Design Sensitivity Analysis of Planar Mechanism and Machine Dynamics

1981 ◽  
Vol 103 (3) ◽  
pp. 560-570 ◽  
Author(s):  
E. J. Haug ◽  
R. Wehage ◽  
N. C. Barman
Keyword(s):  
Sensitivity Analysis ◽  
Equations Of Motion ◽  
Computer Code ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Algebraic Equations ◽  
Analysis And Design ◽  
Structural Design Optimization ◽  
Mixed Systems ◽  
Crank Mechanism

A method of formulating and automatically integrating the equations of motion of quite general constrained dynamic systems is presented. Design sensitivity analysis is carried out using a state space adjoint variable method that has been employed extensively in optimal control and structural design optimization. Both dynamic analysis and design sensitivity analysis formulations are automated and numerical solution of state and adjoint differential equations are carried out using a stiff numerical integration method that treats mixed systems of differential and algebraic equations. A computer code that implements the method is applied to two numerical examples. The first example concerns a relatively simple slider-crank mechanism. The second example treats a more complex agricultural trip plow that undergoes intermittent motion.

Analysis and Optimal Design of Spatial Mechanical Systems

1987 ◽  
Author(s):  
H. Ashrafeiuon ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Sensitivity ◽  
General Purpose ◽  
Design Sensitivity Analysis ◽  
Analysis And Design ◽  
Spatial Systems

Abstract This paper presents a new approach to optimal design of large multibody spatial mechanical systems. This approach uses symbolic computing to generate the necessary equations for dynamic analysis and design sensitivity analysis. Identification of system topology is carried out using graph theory. The equations of motion are formulated in terms of relative joint coordinates through the use of velocity transformation matrix. Design sensitivity analysis is carried out using the Direct Differentiation method applied to the relative joint coordinate formulation for spatial systems. Symbolic manipulation programs are used to develop subroutines which provide information for dynamic and design sensitivity analysis. These subroutines are linked to a general purpose computer program which performs dynamic analysis, design sensitivity analysis, and optimization. An example is presented to demonstrate the efficiency of the approach.

Analysis and Optimal Design of Spatial Mechanical Systems

1990 ◽  
Vol 112 (2) ◽  
pp. 200-207 ◽  
Author(s):  
H. Ashrafiuon ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Design Sensitivity ◽  
General Purpose ◽  
Design Sensitivity Analysis ◽  
Sensitivity Analyses ◽  
Spatial Systems ◽  
Spatial System

This paper presents a new approach to optimal design of large multibody spatial mechanical systems which takes advantage of both numerical analysis and symbolic computing. Identification of system topology is carried out using graph theory. The equations of motion are formulated in terms of relative joint coordinates through the use of a velocity transformation matrix. Design sensitivity analysis is carried out using the direct differentiation method applied to the relative joint coordinate formulation for spatial systems. The symbolic manipulation program MACSYMA is used to automatically generate the necessary equations for both dynamic and design sensitivity analyses for any spatial system. The symbolic equations are written as FORTRAN statements that are linked to a general purpose computer program which performs dynamic analysis, design sensitivity analysis, and optimization, using numerical techniques. Examples are presented to demonstrate reliability and efficiency of this approach.

Supercomputer-Based Sensitivity Analysis of Constrained Dynamic Systems

1987 ◽  
Author(s):  
P. Krishnaswami ◽  
S. Ramaswamy
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Large Scale ◽  
Computing Time ◽  
Computer Code ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Dramatic Reduction ◽  
Computational Performance ◽  
Computationally Intensive

Abstract Generalized design sensitivity analysis of constrained dynamic systems is a computationally intensive process that is well-suited for implementation on a modern supercomputer. A matrix oriented method for design sensitivity analysis, based on direct differentiation, is developed. An algorithm based on this development was implemented in a computer code which was then run on a Cray X-MP supercomputer. The implementation attempts to make full use of the vectorization capabilities of this machine. The numerical examples that were run on this implementation were compared with results presented in the literature in order to verify the program and to assess its computational performance. The results show that the use of supercomputers for performing design sensitivity analysis of dynamic systems using this method produces a dramatic reduction in the computing time; it is anticipated that this will make the optimization of very large-scale dynamic systems computationally viable.

Design Sensitivity Analysis of Large-Scale Constrained Dynamic Mechanical Systems

1984 ◽  
Vol 106 (2) ◽  
pp. 156-162 ◽  
Author(s):  
E. J. Haug ◽  
R. A. Wehage ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Adjoint Equations ◽  
Design Sensitivity Analysis ◽  
Integration Algorithm ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

A method for computer-aided design sensitivity analysis of large-scale constrained dynamic systems is presented. A generalized coordinate partitioning method is used for assembling and solving sets of mixed differential-algebraic equations of motion and adjoint equations required for calculation of derivatives of dynamic response measures with respect to design variables. The reduction in dimension of the equations of motion and associated adjoint equations obtained through use of generalized coordinate partitioning significantly reduces the computational burden, as compared to methods previously employed. Use of predictor-corrector numerical integration algorithms, rather than an implicit integration algorithm used in the past is shown to greatly simplify the equations that must be formulated and solved. Two examples are presented to illustrate accuracy of the design sensitivity analysis method developed.

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