Application of Trigonometric and Conventional Finite Difference Approximations to Beam Buckling.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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A relatively new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by both virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wave-length parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter and the optimizing value of the wavelength parameter corresponded to the half wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function.
- Numerical Mathematics