Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians
Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems; For Engineers, Physicists, and Mathematicians
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DOI：
10.1115/1.1553435
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Jg Papastavridis;K. Yagasaki
中科院分区：
文献类型：
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作者：
Jg Papastavridis;K. Yagasaki
这是第1卷的两卷集提供了一个全面的治疗的基本原理和应用的边界元法边界元在热流体，声学和固体力学。第一卷由布鲁内尔大学的Luis Wrobel教授撰写，第二卷由伦敦学院的Ferri Aliabadi教授撰写，他们都是公认的BEM发展权威和长期贡献者。边界元法是一种求解边界积分方程的数值方法，可以用于各种工程领域的问题。这是可能的，如果一个基本的解决方案是可用于微分算子管理的领域问题的兴趣，在这种情况下，边界元法只需要一个离散化的边界表面，一个明显的优势，体积网格技术，如有限体积和有限元方法。这种优势在处理移动曲面和逆问题以及优化时更加明显。这11章书开始与历史回顾积分方程和边界元法在过去的40年。基本的数学符号和积分方程的方法，在发展中的边界元法在潜在的理论方法的理论涵盖在随后的章节。超奇异方程，双重和多重互惠，轴对称，伽辽金边界元法制定，快速求解器的简要处理也提供。接下来的两章讨论了边界元法在稳态和非稳态传热中的应用。线性和非线性传热都涵盖了非线性材料，辐射，相变和材料加工的应用。对流扩散，生物传热，双曲线热传导，以及耦合的热质传递处理的一些细节。下一章将在频域中发展声学建模的边界元法。注意随后的超奇异积分和正则化的积分方程，以及治疗所产生的外部声学问题的著名的非唯一性。在声学中的边界元法的制定和实施以及从消声器模拟到声屏障建模的广泛应用中提供了很多细节。对偶边界元法是针对薄障碍物的情况而发展的。最后，利用时变基本解沿着时间推进格式，给出了瞬态声学边界元法。本章最后简要回顾了边界元法在声学中的应用，包括FEM/BEM耦合、生物工程应用和乐器建模。接下来的一章介绍了边界元法在电化学中的应用，首先推导了控制电化学问题的电势方程，并定义了作为这些问题边界条件的极化曲线。列举了几个应用实例，从二维到三维，包括圆形腐蚀电池、埋地储罐、海水泵分析、海上平台阴极保护以及电沉积。接下来的三章讨论了理想流、慢粘性流和由纳维尔-斯托克斯方程控制的一般粘性流中的流体力学问题。详细介绍了理想流理论在承压和非承压含水层盐水入侵、非均质多孔介质渗流、粘性指进、毛细喷泉演化和非线性表面波传播等方面的理论和应用。本文详细讨论了由Stokes方程控制的粘性慢流的积分方程理论，并给出了完全双层位势边界积分方程。
This is Volume 1 of a two-volume set offering a comprehensive treatment of the fundamentals and applications of the boundary element method BEM in thermo-fluids, acoustics, and solid mechanics. Volume 1 is authored by Prof Luis Wrobel of Brunel University, and Volume 2, by Prof Ferri Aliabadi, of the College of London, both of whom are recognized authorities on and long-standing contributors to the development of the BEM. The BEM is a numerical method for the solution of boundary integral equations that can be derived for a variety of engineering field problems. This is possible if a fundamental solution is available for the differential operator governing the field problem of interest, and in such cases, the BEM only requires a discretization of the bounding surface, a distinct advantage over volume meshing techniques such as the finite volume and finite element method. This advantage is even more pronounced when dealing with moving surface and inverse problems as well as optimization. This 11-chapter book begins with a historical review of integral equations and the BEM over the last 40 years. Basic mathematical notations and theory of integral equations methods useful in development of the BEM in potential theory are covered in the ensuing chapters. A brief treatment of hypersingular equations, dual and multiple reciprocity, axi-symmetry, Galerkin BEM formulation, and fast solvers is also provided. The next two chapters address heat transfer applications of the BEM in steady and unsteady regimes. Linear as well as nonlinear heat transfer are both covered with applications to nonlinear materials, radiation, phase change, and materials processing. Convection-diffusion, bio-heat transfer, hyperbolic heat conduction, as well as coupled heat and mass transfer are treated in some detail. The next chapter develops the BEM for acoustics modeling in the frequency domain. Attention is given to the ensuing hyper-singular integrals and to regularization of the integral equations as well as to the treatment of the well-known nonuniqueness arising in exterior acoustics problems. Much detail is provided in the formulation and implementation of the BEM in acoustics as well as a wide range of applications ranging from muffler simulations to acoustic barrier modeling. The dual BEM is developed for the case of thin barriers. Finally, BEM in transient acoustics is presented using the time dependent fundamental solution along with time marching schemes. The chapter closes with a brief review of BEM in acoustics including FEM/BEM coupling, bio-engineering applications, and modeling of musical instruments.The following chapter treats the application of the BEM in electrochemistry, which begins with a derivation of the potential equation governing the problem of electrochemistry as well as the definition of the polarization curve that serves as a boundary condition for these problems. Several examples are presented ranging from 2D to 3D applications in circular corrosion cells, buried tanks, seawater pump analysis, and cathodic protection of offshore platforms as well electro-deposition. The next three chapters address fluid mechanics problems in ideal flows, slow viscous flows, and general viscous flows governed by the Navier-Stokes equations. The theory and applications of ideal flow to saltwater intrusion in confined and unconfined aquifers, flow in heterogeneous porous media, viscous fingering, evolution of capillary fountains, and propagation of nonlinear surface waves are all detailed. Integral equation theory for slow viscous flows governed by the Stokes equation is considered in detail, and the complete double layer potential boundary integral …