| Summary: | 博士 === 國立中興大學 === 應用數學系所 === 100 === There are two parts in this dissertation. In part I, the analytical solutions are derived for a general 3-D helical curved beam. The equilibrium equations are listed as twelve ordinary differential equations. All force, moment, rotation and displacement components form a set of differential equations of the same pattern. Once the curvature and torsion are specified, the analytical solutions can be derived, if the pattern of differential equations can be solved. Helical curved is found to be solvable. Some examples of the analytical solutions of 2-D curves are demonstrated here. The analytical solution of 3-D helical curve with variable curvature is also demonstrated.
The second part will derive the general analytical solutions of 2D static curved beams. The solutions are valid for all curvatures. All quantities of axial force, shear force, moment, radial and tangential displacements are decoupled and are expressed as harmonic differential equations in terms of angle of tangent slope. The first and second moments of the curve with respect to x and y axes are defined as fundamental geometric properties. The studies of parabola, elliptical, hyperbolic, caternary, spiral, exponential spiral, cycloid curved beams are shown. The elliptical and some close rings are studied as well. Comparison with other results is demonstrated. The results show that for a thin curved beam, the inextensional assumption is practically adequate. However extensional effect must be included in the case of cantilever arcs.
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