A novel computational method for simulating fatigue-driven mixed-mode delamination cracks in laminated structures under cyclic loading is presented. The proposed fatigue method is based on linking a cohesive zone model for quasi-static crack growth and a Paris' law-like model described as a function of the energy release rate for the crack growth rate during cyclic loading. The J-integral has been applied to determine the energy release rate. Unlike other cohesive fatigue methods, the proposed method depends only on quasi-static properties and Paris' law parameters without relying on parameter fitting of any kind. The method has been implemented as a zero-thickness eight-node interface element for Abaqus and as a spring element for a simple finite element model in MATLAB. The method has been validated in simulations of mode I, mode II, and mixed-mode crack loading for both self-similar and non-self-similar crack propagation. The method produces highly accurate results compared with currently available methods and is capable of simulating general mixed-mode non-self-similar crack growth problemsThe work was supported by the Danish Centre for Composite Structures and Materials forWind Turbines (DCCSM), grant no. 09-067212 from the Danish Strategic Research Council. This support is gratefully acknowledged. The second author acknowledges the support of the Spanish government through the Ministerio de Economía y Competitividad under the contract DPI2012-3446
This paper deals with topology optimization of static geometrically nonlinear structures experiencing snapthrough behaviour. Different compliance and buckling criterion functions are studied and applied for topology optimization of a point loaded curved beam problem with the aim of maximizing the snap-through buckling load. The response of the optimized structures obtained using the considered objective functions are evaluated and compared. Due to the intrinsic nonlinear nature of the problem, the load level at which the objective function is evaluated has a tremendous effect on the resulting optimized design. A well-known issue in buckling topology optimization is artificial buckling modes in low density regions. The typical remedy applied for linear buckling does not have a natural extension to nonlinear problems, and we propose an alternative approach. Some possible negative implications of using symmetry to reduce the model size are highlighted and it is demonstrated how an initial symmetric buckling response may change to an asymmetric buckling response during the optimization process. This problem may partly be avoided by not exploiting symmetry, however special requirements are needed of the analysis method and optimization formulation. We apply a nonlinear path tracing algorithm capable of detecting different types of stability points and an optimization formulation that handles possible mode switching. This is an extension into the topology optimization realm of a method developed, and used for, fiber angle optimization in laminated composite structures. We finally discuss and pinpoint some of the issues related to buckling topology optimization that remains unsolved and demands further research.
The paper presents an approach to nonlinear buckling fiber angle optimization of laminated composite shell structures. The approach accounts for the geometrically nonlinear behaviour of the structure by utilizing response analysis up until the critical point. Sensitivity information is obtained efficiently by an estimated critical load factor at a precritical state. In the optimization formulation, which is formulated as a mathematical programming problem and solved using gradient-based techniques, a number of the lowest buckling factors is included such that the risk of "mode switching" during optimization is avoided. The presented optimization formulation is compared to the traditional linear buckling formulation and two numerical examples, including a large laminated composite wind turbine main spar, clearly illustrate the pitfalls of the traditional formulation and the advantage and potential of the presented approach.
a b s t r a c tNonlinear buckling optimization is introduced as a method for doing laminate optimization on generalized composite shell structures exhibiting nonlinear behaviour where the objective is to maximize the buckling load. The method is based on geometrically nonlinear analyses and uses gradient information of the nonlinear buckling load in combination with mathematical programming to solve the problem. Thin-walled optimal laminated structures may have risk of a relatively high sensitivity to geometric imperfections. This is investigated by the concepts of ''worst" imperfections and an optimization method to determine the ''worst" shape imperfections is presented where the objective is to minimize the buckling load subject to imperfection amplitude constraints. The ability of the nonlinear buckling optimization formulation to solve the laminate problem and determine the ''worst" shape imperfections is illustrated by several numerical examples of composite laminated structures and the application of both formulations gives useful insight into the interaction between laminate design and geometric imperfections.
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