• Structural Engineering and Mechanics
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• v.22 no.4
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• pp.433-447
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• 2006

The problem of very large deflection of a circular cantilever arc device subjected to inward or outward polar force is studied. An exact elliptic integral solution is derived for the two cases and the results are checked using large displacement finite element analysis via the ANSYS package by performing a new novel modeling simulation technique for this problem. Excellent agreements have been obtained between the exact analytical solution and the numerical approach. From this study, a design chart for engineers is developed to predict the required value for the inward polar force for the device to switch on for a given angle forming the circular arc (${\theta}_o$). This study has several interesting applications in mechanical engineering, integrated circuit technology, nanotechnology and especially in microelectromechanical systems (MEMs) such as a MEM circular device switch subjected to attractive or repulsive magnetic forces due to the attachments of two magnetic poles at the fixed and at the free end of the circular cantilever arc switch device.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.102-105
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• 2001

In this paper, the solution of two dimensional deflection of circular wavy elastica beam was obtained for one end clamped boundary and concentrated load condition. The beam was regarded as a linear elastic material. Wavy shape was described as a combination of half-circular arc smoothly connected each other with constant curvature of all the same magnitude and alternative sign. Also load direction was taken into account. As a result, the solution was expressed in terms of a series of integral equations. While we found the exact solutions and expressed them in terms of elliptic integrals, the recursive ignition formulae about the displacement and arc length at each segment of circular section were obtained. Algorithm of determining unknown parameters was established and the profile curve of deflected beam was shown compared with initial shape.

• Structural Engineering and Mechanics
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• v.3 no.2
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• pp.163-172
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• 1995

A simple numerical method is applied to calculate the large deflection of a cantilever beam under an elastic-plastic deformation by dividing the deformed axis into a number of small segments. Assuming that each segment can be approximated as a circular arc, the method allows large deflections and plastic deformation to be analyzed. The main interests are the load-deflection relationship, curvature distribution along the beam and the length of the plastic region. The method is proved to be easy and particularly versatile. Comparisons with other studies are given.

• International Journal of Ocean System Engineering
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• v.2 no.3
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• pp.195-199
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• 2012

This paper reports a new analytical method to calculate the planar displacement of structures. The cross-sections were assumed to remain in plane and the deflection curve was evaluated using the curvature values geometrically, despite being solved with differential equations. The deflection curve was parameterized with the arc-length of the curvature values, and was taken as an assembly of chains of circular arcs. Fast and accurate solutions of complex deflections can be obtained easily. This paper includes a comparison of the nonlinear displacements of an elastic tapered cantilever beam with a uniform moment distribution among the proposed analytical method, numerical method of the theory and large deflection FEM solutions.