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The 3-D formulation of flexible rods with embedded line actuators is presented in this paper. Both the rods and the line actuator are assumed to be initially curved and relatively positioned in an arbitrary way. The deformed configurations of the rod and actuator are connected by assuming that the principal planes of the rod remain in plane and inextensible in the deformed configuration. The resultant forces and moments in the rod and actuator are found by solving the equilibrium equations for both the rod and actuator and applying continuity of tractions on the rod-actuator interface. The formulation is reduced to 2-D and applied to the case of a Shape Memory Alloy (SMA) fiber embedded in a cylindrical rod. The deformed shapes of the rod under repeated thermal actuation and the resulting shape memory loss due to the development of residual stresses are-evaluated. Finally, the inverse problem of finding the required actuation force and initial curvature, to acquire a predetermined deformed shape, is solved in closed form for the 2-D cases.

Flexible Mechanisms such as slider crank and four-bar mechanisms are modeled and their dynamic instability and optimum design analyzed. The primary aim of the project was a thorough understanding and analysis of conditions of dynamic instability in flexible components of mechanisms and robots. Dynamic instability characterizes the behavior when amplitude of vibrations have a tendency to become unbounded with the passage of time. Other aims of the study included the optimal design of mechanisms on the basis of flexibility and control of stresses and deflections.

Dynamic behavior of flexible components of mechanisms is prone to instabilities which create resonant speed barriers. By considering small deformations superimposed on the steady dynamic state equations governing evolution of disturbances can be obtained. For the case of mechanisms driven by periodic inputs these equations reduce to a system of coupled Mathieu-Hill equations for the amplitudes of modes of vibrations. Application of the Floquet theory determines the critical conditions of speed, geometry and material properties causing dynamic instability. (Author), This article is from 'Transactions of the Army Conference on Applied Mathematics and Computing (2nd) Held at Washington, DC on 22-25 May 1984,' AD-A154 047, p105-116.

Static stability of an elastic system composed of a flexible and a rigid link leads to a nonlinear eigenvalue problem with a single buckling load or infinite buckling loads when the flexible link is in tension or compression, respectively. Integration of equations of equilibrium leads to nonlinear singular integral equations which can be analyzed and solved numerically. (Author), This article is from 'Transactions of the Army Conference on Applied Mathematics and Computing (2nd) Held at Washington, DC on 22-25 May 1984,' AD-A154 047, p597-610.

The hydrodynamic theory of foil bearings is reviewed. The relationship between fluid pressure and film thickness is discussed. The compressibility of gas is included in the analysis. It is shown that the basic equation for determination of pressure distribution becomes a third order boundary value problem in terms of film thickness. A simple numerical scheme for solution of the nonlinear boundary value problem is developed and some examples are considered and discussed. (Author), This article is from 'Transactions of the Army Conference on Applied Mathematics and Computing (1st) Held at Washington, DC on 9-11 May 1983,' AD-A139 224, p659-677. Prepared in cooperation with Clarkson Coll., Potsdam, NY. Dept. of Mechanical and Industrial Engineering.