Final Project1 3/19/2010 Isogrid Buckling With Varying Boundary Conditions Jeffrey Lavin RPI Masters Project

Final Project2 3/19/2010 Topic Overview Geometry Definitions Simplification Buckling Analytical Solution Model Creation And Meshing Mode Shape Verification Modeling Approach Modeling Results Summary

Final Project3 3/19/2010 Isogrid Geometry Created by individual equilateral triangular panels –Triangle geometry defined by height (h) and side (s) –Geometry is reducible to single panel for all h and s Non-dimensional parameters identified –Based on NASA report CR –No cap shown =0,  =0 h a t b d 1.000” Section View

Final Project4 3/19/2010 Isogrid Simplification Reduce isogrid to single sheet –Maintain bending (D) and tensile (K) stiffness –Transformed area with parallel axis theorem Solve K and D simultaneously for t * and E * –t* is equivalent single sheet thickness –E* is equivalent single sheet modulus E * and t * provide equivalent stiffness –Do not provide equivalent stress

Final Project5 3/19/2010 x y a b Analytical Solution Calculate critical load required for elastic instability Multiple load cases established Simple supported plate Half wave buckling modes vary –M controls load direction half wave –N controls load perpendicular half wave

Final Project6 3/19/2010 Model Creation And Meshing Model Created Using Something Mesh Creation –Determine mesh density

Final Project7 3/19/2010 Mode Shape Visualization M=2 N=1 F F M M F F M M N N N N M=1 N=1

Final Project8 3/19/ = Final Modeling Approach Model single isogrid panel (4.000” x 4.618”) Represents specific geometry based on h, s, d, b –Similar configuration to existing hardware Multiple mode shapes produced

Final Project9 3/19/2010 Final Modeling Results Compare analytical solution to numerical solutions –Plate model completed using E * t * –Isogrid model completed based on geometry Analytical solution comparison –Results show good correlation between models and predicted solution

Final Project10 3/19/2010 Rib Buckling Study completed for 4 different rib heights –.050”,.100”,.250”,.500” Each model run with load applied to both edges Parameter  used for comparison of E * t * applicability – –  <.23 shows good correlation to E * t * method

Final Project11 3/19/2010 Conclusions Analytical solution matches numerical approximation –Plate model critical loads off 1.3% –Isogrid model critical loads off 3.5% Model accuracy does not decrease as deflection increases –Mesh density appropriate to calculate complex deflections Highly dependant on boundary conditions –Small change creates large difference in results Rib buckling can dominate final results –Increased rib stiffness dominates buckling solution

Final Project12 3/19/2010 Questions ?