Integrodifferential relations in linear elasticity. (Q441291)

The authors propose an integral statement of stress-strain relations. The book can be divided into three main parts. In Chapter 1 and 2, the governing BVPs and the classical and generalized variational principles of linear elasticity are introduced and discussed. Chapters 4-7 are devoted to the method of integrodifferential relations. In Chapter 4, the authors discuss various ways to weaken the constitutive relation for equilibrium stresses and kinematically admissible displacements. Chapter 5 describes the variational properties of the quadratic error functional. Chapter 6 focuses on numerical methods for integrodifferential relations and on advanced FEM. In Chapter 7, the original BVPs formulated in terms of PDE are approximated by the systems of ODE. The last part of the book (Chapter 8-11) deals with an alternative to the approaches discussed in the previous chapters. The asymptotic approaches are considered in Chapter 8. In Chapter 9, the authors examine the relations among projection, asymptotic and variational approaches. Chapter 10 focuses on the application of the projection approach to special static problems for elastic beams with asymmetric cross-section. In Chapter 11, the projection technique is extended to the three-dimensional dynamical case. An appendix contains the information on vector and tensor algebra and functional analysis.NEWLINENEWLINE This well-written and good-organized monograph can be recommended to highly-qualified experts in the field.