

Thermoelastic bending of orthotropic plates acted on by concentrated heat sources with arbitrary heat transfer

The thermoelastic problem is solved for an infinite thin orthotropic plate acted on by internal heat sources. Arbitrary heat transfer is assumed between the plate and its surroundings. Results from a numerical study are presented. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 96–102, 1999.     

Optimization of vertical axisymmetric thermal displacements in a round plate using heat sources

We consider the problem of using heat sources for optimal control of the distribution of the vertical axisymmetric thermal displacements of a thin round plate with edge clamped at an angle of revolution. On the basis of the method of the inverse thermoelasticity problem we construct a solution of the control problem. For specific cases of heating the plate we carry out a numerical analysis of the behavior of the optimal control.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Poly a, Issue 36, 1992, pp. 105–110.     

The determination of two moving heat sources in two-dimensional inverse heat problem

There are some restrictions in the estimation of location and strength problems in recent studies. One of the restrictions is that the problem is limited to the static sources and the single moving source. In other words, there is no method available to estimate the location and the strength of two moving sources presently. Therefore, it is necessary to develop a robust method to estimate the location and the strength of two moving heat sources. In this paper, a numerical algorithm is proposed to determine the problem sequentially. Special feature about this method is that no preselect functional form for the unknown sources is necessary and no sensitivity analysis is needed in the algorithm. Two examples are used to demonstrate the characteristics of the proposed method. From the results, they show that the proposed method is an accurate and efficient method to determine the location and the strength of two moving sources in the inverse heat conduction problem.     

The stress-strain state of shells under the action of concentrated heat sources

We construct a fundamental solution of a static problem of heat conduction for thin isotropic shells of positive curvature under the action of concentrated heat sources. We study the problems involved in simplifying the heat equations. Four figures. Two tables. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 70–80.     

Thermoelasticity of orthotropic shells under the action of a moving concentrated heat source

We solve the problem of thermoelasticity for thin orthotropic shells of nonnegative curvature under the action of a concentrated heat source that moves over the surface of the shell. A linear temperature distribution over the thickness of the shell and convective heat exchange from its lateral surfaces by the Newton law are established. Using Fourier and Laplace integral transformations, we obtain a solution in the analytic form. The influences of the thermomechanical properties of the material and parameters of heat exchange with the surrounding medium on the stress-strain state of the shell are investigated.     

Optimal heating of a piecewise-homogeneous cylindrical glass shell by the surrounding medium and heat sources

We state the problem of stress-optimization of regimes for heating a piecewise-homogeneous cylindrical glass shell from the surrounding medium and heat sources and give an analytic/numerical solution of the problem under given bounds on the parameters of the thermostressed state.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 154–159.     

带移动奇异源热方程的移动网格方法

研究了一个带若干奇异源热方程的数值求解,其源的移动由一个常微分方程描述.基于移动观察区域和区域分解思想提出了一个移动网格预估校正算法.网格方程可自然的通过并行高效求解,算法避免了跳跃信息[u]的计算而使物理方程的离散格式变得非常简单,且仍保持了空间上的二阶收敛性.数值例子验证了算法的收敛性和高效性,并模拟了非线性源函数带来的爆破现象.     

The influence of two moving heat sources on blow-up in a reactive-diffusive medium

Two concentrated heat sources move through a one-dimensional reactive-diffusive medium. The sources, moving at constant speed in the same direction, are separated by a fixed distance. The leading source serves to preheat the medium ahead of the trailing source. Sufficient conditions, involving the speed and the separation distance, are found for blow-up at the site of the trailing source. Also, the asymptotic behavior of the solution near blow-up is examined.     

Propagation of perturbations in fluids excited by moving sources

A large series of A.A. Dorodnicyn’s works deals with rigorous mathematical formulations and development of efficient research techniques for mathematical models used in inhomogeneous fluid dynamics. Numerous problems he studied in these directions are closely related to stratified fluid dynamics, which were addressed in a series of works having been published in this journal by this paper’s authors and their coauthors since 1980. This paper describes the results of a series of works analyzing the propagation of small perturbations in various stratified and/or uniformly rotating inviscid fluids. It is assumed that each of the fluids either occupies an unbounded lower half-space with a free surface or is a semi-infinite two-component fluid layer. The perturbations are excited by a moving source specified as a periodic plane wave traveling along the interface of the fluids. Problems for five mathematical fluid models are formulated, their explicit analytical solutions are constructed, and their existence and uniqueness are discussed. The asymptotics of the solution as t → +∞ are studied, and the long-time wave patterns developing in five fluid models are compared.     

