Nonlinear buckling optimization of composite structures considering “worst” shape imperfections

• Published in: International journal of solids and structures Vol. 47; no. 22; pp. 3186 - 3202
• Main Authors: Lindgaard, Esben, Lund, Erik, Rasmussen, Kim
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.11.2010; Elsevier
• Subjects: Buckling; Composite laminate optimization; Composite structures; Defects; Design sensitivity analysis; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Geometric imperfections; Laminates; Mathematical models; Nonlinearity; Optimization; Physics; Shells; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Design sensitivity analysis; Geometric imperfections; Composite structures; Buckling; Composite laminate optimization; Geometrical shape; Sensitivity analysis; Stratified material; Constraint; Form defect; Laminated structure; Displacement(deformation); Non linear programming; Large displacement; Composite material; Geometrical model; Optimization; Shell; High sensitivity; Critical load; Non linear effect; Thin wall; Mathematical programming
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2010.07.020

Nonlinear 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.