On the static analysis of constrained structural systems

2004 ◽  
Vol 31 (6) ◽  
pp. 1119-1122 ◽  
Author(s):  
Hee-Chang Eun ◽  
Eun-Taik Lee ◽  
Heon-Soo Chung
Keyword(s):  
Structural Analysis ◽  
Quadratic Form ◽  
Degrees Of Freedom ◽  
Generalized Inverse ◽  
Linear Displacement ◽  
Structural Systems ◽  
Constraint Forces ◽  
Equilibrium Equations ◽  
Compatibility Conditions ◽  
Entire Structure

Complete structures might contain so many degrees of freedom that it would be infeasible to perform a structural analysis. The derivation of the equilibrium equations of an entire structure to utilize kinematical compatibility conditions at the interfaces of the substructures requires complicated intermediate processes or numerical schemes for determining multipliers. This study derives an explicit matrix form of the equilibrium equations of structural systems subjected to constraints like compatibility conditions or linear displacement relations. The equation is obtained by minimizing a quadratic form of the variation in unconstrained and constrained displacements with respect to all constrained displacements that satisfy the constraints. And the physical meaning of the constraint forces required to satisfy the constraints is investigated. The validity of the proposed method is illustrated by several applications.Key words: constraints, compatibility, equilibrium equation, generalized inverse.

Structural reanalysis for a modified structure

2008 ◽  
Vol 35 (9) ◽  
pp. 1018-1023 ◽  
Author(s):  
Eun-Taik Lee ◽  
Hee-Chang Eun
Keyword(s):  
Inverse Method ◽  
Degrees Of Freedom ◽  
Generalized Inverse ◽  
Design Parameters ◽  
Initial Structure ◽  
Structural Elements ◽  
Static Behavior ◽  
Compatibility Conditions ◽  
Structural Reanalysis ◽  
Generalized Inverse Method

Structural reanalysis aims to determine the variations in the displacement of a structure due to the addition or deletion of elements without solving the full degrees of freedom. The iterations change the design parameters at each step and utilize the factorization of the stiffness matrix of the initial design. This study develops a new reanalysis method to determine the additional forces that act on the initial structure and the displacements of the modified structure. It utilizes the compatibility conditions at the interfaces between the initial structure and the added or deleted members as static constraints, and applies the generalized inverse method to describe the static behavior of the constrained structure. The structural elements that are added may be statically stable substructures or floating members that possess rigid-body freedom. Examples are included to show the effectiveness of the proposed method.

scholarly journals Disassembling-Based Structural Damage Detection Using Static Measurement Data

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Eun-Taik Lee ◽  
Hee-Chang Eun
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Degrees Of Freedom ◽  
Measurement Data ◽  
Truss Structures ◽  
Detection Methods ◽  
Internal Stresses ◽  
Structural Damage Detection ◽  
Constraint Forces ◽  
Entire Structure

Damage detection methods can be classified into global and local approaches depending on the division of measurement locations in a structure. The former utilizes measurement data at all degrees of freedom (DOFs) for structural damage detection, while the latter utilizes data of members and substructures at a few DOFs. This paper presents a local method to detect damages by disassembling an entire structure into members. The constraint forces acting at the measured DOFs of the disassembled elements at the damaged state, and their internal stresses, are predicted. The proposed method detects locally damaged members of the entire structure by comparing the stress variations before and after damage. The static local damage can be explicitly detected when it is positioned along the constraint load paths. The validity of the proposed method is illustrated through the damage detection of two truss structures, and the disassembling (i.e., local) and global approaches are compared using numerical examples. The numerical applications consider the noise effect and single and multiple damage cases, including vertical, diagonal, and chord members of truss structures.

scholarly journals Reanalysis of Modified Structures by Adding or Removing Substructures

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yong-Su Kim ◽  
Hee-Chang Eun
Keyword(s):  
Inverse Method ◽  
Generalized Inverse ◽  
Original Structure ◽  
Structural Elements ◽  
Equilibrium Equations ◽  
Compatibility Conditions ◽  
Design Variables ◽  
Constrained Equilibrium ◽  
Structural Reanalysis ◽  
Generalized Inverse Method

This study considers structural reanalysis owing to the modification of structural elements including (1) addition of substructures, (2) removal of substructures, and (3) changes in design variables. Coupling and decoupling reanalysis methods proposed in the study are performed by using the concept of compatibility conditions at interface nodes between the substructures or between the original structure and the substructures. Subsequently, a generalized inverse method to describe constrained responses is modified to obtain the reanalysis responses. In this study, constrained equilibrium equations are modified to consider a reanalysis of a structure with the addition and removal of statically stable or unstable substructures. The proposed reanalysis method is examined by using five examples of handling coupling and decoupling reanalysis of a truss structure.

