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Tangent stiffness matrix
About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.
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TL;DR: In this article, the authors present a stick-and-spring theory with potential application to the statics and the dynamics of such nanostructures as graphene, carbon nanotubes, viral capsids, and others.
19 citations
TL;DR: In this article, the authors extend the original Koiter-Newton approach with a reliable and accurate bifurcation indicator which is based on an eigenanalysis of the reduced order tangent stiffness matrix.
Abstract: The Koiter–Newton method is a reduced order modeling technique which allows us to trace efficiently the entire equilibrium path of a non-linear structural analysis. In the framework of buckling the method is capable to handle snap-back and snap-through phenomena but may fail to predict reliably bifurcation branches along the equilibrium path. In this contribution we extend the original Koiter–Newton approach with a reliable and accurate bifurcation indicator which is based on an eigenanalysis of the reduced order tangent stiffness matrix. The proposed indicator has a negligible numerical effort since all computations refer to the reduced order model which is typically of very small dimension. The extension allows the identification of bifurcation points and a tracing of corresponding bifurcation branches in each sector of the equilibrium path. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with several examples.
19 citations
TL;DR: The proposed approach presents an effective design tool for evaluation and limitation of stiffness of machines and robots.
Abstract: New stiffness performance indices using the collinear stiffness value (CSV) associated with a given configuration of the machine are proposed. The minimal CSV (MinCSV) is applied to stiffness evaluation for all types of configurations. Similar to the determinant, the MinCSV equals zero in singular configurations. In regular configurations, the MinCSV is applied to evaluation of local stiffness for a given configuration and global stiffness in the workspace, wherein stiffness limitations are satisfied. A screw stiffness value, i.e., the CSV during a screw displacement, presents the general case of the CSV. There are two important special cases: rotational and translational stiffness values. Procedures for evaluation of the MinCSV are developed in natural and dimensionless forms. The CSV of the hexapod are simulated and compared with those of serial-type mechanisms. The proposed approach presents an effective design tool for evaluation and limitation of stiffness of machines and robots.
19 citations
TL;DR: In this paper, the authors derived a 12 by 12 tangent stiffness matrix for a space frame member with constant cross-section, where the member end forces are expressed in the coordinate axes of the deformed geometry of the member in terms of the total end displacements.
Abstract: This presentation is concerned with the derivation of a 12 by 12 tangent stiffness matrix for a space frame member with constant cross-section. At first, the member end forces are expressed in the coordinate axes of the deformed geometry of the member in terms of the total end displacements. Then, in accordance with the Taylor expansion method, the stiffness influence coefficients are obtained as the partial derivatives of the force vector with respect to each one of the twelve member end displacements. It is believed that when this tangent stiffness matrix is used in connection with the Newton-Raphson iteration scheme in analyzing geometrically nonlinear structures, both the speed of convergence and the accuracy of the results are substantially increased. Numerical results are included to demonstrate the efficiency of the tangent stiffness matrix presented.
19 citations
19 citations