High precision integration for dynamic structural systems with holonomic constraints

Xiaojian Liu; D. W. Begg; M. A. Devane; Wanxie Zhong

doi:10.12989/sem.1997.5.3.283

High precision integration for dynamic structural systems with holonomic constraints

Xiaojian Liu^*, D. W. Begg, M. A. Devane, Wanxie Zhong

^*Corresponding author for this work

School of Civil Engineering & Surveying

Dalian University of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using 2^N algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.

Original language	English
Pages (from-to)	283-295
Number of pages	13
Journal	Structural Engineering and Mechanics: An International Journal
Volume	5
Issue number	3
DOIs	https://doi.org/10.12989/sem.1997.5.3.283
Publication status	Published - 25 May 1997

Keywords

Algebraic and differential equations
Dynamic structures
Holonomic constraints
Matrix exponential
Numerical integration

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10.12989/sem.1997.5.3.283

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title = "High precision integration for dynamic structural systems with holonomic constraints",

abstract = "This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using 2N algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.",

keywords = "Algebraic and differential equations, Dynamic structures, Holonomic constraints, Matrix exponential, Numerical integration",

author = "Xiaojian Liu and Begg, {D. W.} and Devane, {M. A.} and Wanxie Zhong",

year = "1997",

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language = "English",

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T1 - High precision integration for dynamic structural systems with holonomic constraints

AU - Liu, Xiaojian

AU - Begg, D. W.

AU - Devane, M. A.

AU - Zhong, Wanxie

PY - 1997/5/25

Y1 - 1997/5/25

N2 - This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using 2N algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.

AB - This paper presents a high precision integration method for the dynamic response analysis of structures with holonomic constraints. A detail recursive scheme suitable for algebraic and differential equations (ADEs) which incorporates generalized forces is established. The matrix exponential involved in the scheme is calculated precisely using 2N algorithm. The Taylor expansions of the nonlinear term concerned with state variables of the structure and the generalized constraint forces of the ADEs are derived and consequently, their particular integrals are obtained. The accuracy and effectiveness of the present method is demonstrated by two numerical examples, a plane truss with circular slot at its tip point and a slewing flexible cantilever beam which is currently interesting in optimal control of robot manipulators.

KW - Algebraic and differential equations

KW - Dynamic structures

KW - Holonomic constraints

KW - Matrix exponential

KW - Numerical integration

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EP - 295

JO - Structural Engineering and Mechanics: An International Journal

JF - Structural Engineering and Mechanics: An International Journal

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ER -

High precision integration for dynamic structural systems with holonomic constraints

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Keywords

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