A solution method of equilibrium equations for large structural systems

1985 ◽  
Vol 20 (1-3) ◽  
pp. 107-114 ◽  
Author(s):  
T.C. Cheu ◽  
C.P. Johnson ◽  
R.R. Craig
Keyword(s):  
Solution Method ◽  
Structural Systems ◽  
Equilibrium Equations

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Instability of Discrete Pseudo-Conservative Structural Systems

1991 ◽  
Vol 44 (11S) ◽  
pp. S194-S198 ◽  
Author(s):  
Anibal E. Mirasso ◽  
Luis A. Godoy
Keyword(s):  
Classical System ◽  
Potential Energy Function ◽  
Structural Systems ◽  
Equilibrium Path ◽  
Equilibrium Equations ◽  
Total Potential ◽  
Approximate Form ◽  
Nonlinear Equilibrium ◽  
Mechanical Models ◽  
New Formulation

Critical and postcritical states of pseudo-conservative discrete structural systems are studied by means of a new formulation leading to a classification of critical states and to an approximate form of the postcritical equilibrium path. The nonlinear equilibrium equations are derived from the total potential energy function of a classical system, but with the addition of at least one control parameter. The follower force effect is thus included by nonlinear constraints to the equilibrium equation. The nonlinear equations are solved by perturbation techniques. Finally the theory is applied to investigate the instability of some simple mechanical models.

On MBS Constraints and Projections

2021 ◽  
Author(s):  
Friedrich Pfeiffer
Keyword(s):  
Quadratic Form ◽  
Differential Equations ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Machine Process ◽  
Constraint Forces ◽  
Process Dynamics ◽  
Robot Tracking ◽  
Minimal Coordinates ◽  
Linear Differential

Abstract Constraints in multibody systems are usually treated by a Lagrange I - method resulting in equations of motion together with the constraint forces. Going from non-minimal coordinates to minimal ones opens the possibility to project the original equations directly to the minimal ones, thus eliminating the constraint forces. The necessary procedure is described, a general example of combined machine-process dynamics discussed and a specific example given. For a n-link robot tracking a path the equations of motion are projected onto this path resulting in quadratic form linear differential equations. They define the space of allowed motion, which is generated by a polygon-system.

scholarly journals Statistics Learning Network Based on the Quadratic Form for SAR Image Classification

2019 ◽  
Vol 11 (3) ◽  
pp. 282 ◽  
Author(s):  
Chu He ◽  
Bokun He ◽  
Xinlong Liu ◽  
Chenyao Kang ◽  
Mingsheng Liao
Keyword(s):  
Quadratic Form ◽  
Image Classification ◽  
Degrees Of Freedom ◽  
Image Interpretation ◽  
Sar Image ◽  
Statistical Features ◽  
Image Description ◽  
Linear Transformations ◽  
Sar Images ◽  
Learning Network

The convolutional neural network (CNN) has shown great potential in many fields; however, transferring this potential to synthetic aperture radar (SAR) image interpretation is still a challenging task. The coherent imaging mechanism causes the SAR signal to present strong fluctuations, and this randomness property calls for many degrees of freedom (DoFs) for the SAR image description. In this paper, a statistics learning network (SLN) based on the quadratic form is presented. The statistical features are expected to be fitted in the SLN for SAR image representation. (i) Relying on the quadratic form in linear algebra theory, a quadratic primitive is developed to comprehensively learn the elementary statistical features. This primitive is an extension to the convolutional primitive that involves both nonlinear and linear transformations and provides more flexibility in feature extraction. (ii) With the aid of this quadratic primitive, the SLN is proposed for the classification task. In the SLN, different types of statistics of SAR images are automatically extracted for representation. Experimental results on three datasets show that the SLN outperforms a standard CNN and traditional texture-based methods and has potential for SAR image classification.

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