Efficient approaches for furnace loading of cylindrical parts

This paper addresses the heat treatment operation in a manufacturing plant that produces different types of cylindrical parts. The immediate prior process to heat treatment is furnace-loading, where parts are loaded into baskets. The furnace-loading process is complex and involves issues relating to geometry, and heterogeneity in the parts and in their processing requirements. Currently, furnace-loading is accomplished by operator ingenuity; consequently, the parts loaded in heat treatment often do not use furnace capacity adequately. Efficiency in furnace operation can be achieved by improving basket utilization, which is determined by the furnace-loading process. This paper describes the development of integer and mixed integer LP models for 3D loading of cylindrical parts into furnace baskets. The models consider the exact location of parts to be loaded on the basket and incorporate three models with different objectives; the first addresses the nesting of parts within one another, the second addresses the number of basket layers used, and the third addresses the number of baskets used.     

Quasistatic thermoelasticity problems for shells heated by moving heart sources

Solutions of thermoelasticity problems for cylindrical and spherical shells heated by moving heat sources distributed according to a normal (Gaussian) law are obtained in a quasistatic formulation. The results of temperature and stress calculations for the case of a plate are given.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 40–44, 1987.     

Integration by parts for heat measures over loop groups

The formula of integration by parts for heat measures over a loop group established by B. Driver is revesited through an alternative approach to this result. We shall first establish directly the integration by parts formula over an unimodular Lie group (which will be the finite product of a compact Lie group with a correlated metric), using the concept of tangent processes. A new expression for Ricci tensor will enable us the passage to the limit.     

Determination of the characteristics of concentrated heat sources in a half-space under prescribed conditions for the heat exchange and temperature distribution on its surface

A method is given for solving the inverse problem for determining the intensity and location of concentrated heat sources in a half-space under prescribed conditions on the heat exchange with the external medium and a distribution of surface temperature with error. Using methods of the variational calculus, we obtain a system of nonlinear equations for the characteristics of subsurface heat sources, leading to a temperature function on the surface which is closest to the given distribution. Several individual examples are solved.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 46–51, 1989.     

Speed-optimal control of heating of inhomogeneous bodies by internal heat sources with constraints on the parameters of the thermal process

We use the method of the inverse heat-conduction problem to state and construct a numerical solution of the problem of speed-optimal control of the one-dimensional nonstationary thermal regimes of inhomogeneous bodies using internal heat sources with constraints on the control and the parameters of the thermal process. The control problem is nonlinear since the maximal values of the constraining parameters are attained at internal points of the body whose position changes during heating. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 110–114.     

Non-linear forced vibration analysis of nanobeams subjected to moving concentrated load resting on a viscoelastic foundation considering thermal and surface effects

Analytical solution for the steady-state response of an Euler–Bernoulli nanobeam subjected to moving concentrated load and resting on a viscoelastic foundation with surface effects consideration in a thermal environment is investigated in this article. At first, based on the Eringen's nonlocal theory, the governing equations of motion are derived using the Hamilton's principle. Then, in order to solve the equation, Galerkin method is applied to discretize the governing nonlinear partial differential equation to a nonlinear ordinary differential equation; solution is obtained employing the perturbation technique (multiple scales method). Results indicate that by increasing of various parameters such as foundation damping, linear stiffness, residual surface stress and the temperature change, the jump phenomenon is postponed and with increasing the amplitude of the moving force and the nonlocal parameter, the jump phenomenon occurs earlier and its frequency and the peak value of amplitude of vibration increases. In addition, it is seen that the non-linear stiffness and the critical velocity of the moving load are important factors in studying nanobeams subjected to moving concentrated load. Presence of the non-linear stiffness of Winkler foundation resulting nanobeam tends to instability and so, the jump phenomenon occurs. But, presence of the linear stiffness will lead to stability of the nanobeam. In the next sections of the paper, frequency responses of the nanobeam made of temperature-dependent material properties under multi-frequency excitations are investigated.     

Numerical estimates of acoustic fields in the ocean generated by moving airborne sources

We investigate the underwater acoustic field in the stratified ocean generated by moving in the air sources. We obtain asymptotic formulas expressed in terms of the retarded time and the Doppler-shifted frequency. The spectral parameter power series method is implemented to find the wave numbers of the propagating modes, their group velocity and an analytic form of the acoustic field in the ocean. Some numerical results are presented.