Analytical form-finding of tensegrities using determinant of force-density matrix

2018 ◽  
Vol 189 ◽  
pp. 87-98 ◽  
Author(s):  
Li-Yuan Zhang ◽  
Shi-Xin Zhu ◽  
Song-Xue Li ◽  
Guang-Kui Xu
Keyword(s):  
Density Matrix ◽  
Analytical Form ◽  
Force Density ◽  
Form Finding

Analytical Form-Finding for Highly Symmetric and Super-Stable Configurations of Rhombic Truncated Regular Polyhedral Tensegrities

2019 ◽  
Vol 86 (3) ◽  
Author(s):  
Li-Yuan Zhang ◽  
Shi-Xin Zhu ◽  
Xiao-Fei Chen ◽  
Guang-Kui Xu
Keyword(s):  
Analytical Form ◽  
Force Density ◽  
High Symmetry ◽  
Form Finding ◽  
Biomechanical Models ◽  
Irregular Shapes ◽  
Mechanical Metamaterials ◽  
Equilibrium Matrix ◽  
Mechanical Devices ◽  
Finding Method

Tensegrities have exhibited great importance and numerous applications in many mechanical, aerospace, and biological systems, for which symmetric configurations are preferred as the tensegrity prototypes. Besides the well-known prismatic tensegrities, another ingenious group of tensegrities with high symmetry is the truncated regular polyhedral (TRP) tensegrities, including Z-based and rhombic types. Although Z-based TRP tensegrities have been widely studied in the form-finding and application issues, rhombic TRP tensegrities have been much less reported due to the lack of explicit solutions that can produce their symmetric configurations. Our former work presented a unified solution for the rhombic TRP tensegrities by involving the force-density method which yet cannot control structural geometric sizes and may produce irregular shapes. Here, using the structural equilibrium matrix-based form-finding method, we establish some analytical equations, in terms of structural geometric parameters and force-densities in elements, to directly construct the self-equilibrated, symmetric configurations of rhombic TRP tensegrities, i.e., tetrahedral, cubic/octahedral, and dodecahedral/icosahedral configurations. Moreover, it is proved, both theoretically and numerically, that all of our obtained rhombic TRP tensegrities are super-stable and thus can be stable for any level of the force-densities without causing element material failure, which is beneficial to their actual construction. This study helps to readily design rhombic tensegrities with high symmetry and develop novel biomechanical models, mechanical metamaterials, and advanced mechanical devices.

Form-finding design of electrostatically controlled deployable membrane antenna based on an extended force density method

2018 ◽  
Vol 152 ◽  
pp. 757-767 ◽  
Author(s):  
Yongzhen Gu ◽  
Jingli Du ◽  
Dongwu Yang ◽  
Yiqun Zhang ◽  
Shuxin Zhang
Keyword(s):  
Force Density ◽  
Form Finding ◽  
Density Method ◽  
Force Density Method

scholarly journals Modal Participation Estimated from the Response Correlation Matrix

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Rune Brincker ◽  
Sandro D. R. Amador ◽  
Martin Juul ◽  
Manuel Lopez-Aenelle
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Correlation Matrix ◽  
Analytical Form ◽  
Mode Shapes ◽  
Transformation Matrices ◽  
Spectral Density Matrix ◽  
Spectral Density Functions ◽  
Input Load ◽  
The Time Domain

In this paper, we are considering the case of estimating the modal participation vectors from the operating response of a structure. Normally, this is done using a fitting technique either in the time domain using the correlation function matrix or in the frequency domain using the spectral density matrix. In this paper, a more simple approach is proposed based on estimating the modal participation from the correlation matrix of the operating responses. For the case of general damping, it is shown how the response correlation matrix is formed by the mode shape matrix and two transformation matrices T1 and T1 that contain information about the modal parameters, the generalized modal masses, and the input load spectral density matrix Gx. For the case of real mode shapes, it is shown how the response correlation matrix can be given a simple analytical form where the corresponding real modal participation vectors can be obtained in a simple way. Finally, it is shown how the real version of the modal participation vectors can be used to synthesize empirical spectral density functions.

scholarly journals Form-Finding of Funicular Geometries in Spatial Arch Bridges through Simplified Force Density Method

2018 ◽  
Vol 8 (12) ◽  
pp. 2553 ◽  
Author(s):  
Juan Jorquera-Lucerga
Keyword(s):  
Three Dimensional ◽  
Vertical Plane ◽  
Force Density ◽  
Functional Requirements ◽  
Form Finding ◽  
Arch Bridge ◽  
Density Method ◽  
Force Density Method ◽  
Axial Forces ◽  
Arch Bridges

In a “classical” vertical planar arch bridge subjected only to in-plane loads, its funicular geometry (which is the geometry that results in an equilibrium state free from bending stresses, i.e., simply under axial forces) is contained within a vertical plane. In the so-called “spatial arch bridges,” their structural behavior extends from the essentially vertical in-plane behavior of the “classical” arch bridges to a three-dimensional behavior. The paper presents how the Force Density Method, which is a form-finding method originally developed for cable meshes, can be simplified to easily obtain three-dimensional funicular arches. The formulation and flow chart of the method is presented and discussed in detail within this paper. Additionally, some case studies illustrate its scope. This paper intends to be useful at the conceptual stage of bridge design when the three-dimensional geometry for the spatial arch bridge typology is considered either because of functional requirements, structural efficiency, or for aesthetical purposes.

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