About this book

In this textbook analytical methods are developed for the response and failure of the primary structural components of aircraft. Newton’s laws of motion, Hooke’s law, and the first law of thermodynamics are the basis to model the thermoelastic response of thin-walled, straight bars and coplanar curved bars. Analytical methods include energy principles to develop Castigliano’s theorems and to develop the cross-sectional material law for transverse shear and torsion. Stiffened shells typical of aircraft structures are analyzed with the thin-walled bar theory. Externally prescribed loads are due to accelerated flight and the thermal environment. Velocity-load factor (V-n) diagrams for maneuvers and gusts are described to evaluate flight loads.

Initiation of failure is predicted by one of the following criteria: von Mises yield criterion for ductile metals; the critical load to cause buckling (failure by excessive displacements); fracture criteria for the critical stress to cause crack propagation; Puck’s criterion for the brittle failure modes in fiber-reinforced polymer composites (FRP).

The subject of structural stability of discrete conservative systems introduces the methods of stability analysis, classification of bifurcation buckling problems, the concept of imperfection sensitivity, and snap-through at a limit point. Static instability of an elastic column from pre-buckling equilibrium, buckling, and through initial post-buckling is presented in detail. Buckling of flat rectangular plates subject to compression and shear is presented in a qualitative way using the classic charts from the National Advisory Committee for Aeronautics (NACA). The analysis for the static instability of a wing in steady incompressible flow, or divergence, is part of the discussion of aeroelastic phenomena.

• Results from linear elastic fracture mechanics (LEFM) are introduced to illustrate the relation between crack size and the stress to cause crack propagation. Airplane damage-tolerant design is based on LEFM such that subcritical length cracks do not grow to critical length between inspection intervals.
• The incentive to study optimal design is illustrated by the example of an aluminum wing spar. The objective is to achieve minimum weight by a search for two design variables. Constraints on yielding, buckling, and fracture are evaluated with the thin-walled bar theory.
• The analyses are developed for closed and open section bars made from fiber-reinforced polymer composites. The cross-sectional compliance matrix for bars with a closed cross-sectional contour and an open cross-sectional contour include shear-extension coupling. The first ply failure envelope for a graphite epoxy circular tube subject to an axial force and torque is determined by Puck’s intralaminar criterion. Interlaminar failure, or delamination, is modeled with fracture mechanics, and the method is illustrated by analyses of standard fracture test specimens.
• Numerical methods for static analysis begin with the direct stiffness method, which originated to model skeletal structures consisting of bars connected by joints. Applications include coplanar trusses, beams and coplanar frames. The finite element method is developed from the integral formulation of the ordinary differential equations of an axial bar and a beam.
• Analyses for the linear elastic, dynamic response of axial bars, coplanar trusses, beams, and coplanar frames are presented using the finite element method and the mode-separation method. Hamilton’s principle and Lagrange’s equations are developed for discrete mechanical systems.
• Numerous examples to illustrate the application of the structural analysis are presented in each chapter using either U.S. customary units. or SI units.

I acknowledge the technical discussions with Professors William Hallauer, Raphael Haftka, Rakesh Kapania, Raymond Plaut, and Mayuresh Patil whose contributions to the subject matter of this course have been used in the preparation of the text. I accept responsibility for any errors in the text, and would appreciate if the reader would inform me of comments and corrections via email (erjohns4@vt.edu). Thanks to Professor Anita Walz, open education librarian at Virginia Tech, and her staff for all the work necessary to publish this text as an open educational resource. Also, thanks to Mr. Joseph Brooks and Ms. Varakini Sanmugadas who assisted in the preparation of the text.