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Static Analysis of the Free-Free Trusses by Using a Self-Regularization Approach

Published online by Cambridge University Press:  29 March 2017

J. T. Chen ,
Y. L. Chang ,
S. Y. Leu  and
J. W. Lee
J. T. Chen*
Affiliation:
Department of Harbor and River EngineeringDepartment of Mechanical and Mechatronic EngineeringNational Taiwan Ocean UniversityKeelung, Taiwan
Y. L. Chang
Affiliation:
Department of Harbor and River EngineeringNational Taiwan Ocean UniversityKeelung, Taiwan
S. Y. Leu
Affiliation:
Department of Aviation Mechanical EngineeringChina University of Science and TechnologyHsinchu, Taiwan
J. W. Lee
Affiliation:
Department of Harbor and River EngineeringNational Taiwan Ocean UniversityKeelung, Taiwan
*
*Corresponding author ([email protected])
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Abstract

Following the success of static analysis of free-free 2-D plane trusses by using a self-regularization approach uniquely, we further extend the technique to deal with 3-D problems of space trusses. The inherent singular stiffness of a free-free structure is expanded to a bordered matrix by adding r singular vectors corresponding to zero singular values, where r is the nullity of the singular stiffness matrix. Besides, r constraints are accompanied to result in a nonsingular matrix. Only the pure particular solution with nontrivial strain is then obtained but without the homogeneous solution of no deformation. To link with the Fredholm alternative theorem, the slack variables with zero values indicate the infinite solutions while those with nonzero values imply the case of no solutions. A simple space truss is used to demonstrate the validity of the proposed model. An alternative way of reasonable support system to result in a nonsingular stiffness matrix is also addressed. In addition, the finite-element commercial code ABAQUS is also implemented to check the results.

Keywords

Self-regularization approach3D free-free structureBordered matrixStiffness matrixSpace truss
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 4 , August 2018 , pp. 505 - 518
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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