05-10-2016, 03:00 PM
Uncertainty Analysisof Hollow Airfoil Composite Structure by Using Finite Element Method
1457928410-uncertaintyanalysisofairfoilbeam.docx (Size: 370.37 KB / Downloads: 6)
ABSTRACT
This study represents simulation of Airfoil composite beam by using Monte Carlomethod. A three dimensional static analysis of large displacement type has been carried out. Finite element analysis of NACA0012 airfoil composite structure has been carried out and uncertainty in Maximum Deflection is analyzed. Maximum Deflection was objective function. Chord length , beam length ,elastic modulus in XY,YZ,XZ and shear modulus of epoxy graphite in XY,YZ,XZ, ply angle and ply thickness of airfoil section, force are varied within effective range and their effect on Maximum Deflection has been analyzed. In order to validate the results, one loop of simulation is benchmarked from results in literature. Ultimately, best set of probabilistic design variable is proposed to reduce Maximum Deflection under static loading condition.
INTRODUCTION
Composite materials have found increasing use in aerospace and civil engineering construction. One of the common areas of application is panels and airfoils construction where composite materials with complex lay-ups are used. The following beamproperties can be improved when composite materials are used: specific strength, specific stiffness, weight, and fatigue life. The thin-walled beams of open cross-sections are used extensively in space systems as space erectable booms installed on spacecraft; in aeronautical industry both as direct load-carrying members and as stiffener members. In addition, they are used as well in marine and civil engineering, whereas the I-beams, in the fabrication of flex beams of bearing less helicopter rotor [1].Thin- walled structures are integral part of an aircraft [2]. That is the reason why many researchers consider it in their studies and published it in scholarly articles. Chan and his students focused on thin-walled beams with different cross-sections.Among their studies, Chan and Dermirhan [3] considered first a circular cross section thinwalled composite beam. They developed a new and simple closed-form method to calculate its bending stiffness. Then, Lin and Chan [4] continued the work with an elliptical cross section thin-walled composite beam. Later, Syed and Chan [5] included hat-sectioned composite beams. And most recently, Rao and Chan [6] expanded the work to consider laminated tapered tubes. Ascione et al. [7] presented a method that formulates a one-dimensional kinematical model that is able to study the static behavior of fiber-reinforced polymer thin-walled beams. It’s well known that the statics of composite beam is strongly influenced by shear deformability because of the low values of the elastic shear module. Such a feature cannot be analyzed byVlasov’s theory, which assumes that the shear strains are negligible along the middle line of the cross-section. Ferrero et al. [8] proposed that the stress field in thin-walled composite beams due to at twisting moment is not correctly modeled by classical analytical theories, so numerical modeling is essential. Therefore, they developed a method with a simple way of determining stress and stiffness in this type of structures where the constrained warping effect can be taken into account. They worked with both open and closed cross sections. Also, to check the validity of the method for structures made of composite materials, a beam with thin, composite walls were studied. Wu et al. [9] presented a procedure for analyzing the mechanical behavior of laminated thin-walled composite box beam under torsional load without external restraint. Some analyses have been formulated to analyzed composite box beam with varying levels of assumptions [10-13]. Therefore, analysis of airfoil beam under varying loading condition is key to improve the design and provide good agreement in results.
II. SIMULATION
The Monte Carlo Simulation method is the most common and traditional method for a probabilistic analysis. This method simulates how virtual components behave the way they are built. Present work uses FEM package ANSYS for analysis of composite beam of hollowNACA0012 airfoil shape. Element selected for meshing the geometry of the specimen is shell 181.Material properties of epoxy graphite are entered. Geometry of model is drawn in ANSYS software. Geometry is meshed by giving element size 1mm. Mapped type of meshing is used.
CONCLUSION
The influence of the design parameters on Maximum Deflection under variable loading condition is studied.The conclusions obtained are summarised as follows.
• Baseline analysis deflection results perfectly match with literature results for all three cases and percentage error is less than 3%.
• -Successfully carried out probabilistic analysis to study effect of input uncertainties on Maximum Deflection of static analysis for circular composite beam. From analysis it appears that not all input uncertainties affect Maximum Deflection.
• Co-relation coefficients and rank order coefficients of selected parameters are obtained to know the relationship between Maximum Deflection and design variables.
In Monte Carlo simulation, it was observed that maximum probable value of Maximum Deflection was shows minimum 46.46 mm and maximum 520.57 mm.