Stability Loss and Buckling Delamination: Three-dimensional Linearized Approach for Elastic and Viscoelastic Composites

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.

This book investigates stability loss and buckling delamination problems of the viscoelastic composite materials and structural members made from these materials within the framework of the Three-Dimensional Linearized Theory of Stability (TDLTS).

The investigation of stability loss problems is based on the study of an evolution of the initial infinitesimal imperfection in the structure of the material or of the structural members with time (for viscoelastic composites) or with external compressing forces (for elastic composites).

This study is made within the scope of the Three-Dimensional Geometrically Non-Linear Theory of the Deformable Solid Body Mechanics. The solution to the corresponding boundary-value problems is presented in the series form in a small parameter which characterizes the degree of the initial imperfection.

The boundary form perturbation technique is employed and nonlinear problems for the domains bounded by noncanonical surfaces are reduced to the same nonlinear problem for the corresponding domains bounded by canonical surfaces and to series subsequent linearized problems.

Corresponding boundary value problems are solved by employing Laplace transformation with respect to time, analytical and numerical (FEM) methods of the system of the partial itegro-differential equations.

The viscoelasticity of the materials is described through the fractional exponential operators.

Numerical results on the critical time and on the critical force obtained for various problems on the stability loss of the structural members made of elastic and viscoelastic composite materials and on the stability loss in the structure of these materials are presented and discussed. As well as the results of investigations on buckling delamination problems for elastic and viscoelastic composite plates contained cracks are presented and discussed.

The book has been designed for graduate students, researchers and mechanical engineers who employ composite materials in various key branches of modern industry.