Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics

2003 ◽  
Vol 59 (5) ◽  
pp. 597-668 ◽  
Author(s):  
X. Zhou ◽  
K. K. Tamma
Keyword(s):  
Structural Dynamics ◽  
Single Step ◽  
Design Analysis ◽  
Optimal Algorithms ◽  
Analysis And Synthesis

Algebraic Representation of Geometric and Size Tolerances

1995 ◽  
Author(s):  
S. H. Mullins ◽  
D. C. Anderson
Keyword(s):  
Tolerance Analysis ◽  
Design Analysis ◽  
Algebraic Representation ◽  
Dimensional Metrology ◽  
Algebraic Form ◽  
Worst Case ◽  
Mechanical Component ◽  
Analysis And Synthesis ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis

Abstract Presented is a method for mathematically modeling mechanical component tolerances. The method translates the semantics of ANSI Y14.5M tolerances into an algebraic form. This algebraic form is suitable for either worst-case or statistical tolerance analysis and seeks to satisfy the requirements of both dimensional metrology and design analysis and synthesis. The method is illustrated by application to datum systems, position tolerances, orientation tolerances, and size tolerances.

Advanced mechanism design: Analysis and synthesis

1985 ◽  
Vol 20 (1) ◽  
pp. 81 ◽  
Author(s):  
Ferdinand Freudenstein
Keyword(s):  
Mechanism Design ◽  
Design Analysis ◽  
Analysis And Synthesis

Mechanism design: Analysis and synthesis

1985 ◽  
Vol 20 (1) ◽  
pp. 81
Author(s):  
Ferdinand Freudenstein
Keyword(s):  
Mechanism Design ◽  
Design Analysis ◽  
Analysis And Synthesis

Optimization of a Class of n-Sub-Step Time Integration Methods for Structural Dynamics

2021 ◽  
Author(s):  
Yi Ji ◽  
Yufeng Xing
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Single Step ◽  
Numerical Dissipation ◽  
Integration Methods ◽  
Stiffness Matrices ◽  
Difference Formula ◽  
Different Types ◽  
Time Integration Methods ◽  
Methods Numerical

This paper develops a family of optimized [Formula: see text]-sub-step time integration methods for structural dynamics, in which the generalized trapezoidal rule is used in the first [Formula: see text] sub-steps, and the last sub-step employs [Formula: see text]-point backward difference formula. The proposed methods can achieve second-order accuracy and unconditional stability, and their degree of numerical dissipation can range from zero to one. Also, the proposed methods can achieve the identical effective stiffness matrices for all sub-steps, reducing computational costs in the analysis of linear systems. Using the spectral analysis, optimized algorithmic parameters are presented, ensuring that the proposed methods can accurately calculate different types of dynamic problems such as wave propagation, stiff and nonlinear systems. Besides, with the increase in the number of sub-steps, the accuracy of the proposed methods can be enhanced without extra workload compared with single-step methods. Numerical experiments show that the proposed methods perform better in different dynamic systems.

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