Fundamentals Of The Three Dimensional Theory Of Stability Of Deformable Bodies

At the present time stability theory of deformable systems has been developed into a manifold field within solid mechanics with methods, techniques and approaches of its own. We can hardly name a branch of industry or civil engineering where the results of the stability theory have not found their application. This extensive development together with engineering applications are reflected in a flurry of papers appearing in periodicals as well as in a plenty of monographs, textbooks and reference books. In so doing, overwhelming majority of researchers, con cerned with the problems of practical interest, have dealt with the loss of stability in the thin-walled structural elements. Trying to simplify solution of the problems, they have used two- and one-dimensional theories based on various auxiliary hypotheses. This activity contributed a lot to the preferential development of the stability theory of thin-walled structures and organisation of this theory into a branch of solid mechanics with its own up-to-date methods and trends, but left three-dimensional linearised theory of deformable bodies stability (TL TDBS), methods of solving and solutions of the three-dimensional stability problems themselves almost without attention. It must be emphasised that by three dimensional theories and problems in this book are meant those theories and problems which do not draw two-dimensional plate and shell and one-dimensional rod theories.

This book deals with dynamics of pre-stressed or pre-strained bi-material elastic systems consisting of stack of pre-stressed layers, stack of pre-stressed layers and pre-stressed half space (or half plane), stack of pre-stressed layers as well as absolute rigid foundation, pre-stressed compound solid and hollow cylinders and pre-stressed sandwich hollow cylinders. The problems considered in the book relate to the dynamics of a moving and oscillating moving load, forced vibration caused by linearly located or point located time-harmonic forces acting to the foregoing systems. Moreover, a considerable part of the book relate to the problems regarding the near surface, torsional and axisymmetric longitudinal waves propagation and dispersion in the noted above bi-material elastic systems. The book carries out the investigations within the framework of the piecewise homogeneous body model with the use of the Three-Dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies.

This book presents an analysis of eight non-classical problems of fracture and failure mechanics mainly obtained by research in the department of dynamics and stability of continuum of the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (NAS of Ukraine). It focusses on the application of the 3D (three-dimensional) theories of stability, dynamics, and statics of solid mechanics to the investigation of non-classical problems of fracture and failure mechanics.

This book addresses the problems of fracture mechanics of materials with cracks under the loading directed along the cracks. It considers two non-classical fracture mechanisms, namely the fracture of bodies compressed along cracks and the fracture of materials with initial (residual) stresses acting in parallel to the surfaces of cracks location, and presents new approaches (also including combined one) developed in the framework of three-dimensional linearized mechanics of deformable bodies. It then discusses the results of studies on two- and three-dimensional problems for various configurations of crack locations in isotropic and anisotropic materials, and based on these results, critically evaluates the accuracy and applicability limits of the “beam approximation” approach, which is widely used to study various problems of the fracture of bodies under compression along parallel cracks.

This book investigates stability loss problems of the viscoelastic composite materials and structural members within the framework of the Three-Dimensional Linearized Theory of Stability (TDLTS). The stability loss problems are considered the development of the initial infinitesimal imperfection in the structure of the material or of the structural members. This development is studied within the framework of the Three-Dimensional Geometrical Non-Linear Theory of the Deformable Solid Body Mechanics. The solution to the corresponding boundary-value problems is presented in the series form in the small parameter which characterizes the degree of the initial imperfection. In this way, the nonlinear problems for the domains bounded by noncanonical surfaces are reduced for the same nonlinear problem for the corresponding domains bounded by canonical surfaces and the series subsequent linearized problems. It is proven that the equations and relations of these linearized problems coincide with the corresponding ones of the well-known TDLTS. Under concrete investigations as stability loss criterion the case is taken for the initial infinitesimal imperfection that starts to increase indefinitely. Moreover, it is proven that the critical parameters can be determined by the use of only the zeroth and first approximations.

The book presents formulations and examples of three-dimensional non-axisymmetric stability in viscoelastic anisotropic cylindrical shells. The most critical stability loss modes are determined by minimizing the critical loads and critical times with respect to the number of half-waves in radial as well as transverse directions. Currently, there is no literature available on three-dimensional local buckling analysis (or localized warpage) that considers non-axisymmetric stability loss in viscoelastic cylindrical shells. The contents of this book provide the formulation for such a stability loss analysis through the framework of the three-dimensional linearized theory of stability. Additionally, as this book addresses the problem by modeling the material as a viscoelastic fibrous composite, it can be applied to carry out buckling analysis in both elastic and viscoelastic cases. Guide to modelling composite viscoelastic shell elements for buckling analysis Provides a framework for defining the failure criterion for viscoelastic materials Course material for teaching shell buckling and viscoelastic composites

This book offers a current image of modern mechanics. The book reflects current state of the art in the field of continuum mechanics and mechanics of structures including recent achievements in classic and non-classic approaches. The chapters are written by leading specialist in the field, so the book collects cutting edge investigations in the field. As a target we consider the society starting from beginners, i.e. master and PhD students, and also leaders in the field, that is professors of universities and civil, mechanical and aerospace engineers.

Covering various aspects of dynamic fractures this book contains state-of-the-art contributions from leading scientists in the field of crack dynamics.