Sensitivity Analysis and Optimization of Mechanical System Design

The paper follows studies on simulation of three-dimensional mechanical dynamic systems with the help of sparse matrix and stiff integration numerical algorithms. For sensitivity analyses and the application of numerical optimization procedures it is substantial to calculate the effect of design parameters on the system behaviour by means of derivatives of state variables with respect to the design parameters. For static and quasi static analyses the computation of these derivatives from the governing equations leads to a linear equation system. The matrix of this set of linear equations shows to be the Jacobian matrix required in the numerical integration process solving the system of governing equations for the mechanical system. Thus the factorization of the matrix perfomed by the numerical integration algorithm can be reused solving the linear equation system for the state variable sensitivities. Some example demonstrate the simplicity of building the right hand sides of the linear equation system. Also it is demonstrated that the procedure proposed neatly fits into a modular concept for simulation model building and analysis.

Some Issues in the Generation of the Topology of Systems With Constant Power-Flow Input-Output Requirements

In this paper, we examine design problems in which requirements consist of constant power-flows with constant effort and flow variables in various domains. The use of an outgrowth of bond graph structure for design is explored. A spanning set of functional primitives is determined which can assemble an arbitrary system meeting the above functional requirements. Some basic theorems are developed regarding generic assembly algorithms to build systems using elements belonging to the chosen set. Maximum and minimum bounds on complexity are determined. An optimal partitioning of specified requirements is obtained to minimize the number of primitives needed. Power-flows through each primitive used is subsequently minimized to obtain a minimal power-flow graph.

A Modification of Feasible Direction Optimization Method for Handling Equality Constraints

The Feasible Direction Method of Zoutendijk has proven to be one of the efficient algorithm currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of having equality type constraints, there does not exist nonzero direction close to the feasible region, the traditional algorithm can not work properly. In this paper, a modified feasible direction finding technique has been proposed in order to handle nonlinear equality constraints for the Feasible Direction Method. The algorithm is based on searching along directions intersecting the tangent of the equality constraints at some angle which makes the move toward the interior of the feasible region.

Nonlinear Integer and Discrete Programming in Mechanical Design

A general purpose algorithm for the solution of nonlinear mathematical programming problems containing integer, discrete, zero-one and continuous design variables is described. The algorithm implements a branch and bound procedure in conjunction with both an exterior penalty function and a quadratic programming method. Variable bounds are handled independently from the design constraints which removes the necessity to reformulate the problem at each branching node. Examples are presented to demonstrate the utility of the algorithm for solving design problems. The use of zero-one variables to represent design decisions in order to allow conceptual level design to be performed is demonstrated.

A Network Implementation of Real-Time Dynamic Simulation With Interactive Animated Graphics

This paper presents a network based implementation of real-time dynamic simulation methods. An interactive animated graphics environment is presented that permits the engineer to view high quality animated graphics rendering of dynamic performance, to interact with the simulation, and to study the effects of design variations, while the simulation is being carried out. An industry standard network computing system is employed to interface the parallel processor that carries out the dynamic simulation and a high speed graphics processor that creates and displays animated graphics. Multi-windowing and graphics processing methods that are employed to provide visualization and operator control of the simulation are presented. A vehicle dynamics application is used to illustrate the methods developed and to analyze communication bandwidth requirements for implementation with a compute server that is remote from the graphics workstation. It is shown that, while massive data sets are generated on the parallel processor during realtime dynamic simulation and extensive graphics data are generated on the workstation during rendering and display, data communication requirements between the compute server and the workstation are well within the capability of existing networks.

Limitations of Conjugate Gear Tooth Surfaces in Order to Avoid Undercutting and Appearance of Envelope of Lines of Contact

Gear tooth surfaces being in line contact at every instant are considered. The dimensions of the contacting surfaces must be limited in order to avoid: (i) the appearance of the envelope of lines of contact on the generating surface Σ1 and (ii) the appearance of singular points on the generated surface Σ2. The relations between the developed concepts and the Wildhaber’s concept of the limiting pressure angle are investigated. Applications to the worm-gear drive and the generation of a pinion of a formate gear drive are considered. Computer graphics have been used to illustrate the results of computation.

A New Dynamic Basis Algorithm for Solving Linear Programming Problems for Engineering Design

A new linear programming algorithm is proposed which has significant advantages compared to the traditional simplex method. The search direction generated which is always along a common edge of the active constraint set, is used to locate candidate constraints, and can be used to modify the current basis. The dimension of the basis begins at one and dynamically increases but remains less than or equal to the number of design variables. This is true regardless of the number of inequality constraints present including upper and lower bounds. The proposed method can operate equally well from a feasible or infeasible point. The pivot operation and artificial variable strategy of the simplex method are not used. Examples are presented and results are compared with a traditional revised simplex method.

A Generalized Expert System Shell for Implementing Mechanical Design Applications: Review, Introduction and Fundamental Concepts

The foundations for an expert system shell for implementing mechanical design applications are presented in this paper. The shell supports facilities for knowledge acquisition, quasi-reactive planning, design evaluation, and subjective explanation. The underlying philosophy of each of these facilities and some preliminary implementation issues are discussed. A brief summary of a recent research effort and its implications on the development of a generalized expert system shell for implementing mechanical design applications are also presented.

Building an Expert System for Engineering Design Based on the Object-Oriented Knowledge Representation Concept

An expert system is developed for engineering design based on object-oriented knowledge representation concept. The design process is understood as determining design variables and their relationships which compose design model. The design model is represented as a network in the computer system using the object-oriented knowledge representation. The system built with the above concept provides the following abilities: 1) flexible model building and easy modification, 2) effective diagnosis of the design process, 3) supporting method for redesign, 4) a hybrid function with numerical computations and graphics, and 5) applicability for various design problems. Finally, it is applied to the basic design of a ship.

Optimal Design of Wind Turbines Using BIAS, A Method of Multipliers Code

A method has been developed and is demonstrated which determines the chord and twist distribution for a wind turbine with maximum power coefficient. Only small wind turbines (less than 10 kilowatts) are considered in this study, but the method could be used for larger wind turbines. Glauert determined a method for estimating the chord and twist distribution that will maximize the power coefficient if there is no drag. However, the method proposed here determines the chord and twist distribution which will maximize the power coefficient with the effect of drag included. Including drag in the analysis does not significantly affect the Glauert chord and twist distribution for airfoils with a high lift coefficient at the maximum lift to drag ratio. However, if the airfoil has a fairly low lift coefficient at its maximum lift to drag ratio due to its shape or a rough surface then significant improvement can be obtained in power coefficient by altering the Glauert chord and twist distribution according to the method proposed herein.