Large-Deformation Displacement Transfer Functions for Shape Predictions of Highly Flexible Slender Aerospace Structures

ABSTRACT 1NOMENCLATURE 1INTRODUCTION 2CURVATURE-STRAIN RELATIONSHIP 4DIFFERENT CURVATURE EQUATIONS 4Classical (Eulerian) Curvature Equation 4Physical (Lagrangian) Curvature Equation 5Shifted Curvature Equation 6CURVATURE-STRAIN DIFFERENTIAL EQUATIONS 7NONUNIFORM AND UNIFORM BEAMS 8SHIFTED DISPLACEMENT TRANSFER FUNCTIONS 8Based on Piecewise Linear Strain Representations 8Nonuniform Beams 9Slightly Nonuniform Beams 9First Order Expansion 10Second Order Expansion 11Based on Piecewise Nonlinear Strain Representations 11Improved Case 12Log-expanded Case 13Depth-expanded Case 13Characteristics of Displace ment Transfer Functions 14EULERIAN FORMULATION OF DISPLACEMENT TRANSFER FUNCTIONS 15Projected Domain Lengths 15Slope Equation 16Deflection Equation 17Log-Expanded Slope Equation 18Log-Expanded Deflection Equation 19Simplified Deflection Equation 19LAGRANGIAN FORMULATION OF DISPLACEMENT TRANSFER FUNCTIONS 20Slope Equation 21Deflection Equation 22Simplified Deflection Equation 23STRUCTURE USED FOR SHAPE PREDICTION ACCURACY STUDIES 23Finite-Element Analysis 23Surface Strains 24COMPARISONS OF SHAPE PREDICTION ACCURACIES 24Slope Predictions 24