Numerical computation of stress waves in solids (Q2785560)

Propagation of stress waves in solids is governed by a system of hyperbolic partial differential equations. An analytical solution is usually difficult to find analytically. With modern computers, however, numerical solutions are possible even for complicated body geometry, material properties and various loading conditions.NEWLINENEWLINENEWLINEThis book presents methods for numerical modeling of stress wave propagation in solids. The finite difference method is the main tool; other methods (BEM) can be applied to linear elastic problems. The book begins in chapter 2 with the investigation of a one-dimensional problem; stress waves in a rod are examined in order to illustrate basic facts. Then a combined longitudinal and torsional wave in a thin-walled tube is studied. The last section of this chapter introduces the modern TVD method. Chapter 3 examines the numerical modeling of stress wave propagation in a two-dimensional elastic-plastic solid, together with boundary conditions. In chapter 4, some constructions of two-dimensional numerical schemes are presented by using the method of bicharacteristics. Stress wave propagation in an axisymmetrical body is discussed in chapter 5. The finite difference schemes for five kinds of materials are discussed in chapter 6, in particular, for an anisotropic composite material. The last chapter 7 presents a covering domain method which can be classified as a boundary element approach to modeling stress wave propagation in linear elastic solids. This book can be useful for theoretical and engineering research.