Virtual Principles in Aircraft Structures

1. Front Matter

   Pages i-xix

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2. The basic three, two, and one dimensional equations in structural analysis

   • B. E. Gatewood

   Pages 1-36

3. Virtual displacement and virtual force methods in structural analysis

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   Pages 37-61

4. The virtual principles for pin-jointed trusses

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   Pages 62-102

5. The virtual principles for simple beams

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   Pages 103-152

6. Box beam shear stresses and deflections

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   Pages 153-201

7. Shear lag in thin web structures

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   Pages 202-253

8. Allowable stresses of flight vehicle materials

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   Pages 254-296

9. Analysis and design of joints and splices

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   Pages 297-341

10. Structural design of flight vehicle components

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    Pages 342-378

11. Analysis and design of pressurized structures

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    Pages 379-409

12. Approximate solutions using the virtual principles

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    Pages 410-440

13. Dynamics of simple beams

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    Pages 441-463

14. The plate equations

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    Pages 464-504

15. Approximate matrix equations for plate finite elements

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    Pages 505-555

16. Matrix structural analysis using finite elements

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    Pages 556-581

17. Composite materials

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    Pages 582-610

18. Back Matter

    Pages 611-695

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The basic partial differential equations for the stresses and displacements in clas­ sical three dimensional elasticity theory can be set up in three ways: (1) to solve for the displacements first and then the stresses; (2) to solve for the stresses first and then the displacements; and (3) to solve for both stresses and displacements simultaneously. These three methods are identified in the literature as (1) the displacement method, (2) the stress or force method, and (3) the combined or mixed method. Closed form solutions of the partial differential equations with their complicated boundary conditions for any of these three methods have been obtained only in special cases. In order to obtain solutions, various special methods have been developed to determine the stresses and displacements in structures. The equations have been reduced to two and one dimensional forms for plates, beams, and trusses. By neglecting the local effects at the edges and ends, satisfactory solutions can be obtained for many case~. The procedures for reducing the three dimensional equations to two and one dimensional equations are described in Chapter 1, Volume 1, where the various approximations are pointed out.

• Degrees of freedom
• Rigid body
• design
• dynamics
• finite element method
• flows
• vibration

• Dept. of Aeronautical and Astronautical Engineering, The Ohio State University, Columbus, USA

  B. E. Gatewood

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