Optimization of an Orthotropic Composite Beam

Brian Schmalberger

Problem Statement• A composite beam will be constructed to analyze the stress distribution, stiffness,

displacement, and vibration modes as the fiber orientation and loading are changed. The beam will be further optimized for given design constraints, such as maximum torsional stiffness and damping of low frequency vibrations.

• The beam will be subjected to different loadings, including point, distributed and harmonic loads. Each loading will be applied to a beam that is fixed at both ends and to a beam that is fixed at one end and free at the other end.

Background• Composites are widely used in the automobile, aerospace, and athletics industry.

Examples of composites include bumpers, wings, bicycle frames, and downhill skis.• Combined with the light weight and high strength characteristics of composite

materials, the ability to optimize a composite structure for a specific property is useful to a design engineer.

• Properties of the structure, such as stiffness, stress distribution, and dynamic response are affected by fiber and matrix material, fiber orientation, and the number of lamina.

Methodology and Approach• A brief introduction to classical composite theory will also be discussed. • ANSYS will then be used to a construct three-dimensional composite beam with a

given fiber orientation and number of lamina. • The ends of the beam will be constrained as follows:

– Fixed-free– Fixed-fixed

• The beam will be loaded as follows for each set of constraints:– Point loads different locations (e.g. 0.25L, 0.50L, 0.75L and 1.0L)– Distributed loads of varying lengths and locations (e.g. 0.25L centered at 0.5L)– Harmonic loads of varying frequencies at different locations (e.g. 60Hz @ 0.5L)

Milestones• 2/05/10……….Project proposal draft• 2/08/10……….Description of classical composites theory• 2/1510…..……Composites research in ANSYS• 2/22/10……….Construction of model in ANSYS and first analysis• 2/26/10……….Progress report #1• 3/01/10……….Analysis of constraints and loads• 3/15/10……….Optimization of model for design constraints• 4/09/10……….Final draft• 4/21/10……….Final report

References• Adams, R. D. and M. R. Maheri. “Dynamic Flexural properties of Anisotropic

Fibrous Composite Beams.” Composites Science and Technology 50 (1994) 497-514.

• Assarar, Mustapha, Jean-Marie Berthelot, Abderrahim El Mahi, and Youssef Sefrani. “Damping analysis of Orthotropic Composite Materials and Laminates.” Composites: Part B 39 (2008) 1069-1076.

• Benchekchou, B., M. Coni, and R. G. White. “The Structural Damping of Composite Beams with Tapered Boundaries.” Composites Structures 35 (1996) 207-212.

• Chawla, Krish, Uday K. Vaidya, and Ashutosh Goel. “Fatigue and Vibration Response of Long Fiber Reinforced Thermoplastics.” Univ. of Birmingham.

• Della, Christian N. and Dongwei Shu. “Free Vibration of Composite Beams with Two Non-overlapping Delaminations.” International Journal of Mechanical Sciences 46 (2004) 509-526.