Henry R. Busby

OPTIMAL REGULARIZATION OF AN INVERSE DYNAMICS PROBLEM

Abstract Solving the inverse dynamics problem using Tikhonov regularization and dynamic programming requires the selection of an optimal smoothing parameter. One popular method for choosing the smoothing parameter is the generalized cross-validation method. This method works very well but is computationally expensive for large systems. Another method for selecting an optimal smoothing parameter is the L-curve method. This L-curve is easily computed and may prove very useful for large systems which preclude other methods. In this paper we investigate both of these methods for a simple cantilever beam that is subjected to an unknown force. A simulated strain measurement is used to provide the experimental data.

Solution of an inverse dynamics problem using an eigenvalue reduction technique

Abstract The inverse dynamics problem is one in which measurements are made on some of the state variables and it is desired to find the unknown forcing function. This paper describes the use of an eigenvalue reduction technique to reduce the order of the system, in conjunction with dynamic programming, to estimate the forcing function. Several numerical experiments were performed to ascertain the effects of noise, the weighting parameters, and the reduction of modes on the solution.

Design of a mechanical proximity sensor

A proximity sensor using a mechanical contact principle is under development for robotic applications. Good discrimination between contact loads and inertial windage loads is essential. Rugged design and easy replacement of sensing elements is also necessary. The sensor is under consideration for use on the feet of the Adaptive Suspension Vehicle.

Linearization of multibody frictional contact problems

Abstract A Simplex type algorithm is used to impose frictional contact conditions on finite element models of bodies that move close to trajectories that can be determined from kinematic constraints on the bodies. The method is demonstrated by computing the load dependent static transmission error and load sharing of a pair of gears in mesh.

Elasticity solutions for constant and linearly varying loads applied to a rectangular surface patch on the elastic half-space

The solution of the point load problem in the half-space is well known in the theory of elasticity. Using direct integration, the point solution can theoretically be used to develop the solution for loading various contact areas with a variety of loading profiles. Unfortunately, anything more complicated than constant pressure loading has previously required numerical integration, and hence, no closed form solution was obtainable. Partial solutions, i.e. solutions valid only on the surface of the half-space have also been available. This paper presents the methodology to generate complete solutions to the integrals for constant and linearly varying loads applied in both the normal and tangential directions everywhere in the half-space.

Finite element analysis of three-dimensional conformal contact with friction

Abstract A specialized finite element formulation designed to deal with the frictional contact problem in three-dimensional bodies where one of the principal relative curvatures is zero or close to zero is described. Numerical examples of contact between three-dimensional gears has been presented.

Optimal regularization of the inverse‐heat conduction problem using the L‐curve

Solving the inverse heat conduction using Tikhonov regularization requires the selection of an optimal smoothing parameter. One popular method for choosing the smoothing parameter is the generalized cross‐validation method. This method works very well but is computationally expensive. In this paper we investigate the L‐curve method for selecting an optimal smoothing parameter. This L‐curve is easily computed and may prove very useful for large systems which preclude other methods.

A rayleigh-ritz approach to modeling bending and shear deflections of gear teeth

Abstract The Rayleigh-Ritz energy method was used to study the shear effect of an involute gear tooth. The gear tooth was simulated by a tapered plate model subjected to a concentrated load. The plate deflections, including shear deformation, were determined and compared with the theoretical values and experimental data. The comparisons indicate that the deflections of the shear plate model are higher than those computed from the thin plate models which neglects the shear effects. On the other hand, the experimental results are higher than those of the shear plate model due to the base flexibilities of the experimental models. The shear model deflections are also shown to be in excellent agreement with finite element results. The shear plate model could replace the finite element model since it is more computationally efficient and its results are accurate enough for most engineering purposes.

An effective curved composite beam finite element based on the hybrid-mixed formulation

Abstract A laminated curved-beam finite element with six displacement degrees of freedom and three stress parameters is derived and evaluated. Both thermal and hygrothermal effects are included. The element is based on the Hellinger-Reissner principle and the hybrid-mixed formulation. The Timoshenko beam theory and classical lamination theory are employed in the finite element description. Within an element linear displacement interpolation is used; the generalized stresses are interpolated by either stress functions based on the equilibrium equations ( P 1 ) or constant stress approximation ( P 2 ). The beam element stiffness is obtained explicitly and numerical results show very good displacement prediction compared to analytical solutions. Generalized stresses are predicted accurately at the mid-point of the finite element only for constant stress interpolation. The P 1 -type element yields more accurate displacement and stress prediction.

A numerical approach to the static analysis of an annular sector mindlin plate with applications to bevel gear design

Abstract A numerical procedure based on the Rayleigh-Ritz method is used to determine the flexural behavior of a cantilevered annular sector plate of variable rigidity, including the effects of shear deformation. The Ritz method used employs algebraic polynomial trial functions in two dimensions to obtain the deflections and stresses in the shear flexible sector plate. Convergence is investigated, with attention being given to the number of terms taken for each coordinate direction. The application of the mathematical model to predict the deflections and root stresses in a straight bevel gear is demonstrated. The compliance computations based on the sector plate model can be readily integrated into existing computer codes for bevel gear design to determine the load distribution and transmission error. Numerical results are compared with previously published results wherever available and finite element methods.