Bifurcation Buckling as an Approximation of the Collapse Load for General Shells

Computer Methods in Applied Mechanics and Engineering

2010

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.

Section: Linear Buckling Analysis Of Laminated Composite Shell Structmentioning

confidence: 99%

Nonlinear buckling optimization of composite structures

Computer Methods in Applied Mechanics and Engineering

2010

“…In engineering applications linear buckling analysis is often used as a generalized stability predictor for shell structures, see e.g. [51]. Within linear buckling analysis the structure is assumed to behave linearly up until the buckling point neglecting all types of nonlinearity.…”

Section: Asymmetric Solutionmentioning

confidence: 99%

A unified approach to nonlinear buckling optimization of composite structures

2011

Computers & Structures

A unified approach to nonlinear buckling fiber angle optimization of laminated composite shell structures is presented. The method includes loss of stability due to bifurcation and limiting behaviour. The optimization formulation is formulated as a mathematical programming problem and solved using gradient-based techniques. Buckling of a well-known cylindrical shell benchmark problem is studied and the solutions found in literature are proved to be incorrect. The nonlinear buckling optimization formulation is benchmarked against the traditional linear buckling optimization formulation through several numerical optimization cases of a composite cylindrical shell panel which clearly illustrates the advantage and potential of the presented approach.

“…singular tangent stiffness. For shell structures it is often used as a generalized stability predictor, as described in Almroth and Brogan (1972), when the stability point is of bifurcation or even limit point type. Linear buckling analysis is based upon linear static analysis where the static equilibrium equation for the structure may be written as…”

Section: Linear Buckling Analysismentioning

confidence: 99%

Optimization formulations for the maximum nonlinear buckling load of composite structures

2010

Struct Multidisc Optim

This paper focuses on criterion functions for gradient based optimization of the buckling load of laminated composite structures considering different types of buckling behaviour. A local criterion is developed, and is, together with a range of local and global criterion functions from literature, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization.