An analytical framework which incorporates damage propagation/growth into the general structural stability analysis is presented. Therefore, the conventional total potential energy approach is extended by introducing an extended total potential energy-like functional capable of describing inelastic processes in which equilibrium holds between available and the required force for producing a change in structure. The work deals with systems which are described by I generalized coordinates and K damage parameters. The damage parameters are found to be functions of I generalized coordinates and M load parameters. The underlying variational principle for inelastic solids may be solved using discrete formulations or approximate methods such as a Rayleigh-Ritz formulation. This leads to a set of non-linear algebraic equations, comprising post-critical equilibrium paths and damage propagation. In order to verify the framework, it is applied to the well-known problem in which a delaminated composite strut/plate is subjected to an in-plane compressive load.
The buckling and postbuckling behaviour of composite struts under uniaxial compression is investigated. A geometrically nonlinear model comprising only four generalized coordinates is applied to multi-layered struts built up of transversally isotropic unidirectional layers. Laminates with a cross-ply layup are investigated. By minimizing the total potential energy of the system, equilibrium paths and critical buckling loads for varying lengths and depths of delamination are determined. Thus, the systems response in the postbuckling range is analysed and areas of stable and unstable behaviour are determined. The outcome of the work provides detailed information about the influence of delaminations on the buckling behaviour of composite struts.
The effect of pre-stress on the buckling behaviour of geometric unit cells of collinear square lattices is investigated experimentally and numerically. The geometric unit cells are manufactured using fused deposition modelling. Manufacturing strategies are presented which incorporate fibres subjected to pre-stress within the unit cell. The effect of pre-stressed fibres is analysed by comparing the compressive behaviour of unit cells with and without fibre reinforcement. The buckling behaviour of the unit cells is also investigated numerically by employing a parametric study within Abaqus varying the pre-stress in the fibres. The experimental test series shows that the addition of pre-stressed fibres to the system results in an increase in buckling and maximum load of 260 % to 480 % and 220 % to 350 % respectively. The increase strongly relates to the manufacturing quality, i.e. the bonding between the lattice material and the fibres, where a sufficient bonding yields significantly larger loads. The experimental findings on the qualitative and quantitative buckling behaviour correspond well with results obtain from the numerical study.
The problem of a delaminated composite plate subjected to in-plane compressive loading is investigated by employing a novel analytical framework previously developed by the authors. The framework is capable of modelling the post-buckling behaviour considering damage growth by using a set of generalized coordinates only. Therefore, in order to model the post-buckling responses of delaminated composite plates a Rayleigh-Ritz formulation is employed. Thus, the post-buckling behaviour as well as the delamination growth characteristics are determined by solving a set of non-linear algebraic equations only. For the cases investigated, the study reveals that delamination growth is associated with the the global buckling response. So long as stable delamination growth is present, the post-buckling response remains also stable. However, unstable delamination growth may be caused which would occur unexpectedly yielding sudden failure of the structure. This underlines the importance of considering delamination growth when studying the structural stability behaviour of these structures.
An analytical modelling approach is presented which is capable of determining the post-buckling responses as well as the onset of delamination growth of multi-layered composite plates with an embedded circular delamination. In order to overcome current drawbacks of analytical models regarding embedded delaminations, the model employs a problem description in cylindrical coordinates and a novel geometric representation of delamination growth in conjunction with a R�������-R��� formulation and the so-called crack-tip element analysis. The modelling approach is applied to study the compressive response of composite plates with thin-film delaminations loaded under radial compressive strain. Post-buckling responses and the onset of delamination growth are determined for several layups. The results are in very good agreement with finite element simulations while requiring low computational cost.
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