Functionally Graded Sandwich Panels with Variable Fiber Volume Fraction in the Facings
An approach to optimization of lightweight sandwich panels using a variable spatial distribution of fibers in the facings is considered on the example of the buckling problem. The volume fraction of fibers continuously varies throughout the facing enabling us to maximize the buckling load subject to the constraint on the weight of the panel as well as structural constraints superimposed to avoid wrinkling and the shear failure of the core. Micromechanical theories employed to evaluate the local stiffness of the facings include the model of Chamis (NASA) whose accuracy is verified through the comparison with the Silnutzer three-point lower bound on transverse shear and bulk moduli, the Gibiansky-Torquato upper bound on the transverse bulk modulus, the Hashin-Rosen bounds for the longitudinal-transverse shear modulus, and the Hill-Torquato bounds for the longitudinal elastic modulus and the major Poisson ratio. The overall computational problem can be formulated as a non-linear multi-design variable (i.e., fiber density, spatial distribution, etc.) optimization problem with structural and geometric constraints. The optimization process includes the development of a FEA model for the structural analysis of the sandwich panel and subsequently coupling the FEA analysis results with an optimization "toolkit” in an iterative procedure until a minimum weight (optimum) structure satisfying all the constraints is obtained. By utilizing various constraint-optimization algorithms in the toolkit (DAKOTA program developed in SANDIA Labs) the design variables and objective function (weight of the panel) can be updated in the feasible design space iteratively. Upon the input (updated design variable vector) from the toolkit at each iteration, the update for structural analysis involves the micromechanical phase adjusting the local stiffness tensor of the facing dependent on the fiber volume fraction in selected layers, the update of the FEA model, generating results for the global buckling load (target), and a check of the local failure modes of the facings and core. The process begins with the choice of the baseline model of the sandwich panel that is subsequently optimized, keeping the weight nearly constant. This process continues until the structural configuration change from one iteration step to the next is reduced to a desirable range. A continuous control is conducted to distinguish between local and global optima and screen out the former. The optimum design has the highest buckling load, while maintaining the desired weight and local strength. Considering a relative ease of manufacture of sandwich panels with variable fiber volume fraction, the optimization approach considered in the paper may serve as an attractive solution to design of efficient lightweight functionally graded sandwich structures.
T. J. Keil et al., "Functionally Graded Sandwich Panels with Variable Fiber Volume Fraction in the Facings," ASME International Mechanical Engineering Congress and Exposition (IMECE 2010), American Society of Mechanical Engineers (ASME), Nov 2010.
Mechanical and Aerospace Engineering
Keywords and Phrases
Facings; Fibers; Lightweight Sandwich Panels; Spatial Distribution
Article - Conference proceedings
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